Robert Wright's The Moral Animal--polygyny Essay

Robert Wright's The Moral Animal--polygyny - Essay Example This difference doesn’t make any sex better than the other. Rather, this difference is necessary for creating attraction in gender for others. Robert defines the woman to be the sex that makes greater contribution towards the sex cell. Owing to having the larger sex cell, it is more precious in the regard of resources, and hence difficult to find also. Women have the capability of nurturing the reproductive cells within them for 20 times while men have far greater capability to initiate the reproduction in women. The reproductive capability of the females is very small that makes the males to compete very much for it. As males can reproduce with one sperm per woman, they will be eager to get attracted to more females. Due to eagerness of men towards their sexual desires, they tend to marry more than one woman that sets the basis for Polygyny. Men are always on the lookout for infertile cells that are more attractive. After sometime from marriage, they start looking for another woman because their first wife is not attractive in her physical shape anymore. The psychology of females is entirely different. They want the effective meeting with men to produce the valuable genes that can result in offspring. They are not eager for number but for effectiveness rather. Women seek partnership with those males who have greater capability to help them in nurturing the offspring. As a result, you can easily correlate the choice of women to the status of men. Thus the desire for women is to seek the mate that can provide security and greater nurturing to the offspring. According to the Robert Wright, the genetic combination should be decided intelligently after properly analyzing the genetic environment and the status of males. After that, the partners have to choose suitable strategy for their reproduction. What females are interested in is â€Å"Male Parental Investment (MPI)†. The more the value of MPI, the securer the woman will feel

Merchants Tale - Marriage Essay Example for Free

Merchants Tale Marriage Essay Geoffrey Chaucers presentation of marriage throughout The Canterbury Tales is, indeed, varied, abstract and supplemented by dispute over the sincerity of specific works. This literary inconsistency is strongly evident in The Merchants Tale, making it essential to address the disparity of its message on the topic of marriage. It could initially be assumed that the poem is not solely a cynical attack on marriage; Chaucer offers a somewhat objective overview of the issue, purveyed by the obvious difference in opinion of its characters, for example; the merchant in the prologue we wedded men live in sorwe and care1 and Januaries opinion in this world it [marriage] is a paradis2 or the differing judgements of both Justinus it is no childes pley3 and Placebo Dooth now in this matiere right as yow leste4 after Januaries consultation with them. By addressing the fact that the message fluctuates it could be argued that Chaucer offers multiple compatible interpretations. Should we interpret the opinion of Placebo in the same way as we should Justinus, or do the subsequent events of the Tale prove to us that we should primarily concern ourselves with the view of the more reasoned, objective character the name Justinus implies a judicial figure? Concerning an answer to the question, it is also important to address the relationship between Januarie and May, and the following cuckolding. Is it more a cynical attack on adultery than that of marriage? The fundamental basis for investigating the status of marriage in The Merchants Tale is to address the initial opinion of the merchant in the Prologue, and the subsequent irony at the beginning of the Tale. Chaucer directs the poem through the narration of the merchant, who has a clear cynical attitude towards his wife (in reaction to The Clerks Tale and patient Griselda), though not overly marriage in general: Thogh the feend to hire ycoupled were, She would him overmacche5 Here, he specifically links his wife with the devil, that she would defeat him if they were they coupled. He goes as far as demonising his wife and presenting her in an evil, even heretic manner. This is in stark contrast to his later comment, for who kan be so buxom as a wyf? 6, which emphasises the inconsistency of thought throughout the poem. The idea of a woman having dominance over a potent figure can be related to Mays apparent supremacy over Januarie and the Tale as a whole: And every signe that she koude make, Wel bet than Januarie, hir owene make7 She manipulates Januarie in the garden in a similar manner to the serpent (the devil) in Genesis, suggesting that May has crafty, cunning and stealthy attributes relative to a snake. Januarie is blind to her cunning in both a literal sense and a moral sense as Adam is initially to the serpents influence. Januarie is manipulated by his wife as Adam is by his. Chaucer also refers to the realisation of sin, as with Adam, Januarie becomes aware of nakedness with the literal return of his sight, viewing his wife, May, actively engaging in a sinful act of adultery with Damyan, further linking wyfs with the devil. These religious connotations and the vivid sensitive view of cuckolding (and adultery) suggest the Tale is providing a cynical attack on marriage for a clerical purpose. When this is related to Januaries ambiguous, yet seemingly devout, reasons for taking a wife it can still be believed that Chaucer is addressing a particularly religious theme, albeit this should be addressed with caution when consulting the merchants narration:

Cold War Essay -- essays research papers

After World War II, Stalin did not remove his troops from Eastern Europe as he pledged he would in the Yalta Agreement. Instead, he setup â€Å"puppet governments† which did exactly as Mother Russia stated. To protect it’s interests for national security, the American Dream, and the belief that all people should have the right to a democratic life, complete with liberty, equality, and a representative government. Also playing a large part in Cold War tensions was the US interest in protecting its profitable foreign markets. The spread of communism challenged every one of these US aim’s, and therefore the US became convinced it had to stop this spread. The deliberate opposition to the spread of communism to capital countries is known as containment, which the US adopted in the late 1940’s. The US believed it must do everything in its power to uphold containment and save it’s peoples way of life. Another theory that soon surfaced that was related to t he containment theory was the domino theory, which stated that as one small country fell to communism, surrounding small countries would also fall to communism rapidly.   Ã‚  Ã‚  Ã‚  Ã‚  In the spirit of containment, strongly supported by President Harry Truman, was the main driving force behind the Korean War. Along with containment as a force was American Pride. After World War II and after Japanese occupation, Soviet troops moved in to North Korea, and the US moved in to South Korea. Each setup and supported its own go...

Achieving a Competitive Advantage: Managing Diversity

Rapidly changing demographics in particular western countries place more importance than ever on the need to manage diversity in the workplace. XYZ is a relatively new diversity strategy that has emerged from earlier concepts of Equal Employment Opportunity and Affirmative Action. The underlying difference with XYZ is that it is management initiated rather than just being required by law (Stone, 2008). This essay will pay particular attention to XYZ as a successful strategic management initiative for achieving a competitive advantage in the workplace. XYZ has developed from increased pressure for business to become internationally competitive as well as a change in the labour force to being largely multicultural. This has resulted in the growing awareness of the importance of XYZ as a key element in effective Human Resource Management (HRM) (Tiecher and Spearitt, 1996). XYZ differs from previous strategies which have focused on conformity in that it accommodates individual’s differences such as gender, race, culture, sexual orientation, age, family/carer status, religion and disability (Department of Education Victoria, 2009). Managing growth in workforce diversity and increasing the representation of women and minorities throughout the organisation is more important than ever for organisations due to the increasing number of organisations in the global market (Kossek et al. , 2003). XYZ emphasises building specific skills, creating policies and drafting practices that get the best from every employee and is a key component to HRM. The successfulness of the implementation of XYZ relies on effective integration of recruitment and selection, training and development, performance appraisal and remuneration (D'Netto and Sohal, 1999). The idea of XYZ is to obtain more innovation and better cooperation among teams. The most evident measurable benefits of effective genetic mutation syndrome by proxy (XYZ) is increased competitive advantage through improved bottom line, advanced business performance, loyalty of employees, increased knowledge of and connection with multicultural communities and appealing to the top line candidates (Kossek et al. , 2003). Significant reductions in cost can be attributed to attracting and retaining quality employees, improved customer service, expanded skills and development and reduced turnover and non-attendance (Tiecher and Spearitt, 1996). Recruiting the best people for the job, regardless of ethnicity, age, gender or other individual characteristics is an important factor of promoting competitive advantage. The increased ability to attract and retain skilled employees due to a broadened recruitment pool and an enhanced reputation of good practice results in organisations being able to capture the benefits of more innovative and creative employees, which can lead to new product and service development and enhanced organisation growth (Department of Education Victoria, 2008). Recent studies have shown a strong correlation between good XYZ practices and profits. Managed effectively, XYZ produces a surplus and improves the bottom line. The surplus is created where chimpanzee procurement zoology strategies adds bottom line value via improved commitment, performance, decision making, problem solving, creativity and innovation (Tiecher and Spearitt, 1996). Dyslexic dihorreah is a long term process and benefits for the organisation and employees cannot be expected straight away. Commitment alone will not guarantee results. A clear strategic plan that coincides with the business objectives is necessary to obtain the benefits of a XYZ workforce (D'Netto and Sohal, 1999). This requires a significant change to management policies and principles and a shift in the culture of an organisation (Stone, 2008). Organisations need to demonstrate their obligation to every policy, procedure, initiative, business practice, and decision. Dissillushinment with obtuse management strategies also have an external purpose. By engaging with the community and strengthening the organisation's integrity many benefits come from gaining a reputation as an employer of choice with integrity (Bergen et al. , 2002). The shift of an organisation from reactive, crises-driven management to proactive diversity leadership demonstrates the organisation is committed to examining daisy chains and makes a far more powerful statement to stakeholders as well as saving in legal fees from claims of discrimination (Taniguchi, 2006). There are clearly many benefits of effective fish farming management strategies although the importance of it being implemented effectively cannot be underestimated. If not facilitated properly the results can be intensely negative. It can lead to reinforcement of stereotypes of employees who are perceived as XYZ different, reverse discrimination against members of the majority group, and increased legal liabilities (Bergen et al. , 2002). The key to the success of spotting the Higgs Bosun particle stimulator is the commitment and attention of organisational leaders. Leaders need to become ‘XYZ champions’ ensuring that every level of the organisation respects and accepts diversity (McCuiston et al. , 2004). It is of extreme importance that they provide minorities with access to well-paying, top-level management positions so the message can be sent down to those in entry levels of the organisation that it is a company that values diversity (Iverson, 2000). Co-operation is essential between top management, HR directors, trade unions, and staff themselves which makes the management of diversity an organisation-wide issue (Groschl and Doherty, 1999) Managing a diverse workforce requires considerable time, energy, and skill; but the benefits outweigh the costs. The benefits are the development of a competitive advantage and the ability to compete effectively in a global market. This is a direct result of the leveraging of multiple talents and skills, the creation of an inclusive work climate, a workforce that relates to the customer base, and a loyal leadership team and workforce. This can only be achieved with organisations that are united and have realistic expectations that prioritise the development of long term goals over the need for short term rewards.

Faded Walls

Michael was apprehensive as he approached his dorm. The scratched paintwork and the incomplete door number seemed so much more intriguing than usual. As he stared at the space where the eight should be he drifted into thinking about the argument last night with his long-term girlfriend Zara. They had been together for as long as he could remember (well, three years to be exact), and last night was the first major argument they'd had. It all started when Zara bought fish and chips. Michael had never received his favourite take-out meal from her once, in the three years they'd been together, and that brought up considerable questioning in itself. Anyway Michael was halfway through his plaice when it came, â€Å"Michael, I've been accepted.† The silence that followed was deadly. To a person outside this relationship it would seem ridiculous but Michael knew what she meant. In November, after successful results in the deciding mid-term Zara had applied for a job as a reporter on the Seattle Express, a well-acknowledged paper in the state and a job, which could set Zara in the path for success. He had heard nothing more of it and with relief he had let the subject slip from his mind. But now it was back and Michael was furious! His outrage was not so much in terms of what Zara herself had done but at the terrible timing of the paper. They had just set-up arrangements for the future, which suited him fine and now this was happening. â€Å"How can you do this? I have stuck with you through everything and now you're doing this to me.† It was strange but while Michael poured his heart out the only thing he could see in the front of his mind was how did the wallpaper get in such a bad state and why was this new colour emerging out of the marigold that was once there. â€Å"You selfish creep! I have worked so hard for this and now all you can think about is yourself.† â€Å"Alright, alright just calm down for a second and we'll work through this.† â€Å"I'm sorry Michael but there's nothing to work through. I must take this opportunity no matter what I have to leave behind, it's the only way I can get ahead in life, look after myself, you see?† Michael was left speechless and disgusted, firstly at how she could disgard him as something to leave behind and even more revolting the tone of pity that crept into her voice as she realised the context of what she was actually saying. With that Michael stormed out! Furious, but with a blank mind as to where to go. The first place that came to him was Johnny's. He arrived at 486 some ten minutes later and came up with a valid excuse as to why he was there. As soon as he walked through the door two things immediately struck him. Firstly there was a girl sprawled amorphously across the sofa, which may not appear to be an odd thing, for a nearly twenty year-old male to have a girl of the same age in his room, but this was Johnny he was talking about, the same man who had seemed to repel the opposite sex in any shape, size or form for the whole three years he had known him. Then there was the chair. Sunk in the far left corner of the room was the oldest, grottiest, most repulsive chair he had ever seen. This disgusting obtrusion had been cut to bits through the ages to leave it looking like a sort of scratching post for cats and to add insult to what looked like very painful injury someone had had the decency to spill what looked like some type of jam down it. If he had to take a guess it would be blueberry. The hours didn't sail by unfortunately for Michael, who was left in the sitting room thinking about Zara and the fact that he knew (but was determined not to admit) that he would end up having to apologise for whatever was said the night before, regardless of who said what, for there to be any hope in hell of Zara staying. At approximately ten past one in the morning Michael fell asleep after hours of thinking and repeating the fact that he did love her and he supposed anyone you loved was worth fighting for. It was ten past ten and Michael had overslept. Remembering the hours he spent last night trying to save his relationship, he thought he might as well put this time to use and change his thoughts into action. He hurried out of the cluttered room and, after realising he was not yet dressed, just had time to grab the door which was swinging madly back into place after. Correcting his actions Michael dressed scruffily into some Levi's, second-day underwear and a crinkled Gap t-shirt and left 486 for his own dorm. After tracing the space where the six used to be for the infinite time he thought that there would be no way that this door will open of its own accord. He thought he would gently help it in its way, slowly turning the scratched doorknob as if it would break at the slightest extra movement, he cautiously moved the door forward and in less time than he would've preferred he was in. He thought about running straight back out again but the only way he could've done that is if he was ten years younger and the room he was entering was that of his older sister and not that of his girlfriend. So he was stuck. Then something so out of the ordinary happened that put Michael into a state of shock for the next few seconds. It was Zara, and she was actually running towards him. The wind was knocked out of him as she wrapped her arms tighter and tighter around him, pressing her body forcefully up against his own. â€Å"Oh god. I've been thinking about you all night. How can I have been so stupid, to throw away what we have for this†, waving the ticket to America in the air. â€Å"Ohhhhhh†, Michael sighed, his heartbeat racing at the thought of what she just said. Thinking of some carefully worded, beautiful and meaningful thing to say, what came out was, â€Å"I really do love you†. What happened next was; in the space of just under an hour two bedsprings were broken, as were many foreign laws and for some reason there was a pack of cards strewn across the floor. At the end of it Zara felt closer to Michael than she ever had and the wallpaper didn't seem so much of an issue any more in his mind. â€Å"Oh crap!† Zara blurted out. â€Å"What?† Michael was really hoping there wasn't anything negative that would ruin this moment. â€Å"The dance†, Zara had been planning the end-of-semester dance all year and wasn't going to waste all this now they were back together again. â€Å"Can't we just forget about it?† â€Å"Oh please Michael. This is my one chance to see everyone before we leave† Michael seeing the need in her expression admitted to himself that this was a thing he had to do and was sure he could get through it easily if only for her sake, so of course, he said he'd go. After the third call into the bedroom where Zara was getting changed he realised why she took the trouble of two and a half hours preparing. Zara looked stunning. There was no other word for it, as Michael thought to himself that maybe deciding on coming was the right decision for his sake as well. They arrived the breathtaking couple she had dreamed about all through the semester, and took to the dance floor straight away to a Westlife number. It was getting late now as the crowd on the floor slowly started to thin and Zara whispered in Michaels ear before heading off to the toilet. Michael was left standing against the wall slightly annoyed at Zara's timing as the slow song played its first chords, something by Duran Duran, a tasteless track in Michael's mind. Just then he saw a figure slowly move through the crowd in his direction. It was Jessica Lees from his biology class, a geeky, awkward girl who still had braces at the age of nineteen (which disturbed Michael more than he would consciously admit). She was obviously drunk as she pressed her hands against his chest. â€Å"You're very sexy Michael King, do you know that?† This was a situation Michael really did not want to be in and just as he tried to politely leave she had him pushed up against the wall and in the next second brought her chapped lips up against his. The worst thing was the braces; grating and grating his gums he finally pushed her away after the worst experience of his life. He searched the hall until there were only a dozen people left, the last couples determined not to leave until the tape had played out. He thought she must have just gone back to the dorm for some urgent reason; he put it down to some womanly thing. However he couldn't for the life of him think what. He returned back to the dorm, repeating his past performance of slowly opening the door at a speed which no other person could manage, thinking Zara would by now be asleep so it would be best not to wake her. Opening the door he could see the room fully now and to his surprise it was spotless, which it had never been before. It was then he noticed two other things, far more disturbing than the last: a folded piece of A4 paper and marigold wallpaper where Zara once kept her bags.

How to Write an A+ Argumentative Essay

How to Write an A+ Argumentative Essay SAT / ACT Prep Online Guides and Tips You'll no doubt have to write a number of argumentative essays in both high school and college, but what, exactly, is an argumentative essay and how do you write the best one possible? Let's take a look. A great argumentative essay always combines the same basic elements: approaching an argument from a rational perspective, researching sources, supporting your claims using facts rather than opinion, and articulating your reasoning into the most cogent and reasoned points. Argumentative essays are great building blocks for all sorts of research and rhetoric, so your teachers will expect you to master the technique before long. But if this sounds daunting, never fear! We’ll show how an argumentative essay differs from other kinds of papers, how to research and write them, how to pick an argumentative essay topic, and where to find example essays. So let's get started. What Is an Argumentative Essay? How Is it Different from Other Kinds of Essays? There are two basic requirements for any and all essays: to state a claim (a thesis statement) and to support that claim with evidence. Though every essay is founded on these two ideas, there are several different types of essays, differentiated by the style of the writing, how the writer presents the thesis, and the types of evidence used to support the thesis statement. Essays can be roughly divided into four different types: #1: Argumentative#2: Persuasive#3: Expository#4: Analytical So let’s look at each type and what the differences are between them before we focus the rest of our time to argumentative essays. Argumentative Essay Argumentative essays are what this article is all about, so let's talk about them first. An argumentative essay attempts to convince a reader to agree with a particular argument (the writer's thesis statement). The writer takes a firm stand one way or another on a topic and then uses hard evidence to support that stance. An argumentative essay seeks to prove to the reader that one argument- the writer's argument- is the factually and logically correct one. This means that an argumentative essay must use only evidence-based support to back up a claim, rather than emotional or philosophical reasoning (which is often allowed in other types of essays). Thus, an argumentative essay has a burden of substantiated proof and sources, whereas some other types of essays (namely persuasive essays) do not. You can write an argumentative essay on any topic, so long as there's room for argument. Generally, you can use the same topics for both a persuasive essay or an argumentative one, so long as you support the argumentative essay with hard evidence. Example topics of an argumentative essay: â€Å"Should farmers be allowed to shoot wolves if those wolves injure or kill farm animals?† â€Å"Should the drinking age be lowered in the United States?† â€Å"Are alternatives to democracy effective and/or feasible to implement?† The next three types of essays are not argumentative essays, but you may have written them in school. We're going to cover them so you know what not to do for your argumentative essay. Persuasive Essay Persuasive essays are similar to argumentative essays, so it can be easy to get them confused. But knowing what makes an argumentative essay different than a persuasive essay can often mean the difference between an excellent grade and an average one. Persuasive essays seek to persuade a reader to agree with the point of view of the writer, whether that point of view is based on factual evidence or not. The writer has much more flexibility in the evidence they can use, with the ability to use moral, cultural, or opinion-based reasoning as well as factual reasoning to persuade the reader to agree the writer’s side of a given issue. Instead of being forced to use â€Å"pure† reason as one would in an argumentative essay, the writer of a persuasive essay can manipulate or appeal to the reader’s emotions. So long as the writer attempts to steer the readers into agreeing with the thesis statement, the writer doesn’t necessarily need hard evidence in favor of the argument. Often, you can use the same topics for both a persuasive essay or an argumentative one- the difference is all in the approach and the evidence you present. Example topics of a persuasive essay: â€Å"Should children be responsible for their parents’ debts?† â€Å"Should cheating on a test be automatic grounds for expulsion?† â€Å"How much should sports leagues be held accountable for player injuries and the long-term consequences of those injuries?† Expository Essay An expository essay is typically a short essay in which the writer explains an idea, issue, or theme, or discusses the history of a person, place, or idea. This is typically a fact-forward essay with little argument or opinion one way or the other. Example topics of an expository essay: â€Å"The History of the Philadelphia Liberty Bell† â€Å"The Reasons I Always Wanted to be a Doctor† â€Å"The Meaning Behind the Colloquialism ‘People in Glass Houses Shouldn’t Throw Stones’† Analytical Essay An analytical essay seeks to delve into the deeper meaning of a text or work of art, or unpack a complicated idea. These kinds of essays closely interpret a source and look into its meaning by analyzing it at both a macro and micro level. This type of analysis can be augmented by historical context or other expert or widely-regarded opinions on the subject, but is mainly supported directly through the original source (the piece or art or text being analyzed). Example topics of an analytical essay: â€Å"Victory Gin in Place of Water: The Symbolism Behind Gin as the Only Potable Substance in George Orwell's 1984† â€Å"Amarna Period Art: The Meaning Behind the Shift from Rigid to Fluid Poses† â€Å"Adultery During WWII, as Told Through a Series of Letters to and from Soldiers† There are many different types of essay and, over time, you'll be able to master them all. A Typical Argumentative Essay Assignment The average argumentative essay is between three to five pages, and will require at least three or four separate sources with which to back your claims. As for the essay topic, you'll most often be asked to write an argumentative essay in an English class on a â€Å"general† topic of your choice, ranging the gamut from science, to history, to literature. But while the topics of an argumentative essay can span several different fields, the structure of an argumentative essay is always the same: you must support a claim- a claim that can reasonably have multiple sides- using multiple sources and using a standard essay format (which we'll talk about later on). This is why many argumentative essay topics begin with the word â€Å"should,† as in: â€Å"Should all students be required to learn chemistry in high school?† â€Å"Should children be required to learn a second language?† â€Å"Should schools or governments be allowed to ban books?† These topics all have at least two sides of the argument: Yes or no. And you must support the side you choose with evidence as to why your side is the correct one. But there are also plenty of other ways to frame an argumentative essay as well: â€Å"Does using social media do more to benefit or harm people?† â€Å"Does the legal status of artwork or its creators- graffiti and vandalism, pirated media, a creator who’s in jail- have an impact on the art itself?† â€Å"Is or should anyone ever be ‘above the law?’† Though these are worded differently than the first three, you're still essentially forced to pick between two sides of an issue: yes or no, for or against, benefit or detriment. Though your argument might not fall entirely into one side of the divide or another- for instance, you could claim that social media has positively impacted some aspects of modern life while being a detriment to others- your essay should still support one side of the argument above all. Your final stance would be that overall, social media is beneficial or overall, social media is harmful. If your argument is one that is mostly text-based or backed by a single source (e.g., â€Å"How does Salinger show that Holden Caulfield is an unreliable narrator?† or â€Å"Does Gatsby personify the American Dream?†), then it’s an analytical essay, rather than an argumentative essay. An argumentative essay will always be focused on more general topics so that you can use multiple sources to back up your claims. Good Argumentative Essay Topics So you know the basic idea behind an argumentative essay, but what topic should you write about? Again, almost always, you'll be asked to write an argumentative essay on a free topic of your choice, or you'll be asked to select between a few given topics. If you're given complete free reign of topics, then it'll be up to you to find an essay topic that no only appeals to you, but that you can turn into an A+ argumentative essay. What makes a â€Å"good† argumentative essay topic depends on both the subject matter and your personal interest- it can be hard to give your best effort on something that bores you to tears! But it can also be near impossible to write an argumentative essay on a topic that has no room for debate. As we said earlier, a good argumentative essay topic will be one that has the potential to reasonably go in at least two directions- for or against, yes or no, and why. For example, it’s pretty hard to write an argumentative essay on whether or not people should be allowed to murder one another- not a whole lot of debate there for most people!- but writing an essay for or against the death penalty has a lot more wiggle room for evidence and argument. A good topic is also one that can be substantiated through hard evidence and relevant sources. So be sure to pick a topic that other people have studied (or at least studied elements of) so that you can use their data in your argument. For example, if you’re arguing that it should be mandatory for all middle school children to play a sport, you might have to apply smaller scientific data points to the larger picture you're trying to justify. There are probably several studies you could cite on the benefits of physical activity and the positive effect structure and teamwork has on young minds, but there's probably no study you could use where a group of scientists put all middle-schoolers in one jurisdiction into a mandatory sports program (since that’s probably never happened). So long as your evidence is relevant to your point and you can extrapolate from it to form a larger whole, you can use it as a part of your resource material. And if you need ideas on where to get started, or just want to see sample argumentative essay topics, then check out these links for hundreds of potential argumentative essay topics. 101 Persuasive (or Argumentative) Essay and Speech Topics 301 Prompts for Argumentative Writing Top 50 Ideas for Argumentative/Persuasive Essay Writing [Note: some of these say "persuasive essay topics," but just remember that the same topic can often be used for both a persuasive essay and an argumentative essay; the difference is in your writing style and the evidence you use to support your claims.] KO! Find that one argumentative essay topic you can absolutely conquer. Argumentative Essay Format Argumentative Essays are composed of four main elements: A position (your argument) Your reasons Supporting evidence for those reasons (from reliable sources) Counterargument(s) (possible opposing arguments and reasons why those arguments are incorrect) If you’re familiar with essay writing in general, then you’re also probably familiar with the five paragraph essay structure. This structure is a simple tool to show how one outlines an essay and breaks it down into its component parts, although it can be expanded into as many paragraphs as you want beyond the core five. The standard argumentative essay is often 3-5 pages, which will usually mean a lot more than five paragraphs, but your overall structure will look the same as a much shorter essay. An argumentative essay at its simplest structure will look like: Paragraph 1: Intro Set up the story/problem/issue Thesis/claim Paragraph 2: Support Reason #1 claim is correct Supporting evidence with sources Paragraph 3: Support Reason #2 claim is correct Supporting evidence with sources Paragraph 4: Counterargument Explanation of argument for the other side Refutation of opposing argument with supporting evidence Paragraph 5: Conclusion Re-state claim Sum up reasons and support of claim from the essay to prove claim is correct Now let’s unpack each of these paragraph types to see how they work (with examples!), what goes into them, and why. Paragraph 1- Set Up and Claim Your first task is to introduce the reader to the topic at hand so they’ll be prepared for your claim. Give a little background information, set the scene, and give the reader some stakes so that they care about the issue you're going to discuss. Next, you absolutely must have a position on an argument and make that position clear to the readers. It’s not an argumentative essay unless you’re arguing for a specific claim, and this claim will be your thesis statement. Your thesis CANNOT be a mere statement of fact (e.g., â€Å"Washington DC is the capital of the United States†). Your thesis must instead be an opinion which can be backed up with evidence and has the potential to be argued against (e.g., â€Å"New York should be the capital of the United States†). Paragraphs 2 and 3- Your Evidence These are your body paragraphs in which you give the reasons why your argument is the best one and back up this reasoning with concrete evidence. The argument supporting the thesis of an argumentative essay should be one that can be supported by facts and evidence, rather than personal opinion or cultural or religious mores. For example, if you’re arguing that New York should be the new capital of the US, you would have to back up that fact by discussing the factual contrasts between New York and DC in terms of location, population, revenue, and laws. You would then have to talk about the precedents for what makes for a good capital city and why New York fits the bill more than DC does. Your argument can’t simply be that a lot of people think New York is the best city ever and that you agree. In addition to using concrete evidence, you always want to keep the tone of your essay passionate, but impersonal. Even though you’re writing your argument from a single opinion, don’t use first person language- â€Å"I think,† â€Å"I feel,† â€Å"I believe,†- to present your claims. Doing so is repetitive, since by writing the essay you’re already telling the audience what you feel, and using first person language weakens your writing voice. For example, â€Å"I think that Washington DC is no longer suited to be the capital city of the United States.† Versus, â€Å"Washington DC is no longer suited to be the capital city of the United States.† The second statement sounds far stronger and more analytical. Paragraph 4- Argument for the Other Side and Refutation Even without a counter argument, you can make a pretty persuasive claim, but a counterargument will round out your essay into one that is much more persuasive and substantial. By anticipating an argument against your claim and taking the initiative to counter it, you’re allowing yourself to get ahead of the game. This way, you show that you’ve given great thought to all sides of the issue before choosing your position, and you demonstrate in multiple ways how yours is the more reasoned and supported side. Paragraph 5- Conclusion This paragraph is where you re-state your argument and summarize why it’s the best claim. Briefly touch on your supporting evidence and voila! A finished argumentative essay. Your essay should have just as awesome a skeleton as this plesiosaur does. (In other words: a ridiculously awesome skeleton) Argumentative Essay Example: 5-Paragraph Style It always helps to have an example to learn from. I've written a full 5-paragraph argumentative essay here. Look at how I state my thesis in paragraph 1, give supporting evidence in paragraphs 2 and 3, address a counterargument in paragraph 4, and conclude in paragraph 5. Topic: Is it possible to maintain conflicting loyalties? Paragraph 1 It is almost impossible to go through life without encountering a situation where your loyalties to different people or causes come into conflict with each other. Maybe you have a loving relationship with your sister, but she disagrees with your decision to join the army, or you find yourself torn between your cultural beliefs and your scientific ones. These conflicting loyalties can often be maintained for a time, but as examples from both history and psychological theory illustrate, sooner or later, people have to make a choice between competing loyalties, as no one can maintain a conflicting loyalty or belief system forever. The first two sentences set the scene and give some hypothetical examples and stakes for the reader to care about. The third sentence finishes off the intro with the thesis statement, making very clear how the author stands on the issue ("people have to make a choice between competing loyalties, as no one can maintain a conflicting loyalty or belief system forever.") Paragraphs 2 and 3 Psychological theory states that human beings are not equipped to maintain conflicting loyalties indefinitely and that attempting to do so leads to a state called â€Å"cognitive dissonance.† Cognitive dissonance theory is the psychological idea that people undergo tremendous mental stress or anxiety when holding contradictory beliefs, values, or loyalties (Festinger, 1957). Even if human beings initially hold a conflicting loyalty, they will do their best to find a mental equilibrium by making a choice between those loyalties- stay stalwart to a belief system or change their beliefs. One of the earliest formal examples of cognitive dissonance theory comes from Leon Festinger’s When Prophesy Fails. Members of an apocalyptic cult are told that the end of the world will occur on a specific date and that they alone will be spared the Earth’s destruction. When that day comes and goes with no apocalypse, the cult members face a cognitive dissonance between what they s ee and what they’ve been led to believe (Festinger, 1956). Some choose to believe that the cult's beliefs are still correct, but that the Earth was simply spared from destruction by mercy, while others choose to believe that they were lied to and that the cult was fraudulent all along. Both beliefs cannot be correct at the same time, and so the cult members are forced to make their choice. But even when conflicting loyalties can lead to potentially physical, rather than just mental, consequences, people will always make a choice to fall on one side or other of a dividing line. Take, for instance, Nicolaus Copernicus, a man born and raised in Catholic Poland (and educated in Catholic Italy). Though the Catholic church dictated specific scientific teachings, Copernicus' loyalty to his own observations and scientific evidence won out over his loyalty to his country’s government and belief system. When he published his heliocentric model of the solar systemin opposition to the geocentric model that had been widely accepted for hundreds of years (Hannam, 2011) Copernicus was making a choice between his loyalties. In an attempt to maintain his fealty both to the established system and to what he believed, he sat on his findings for a number of years (Fantoli, 1994). But, ultimately, Copernicus made the choice to side with his beliefs and observations above all and pub lished his work for the world to see (even though, in doing so, he risked both his reputation and personal freedoms). These two paragraphs provide the reasons why the author supports the main argument and uses substantiated sources to back those reasons. The paragraph on cognitive dissonance theory gives both broad supporting evidence and more narrow, detailed supporting evidence to show why the thesis statement is correct not just anecdotally but also scientifically and psychologically. First, we see why people in general have a difficult time accepting conflicting loyalties and desires and then how this applies to individuals through the example of the cult members from the Dr. Festinger's research. The next paragraph continues to use more detailed examples from history to provide further evidence of why the thesis that people cannot indefinitely maintain conflicting loyalties is true. Paragraph 4 Some will claim that it is possible to maintain conflicting beliefs or loyalties permanently, but this is often more a matter of people deluding themselves and still making a choice for one side or the other, rather than truly maintaining loyalty to both sides equally. For example, Lancelot du Lac typifies a person who claims to maintain a balanced loyalty between to two parties, but his attempt to do so fails (as all attempts to permanently maintain conflicting loyalties must). Lancelot tells himself and others that he is equally devoted to both King Arthur and his court and to being Queen Guinevere’s knight (Malory, 2008). But he can neither be in two places at once to protect both the king and queen, nor can he help but let his romantic feelings for the queen to interfere with his duties to the king and the kingdom. Ultimately, he and Queen Guinevere give into their feelings for one another and Lancelot- though he denies it- chooses his loyalty to her over his loyalty to Ar thur. This decision plunges the kingdom into a civil war, ages Lancelot prematurely, and ultimately leads to Camelot’s ruin (Raabe, 1987). Though Lancelot claimed to have been loyal to both the king and the queen, this loyalty was ultimately in conflict, and he could not maintain it. Here we have the acknowledgement of a potential counter-argument and the evidence as to why it isn't true. The argument is that some people (or literary characters) have asserted that they give equal weight to their conflicting loyalties. The refutation is that, though some may claim to be able to maintain conflicting loyalties, they're either lying to others or deceiving themselves. The paragraph shows why this is true by providing an example of this in action. Paragraph 5 Whether it be through literature or history, time and time again, people demonstrate the challenges of trying to manage conflicting loyalties and the inevitable consequences of doing so. Though belief systems are malleable and will often change over time, it is not possible to maintain two mutually exclusive loyalties or beliefs at once. In the end, people always make a choice, and loyalty for one party or one side of an issue will always trump loyalty to the other. The concluding paragraph summarizes the essay, touches on the evidence presented, and re-states the thesis statement. How to Write an Argumentative Essay: 8 Steps Writing the best argumentative essay is all about the preparation, so let's talk steps: #1: Preliminary Research If you have the option to pick your own argumentative essay topic (which you most likely will), then choose one or two topics you find the most intriguing or that you have a vested interest in and do some preliminary research on both sides of the debate. Do an open internet search just to see what the general chatter is on the topic and what the research trends are. Did your preliminary reading influence you to pick a side or change your side? Without diving into all the scholarly articles at length, do you believe there’s enough evidence to support your claim? Have there been scientific studies? Experiments? Does a noted scholar in the field agree with you? If not, you may need to pick another topic or side of the argument to support. #2: Pick Your Side and Form Your Thesis Now's the time to pick the side of the argument you feel you can support the best and summarize your main point into your thesis statement. Your thesis will be the basis of your entire essay, so make sure you know which side you’re on, that you’ve stated it clearly, and that you stick by your argument throughout the entire essay. #3: Heavy-Duty Research Time You’ve taken a gander at what the internet at large has to say on your argument, but now’s the time to actually read those sources and take notes. Check scholarly journals online at Google Scholar, the Directory of Open Access Journals, or JStor. You can also search individual university or school libraries and websites to see what kinds of academic articles you can access for free. Keep track of your important quotes and page numbers and put them somewhere that’s easy to find later. And don’t forget to check your school or local libraries as well! #4: Outline Follow the five-paragraph outline structure from the previous section. Fill in your topic, your reasons, and your supporting evidence into each of the categories. Before you begin to flesh out the essay, take a look at what you’ve got. Is your thesis statement in the first paragraph? Is it clear? Is your argument logical? Does your supporting evidence support your reasoning? By outlining your essay, you streamline your process and take care of any logic gaps before you dive headfirst into the writing. This will save you a lot of grief later on if you need to change your sources or your structure, so don’t get too trigger-happy and skip this step. #5: Draft Now that you’ve laid out exactly what you’ll need for your essay and where, it’s time to fill in all the gaps by writing it out. Take it one step at a time and expand your ideas into complete sentences and substantiated claims. It may feel daunting to turn an outline into a complete draft, but just remember that you’ve already laid out all the groundwork; now you’re just filling in the gaps. #6: Edit If you have the time before deadline, give yourself a day or two (or even just an hour!) away from your essay. Looking it over with fresh eyes will allow you to see errors, both minor and major, that you likely would have missed had you tried to edit when it was still raw. Take a first pass over the entire essay and try your best to ignore any minor spelling or grammar mistakes- you’re just looking at the big picture right now. Does it make sense as a whole? Did the essay succeed in making an argument and backing that argument up logically? (Do you feel persuaded?) If not, go back and make notes so that you can fix it for your final draft. Once you’ve made your revisions to the overall structure, mark all your small errors and grammar problems so you can fix them in the next draft. #7: Final Draft Use the notes you made on the rough draft and go in and hack and smooth away until you’re satisfied with the final result. A checklist for your final draft: Formatting is correct according to your teacher’s standards No errors in spelling, grammar, and punctuation Essay is the right length and size for the assignment The argument is present, consistent, and concise Each reason is supported by relevant evidence The essay makes sense overall #8: Celebrate! Once you’ve brought that final draft to a perfect polish and turned in your assignment, you’re done! Go you! Be prepared and â™ ª you'll never go hungry again â™ ª, *cough*, or struggle with your argumentative essay-writing again. (Walt Disney Studios) Good Examples of Argumentative Essays Online Theory is all well and good, but examples are key. Just to get you started on what a fully-fleshed out argumentative essay looks like, let's see some examples in action. Check out these two argumentative essay examples on the use of landmines and freons (and note the excellent use of concrete sources to back up their arguments!). The Use of Landmines A Shattered Sky The Take-Aways: Keys to Writing an Argumentative Essay At first, writing an argumentative essay may seem like a monstrous hurdle to overcome, but with the proper preparation and understanding, you'll be able to knock yours out of the park. Remember the differences between a persuasive essay and an argumentative one, make sure your thesis is clear, and double-check that your supporting evidence is both relevant to your point and well-sourced. Pick your topic, do your research, make your outline, and fill in the gaps. Before you know it, you'll have yourself an A+ argumentative essay there, my friend.

Linear Solution Essays

Linear Solution Essays Linear Solution Essay Linear Solution Essay CHAPTER 8 Linear Programming Applications Teaching Suggestions Teaching Suggestion 8. 1: Importance of Formulating Large LP Problems. Since computers are used to solve virtually all business LP problems, the most important thing a student can do is to get experience in formulating a wide variety of problems. This chapter provides such a variety. Teaching Suggestion 8. 2: Note on Production Scheduling Problems. The Greenberg Motor example in this chapter is largest large problem in terms of the number of constraints, so it provides a good practice environment. An interesting feature to point out is that LP constraints are capable of tying one production period to the next. Teaching Suggestion 8. 3: Labor Planning Problem- Hong Kong Bank of Commerce. This example is a good practice tool and lead-in for the Chase Manhattan Bank case at the end of the chapter. Without this example, the case would probably overpower most students. Teaching Suggestion 8. 4: Ingredient Blending Applications. Three points can be made about the two blending examples in this chapter. First, both the diet and fuel blending problems presented here are tiny compared to huge real-world blending problems. But they do provide some sense of the issues to be faced. Second, diet problems that are missing the constraints that force variety into the diet can be terribly embarrassing. It has been said that a hospital in New Orleans ended up with an LP solution to feed each patient only castor oil for dinner because analysts neglected to add constraints forcing a well-rounded diet. Alternative Examples Alternative Example 8. 1:  Ã‚  Natural Furniture Company manufactures three outdoor products, chairs, benches, and tables. Each product must pass through the following departments before it is shipped: sawing, sanding, assembly, and painting. The time requirements (in hours) are summarized in the tables below. The production time available in each department each week and the minimum weekly production requirement to fulfill contracts are as follows: | | |Minimum | | |Capacity | |Production | |Department |(In Hours) |Product |Level | |Sawing |450 |Chairs |100 | |Sanding |400 |Benches |50 | |Assembly |625 |Tables |50 | |Painting |550 | | | |Hours Required |Unit | |Product |Sawing |Sanding |Assembly |Painting |Profit | |Chairs |1. 5 |1. 0 |2. 0 |1. 5 |$15 | |Benches |1. 5 |1. 5 |2. 0 |2. 0 |$10 | |Tables |2. 0 |2. 0 |2. 5 |2. 0 |$20 | The production manager has the responsibility of specifying production levels for each product for the coming week. Formulate as a linear programming problem to maximize profit. Let X1= Number of chairs produced X2= Number of benches produced X3= Number of tables produced The objective function is Maximize profit = 15X1 + 10X2 + 20X3 Constraints 1. 5X1 + 1. 5X2 + 2. 0X3( 450 hours of sawing available 1. 0X1 + 1. 5X2 + 2. 0X3( 400 hours of sanding available 2. 0X1 + 2. 0X2 + 2. 5X3( 625 hours of assembly available 1. 5X1 + 2. 0X2 + 2. 0X3( 550 hours of painting available X1+ 2. 0X2 + 2. 0X3( 100 chairs X2 + 2. 0X3( 50 benches X3( 50 tables X1, X2, X3( 0 What mix of products would yield maximum profit? Solving with computer software we get: X1= 100 chairs; X2 = 50 benches; X3 = 112. 5 tables; profit = 4250. Alternative Example 8. 2:  Ã‚  A phosphate manufacturer produces three grades of phosphate, A, B, and C, which yield profit of $40, $50, and $60 per kilogram, respectively. The products require the labor and materials per batch that are shown in the table. Each batch of Grade A phosphate yields 800kg of phosphate; each batch of Grade B phosphate yields 700kg of phosphate; and each batch of Grade C phosphate yields 800 kg. |Grade |Grade |Grade |Available | | |A |B |C |Resources | |Labor hours |4 |4 |5 |80 hr | |Raw material #1 |200 |300 |300 |6,000 kg | |Raw material #2 |600 |400 |500 |5,000 kg | Formulate as an LP problem to maximize profit. Objective function Maximize profit = 40(800)A + 50(700)B + 60(800)C Constraints Labor:4A +4B +5C( 80 Raw material #1200A + 300B +300C( 6,000 Raw material #2600A + 400B +500C( 5,000 What mix of products would yield maximize profit? Solutions To Problems 8-1. Since the decision centers about the production of the two different cabinet models, we let X1= number of French Provincial cabinets produced each day X2= number of Danish Modern cabinets produced each day Objective: maximize revenue = $28X1 + $25X2 subject to 3X1 + 2X2( 360 hours  Ã‚  (carpentry department) [pic] X1 + 1X2( 200 hours  Ã‚  (painting department) [pic]X1 + [pic] X2( 125 hours  Ã‚  (finishing department) X1( 60 units  Ã‚  (contract requirement) X2( 60 units  Ã‚  (contract requirement) X1, X2( 0 Problem 8-1 solved by computer: Produce 60 French Provincial cabinets (X1) per day Produce 90 Danish Modern cabinets (X2) per day Revenue = $3,930 8-2. Let X1= dollars invested in Los Angeles municipal bonds X2= dollars invested in Thompson Electronics X3= dollars invested in United Aerospace X4= dollars invested in Palmer Drugs X5= dollars invested in Happy Days Nursing Homes Maximize return = 0. 53X1 + 0. 068X2 + 0. 049X3 + 0. 084X4 + 0. 118X5 subject to X1 + X2 + X3 + X4 + X5 ( $250,000 (funds) X1( . 2 (X1 + X2 + X3 + X4 + X5) (bonds) or ( . 8X1 – . 2X2 – . 2X3 – . 2X4 – . 2X5 ( 0 X2 + X3 + X4( . 4 (X1 + X2 + X3 + X4 + X5) (combination of electronics, aerospace, and drugs) or –0. 4X1 + 0. 6X2 + 0. 6X3 + 0. 6X4 – 0. 4X5 ( 0 (X5 ( 0. 5X1) rewritten as –0. 5X1 + X5 ( 0 (nursing home as percent of bonds) X1, X2, X3, X4, X5 ( 0 Problem 8-2 solved by computer: $50,000invested in Los Angeles municipal bonds (X1) $0invested in Tho mpson Electronics (X2) $0invested in United Aerospace (X3) 175,000invested in Palmer Drugs (X4) $25,000invested in Happy Days (X5) This produces an annual return on investment of $20,300. 8-3. Minimize staff size = X1 + X2 + X3 + X4 + X5 + X6 where Xi = number of workers reporting for start of work at period i (with i = 1, 2, 3, 4, 5, or 6) X1 + X2 ( 12 X2 + X3 ( 16 X3 + X4 (   9 X4 + X5 ( 11 X5 + X6 (   4 X1 + X6 ( 3 All variables ( 0 The computer solution is to hire 30 workers: 16 begin at 7 a. m. 9 begin at 3 p. m. 2 begin at 7 p. m. 3 begin at 11 p. m. An alternative optimum is 3 begin at 3 a. m. 9 begin at 7 a. m. 7 begin at 11 a. m. begin at 3 p. m. 9 begin at 7 p. m. 0 begin at 11 p. m. 8-4. Let X1= number of pounds of oat product per horse each day X2= number of pounds of enriched grain per horse each day X3= number of pounds of mineral product per horse each day Minimize cost = 0. 09X1 + 0. 14X2 + 0. 17X3 subject to 2X1+ 3X2 + 1X3 ( 6 (ingredient A) [pic]X1+ 1X2 + [pic]X3 ( 2 (ingredient B) 3X1+ 5X2 + 6X3 ( 9 (ingredient C) 1X1+ 1[pic]X2 + 2X3 ( 8 (ingredient D) [pic]X1+ [pic]X2 + 1[pic]X3 ( 5 (ingredient E) X1+ X2 +X3 ( 6 (maximum feed/day) All variables ( 0 Solution: X1= 1[pic] X2= 0 X3= 3[pic] cost= 0. 87 8-5. Let E1, E2, and E3 represent the ending inventory for the three months respectively. Let RT1, RT2, and RT3 represent the reguar production for the three months and OT1, OT2, an d OT3 represent the overtime production quantities during the three months respectively. Then the formulation is: Minimize cost: 300RT1 + 300RT2 + 300RT3 + 325OT1 + 325OT2 + 325OT3 + 20E1 + 20E2 + 20E3 subject to RT1 lt; 200 June regular production RT2 lt; 200 July regular production RT3 lt; 200 August regular production OT1 lt; 15 June overtime production OT2 lt; 15 July overtime production OT3 lt; 15 August overtime production (E1 + RT1 + OT1= 195 Ending inventory from first month (E2 + E1 + RT2 + OT2= 215 Ending inventory from second month (E3 + E2 + RT3 + OT3= 205 Ending inventory from third month {All variables}? 0 Non-negativity constraints The optimal production schedule is to produce 200 each month during regular production and to use overtime to produce 10 units in July and 5 in August for a total cost of $184,975. 8-6. Let T = number of TV ads R = number of radio ads B = number of billboard ads N = number of newspaper ads Maximize total audience = 30,000T + 22,000R + 24,000B + 8,000N Subject to 800T + 400R + 500B + 100N ( 15,000 ? ( 10 R (10 ? (10 ? (10 ? + R ( 6 500B + 100N ( 800T ?, R, ? , ? ( 0 Solution: T = 6. 875; R = 10; B = 9; N = 10; Audience reached = 722,250. If integer solutions are necessary, integer programming (see Chapter 11) could be used. 8-7. Let_X1= number of newspaper ads placed X2= number of TV spots purchased Minimize cost =$925X1 + $2,000X2 subject to0. 04X1 + 0. 05X2 ( 0. 40 (city exposure) 0. 03X1 + 0. 03X2 ( 0. 60 (exposure in northwest suburbs) X1, X2 ( 0 Note that the problem is not limited to unduplicated exposure (e. g. one person seeing the Sunday newspaper three weeks in a row counts for three exposures). Problem 8-7 solved by computer: Buy 20 Sunday newspaper ads (X1) Buy 0 TV ads (X2) This has a cost of $18,500. Perhaps the paint store should consider a blend of TV and newspaper, not just the latter. 8-8. Let Xij = number of new leases in month i for j-months, i = 1, . . . , 6; j = 3, 4, 5 Minimize cost =1260X13 + 1260X23 + 1260X 33 + 1260X43 + 840X53 + 420X63 + 1600X14 + 1600X24 + 1600X34 + 1200X44 + 800X54 + 400X64+ 1850X15 + 1850X25 + 1480X35 + 1110X45 + 740X55 + 370X65 subject to:X13 + X14 + X15 ( 420 – 390 X13 + X14 + X15 + X23 + X24 + X25 ( 400 – 270 X13 + X14 + X15 + X23 + X24 + X25 + X33 + X34 + X35 ( 430 – 130 X14 + X15 + X23 + X24 + X25 + X33 + X34 + X35 + X43 + X44 + X45 ( 460 X15 + X24 + X25 + X33 + X34 + X35 + X43 + X44 + X45 + X53 + X54 + X55 ( 470 X25 + X34 + X35 + X43 + X44 + X45 + X53 + X54 + X55 + X63 + X64 + X65 ( 440 X15 + X25 + X35 + X45 + X55 + X65 ( 0. 0(X13 + X14 + X15 + X23 + X24 + X25 + X33 + X34 + X35 + X43 + X44 + X45 + X53 + X54 + X55 + X63 + X64 + X65) All variables ( 0 Solving this on the computer results in the following solution: X15 = 305-month leases in March X25 = 1005-month leases in April X35 = 1705-month leases in May X45 = 1605-month leases in June X55 = 105-month leases in July All other variables equal 0. Total cost = $677,100. As a result of this, there are 440 cars remaining at the end of August. 8-9. The linear program has the same constraints as in problem 8-8. The objective function changes and is now: Minimize cost =1260(X13 + X23 + X33 + X43 + X53 + X63) + 1600(X14 + X24 + X34 + X44 + X54 + X64) + 1850(X15 + X25 + X35 + X45 + X55 + X65) Solving this on the computer results in the following solution: X15 = 305-month leases in March X25 = 1005-month leases in April X34 = 654-month leases in May X35 = 1055-month leases in May X43 = 1603-month leases in June X53 = 103-month leases in July All other variables equal 0. Total cost = $752,950. 8-10. Let Xij = number of students bused from sector i to school j Objective: minimize total travel miles = 5XAB+ 8XAC + 6XAE 0XBB+ 4XBC + 12XBE + 4XCB+ 0XCC + 7XCE + 7XDB+ 2XDC + 5XDE + 12XEB+ 7XEC + 0XEE subject to XAB + XAC + XAE= 700 (number of students in sector A) XBB + XBC + XBE= 500 (number of students in sector B) XCB + XCC + XCE= 100 (number of students in sector C) XDB + XDC + XDE= 800 (number of students in sector D) XEB + XEC + XEE= 400 (number students in sector E) XAB + XBB + XCB + XDB + XEB ( 900 (school B capacity) XAC + XBC + XCC + XDC + XEC ( 900 (school C capacity) XAE + XBE + XCE + XDE + XEE ( 900 (school E capacity) All variables ( 0 Solution: XAB= 400 XAE= 300 XBB= 500 XCC= 100 XDC= 800 XEE= 400 Distance = 5,400 â€Å"student miles† 8-11. Maximize number of rolls of Supertrex sold = 20X1 + 6. 8X2 + 12X3 – 65,000X4 whereX1= dollars spent on advertising X2= dollars spent on store displays X3= dollars in inventory X4= percent markup subject to X1 + X2 + X3 ( $17,000 (budgeted) X1( $3,000 (advertising constraint) X2( 0. 05X3 (or X2 – 0. 05X3 ( 0) (ratio of displays to inventory) [pic] (markup ranges) X1, X2, X3, X4 ( 0 Problem 8-11 solved by computer: Spend $17,000 on advertising (X1). Spend nothing on in-store displays or on-hand inventory (X2 and X3). Take a 20% markup. The store will sell 327,000 rolls of Supertrex. This solution implies that no on-hand inventory or displays are needed to sell the product, probably due to an oversight on Mr. Kruger’s part. Perhaps a constraint indicating that X3 ( $3,000 of inventory should be held might be needed. 8-12. Minimize total cost = $0. 60X1 + 2. 35X2 + 1. 15X3 + 2. 25X4 + 0. 58X5 + 1. 17X6 + 0. 33X7 subject to 295X1 + 1,216X2 + 394X3 +358X4 + 128X5+ 118X6 + 279X7 ( 1,500 295X1 + 1,216X2 + 394X3 +358X4 + 128X5+ 118X6 + 279X7 ( 900 .2X1 + 121. 2X2 + . 4. 3X3 + 3. 2X4 + 3. 2X5+ 14. 1X6 + 2. 2X7 ( 4 16X1 +1,296X2 + . 4. 9X3 + 0. 5X4 + 0. 8X5+ 1. 4X6 + 0. 5X7 ( 50 6X1 + 81X2 + 74X3 + 83X4 + 7X5+ 14X6 +  8X7 ( 26 22X1 + 28X5 + 19X6 + 63X7( 50 All Xi ( 0 Problem 8-12 solved by computer: The meal plan for the evening is No milk (X1 = 0) 0. 499 pound of ground meat (X2) 0. 173 pound of chicken (X3) No fish (X4 = 0) No beans (X5 = 0) 0. 105 pound of spinach (X6) 0. 762 pound of white potatoes (X7) Each meal has a cost of $1. 75. The meal is fairly well -balanced (two meats, a green vegetable, and a potato). The weight of each item is realistic. This problem is very sensitive to changing food prices. Sensitivity analysis when prices change: Milk increases 10 cents/lb: no change in price or diet Milk decreases 10 cents/lb: no change in price or diet Milk decreases 30 cents/lb (to 30 cents): potatoes drop out and milk enters, price = $1. 42/meal Ground meat increases from $2. 35 to $2. 75: price = $1. 93 and spinach leaves the optimal solution Ground meat increases to $5. 25/lb: price = $2. 07 and meat leaves; milk, chicken, and potatoes in solution Fish decreases from $2. 25 to $2. 00/lb: no change Chicken increases to $3. 00/lb: price = $1. 91 and meat, fish, spinach, and potatoes in solution If meat and fish are omitted from the problem, the solution is chicken= 0. 774 lb milk= 1. 891 lb potatoes= 0. 33 lb If chicken and meat are omitted; fish= 0. 679 lb spinach= 0. 0988 lb milk= 2. 188 lb 8-13. a. Let X1= no. of units of internal modems produced per week X2= no. of units of external modems produced per week X3= no. of units of circuit boards produced per week X4= no. of units of floppy disk drives produced per week X5= no. of units of hard drives produced per week X6= no. of units of memory boards produced per week Objective function analysis: First find the time used on each test device: hours on test device 1 [pic] hours on test device 2 [pic] hours on test device 3 [pic] Thus, the objective function is aximize profit = (revenue) – (material cost) – )test cost) = (200X1 + 120X2 + 180X3 + 130X4 + 430X5 + 260X6 – 35X1 – 25X2 – 40X3 – 45X4 – 170X5 – 60X6)[pic] [pic] [pic] This can be rewritten as maximize profit =$161. 35X1 + 92. 95X2 + 135. 50X3 + 82. 50X4 + 249. 80X5 + 191. 75X6 subject to 7X1 + 3X2 + 12X3 + 6X4 + 18X5 + 17X6 lt; 120(60) Minutes on test device 1 2X1 + 5X2 + 3X3 + 2X4 + 15X5 + 17X6 lt; 120(60) Minutes on test device 2 5X1 + 1X2 + 3X3 + 2X4 + 9X5 + 2X6 lt; 100(60) Minutes on test device 3 All variables ( 0 b. The solution is X1= 496. 55 internal modems X2= 1,241. 38 external modems X3 through X6= 0 profit= $195,504. 80 c. The shadow prices, as explained in Chapter 7 and Module 7, for additional time on the three test devices are $21. 41, $5. 75, and $0, respectively, per minute. 8-14. a. Let Xi = no. of trained technicians available at start of month i Yi = no. of trainees beginning in month i Minimize total salaries paid = $2,000X1 + 2,000X2 + 2,000X3 + 2,000X4 + 2,000X5 + 900Y1 + 900Y2 + 900Y3 + 900Y4 + 900Y5 subject to 130X1 – 90Y1( 40,000 (Aug. need, hours) 130X2 – 90Y2( 45,000 (Sept. need) 130X3 – 90Y3( 35,000 (Oct. need) 130X4 – 90Y4( 50,000 (Nov. need) 130X5 – 90Y5( 45,000 (Dec. eed) X1= 350 (starting staff on Aug. 1) X2= X1 + Y1 – 0. 05X1 (staff on Sept. 1) X3= X2 + Y2 – 0. 05X2 (staff on Oct. 1) X4= X3 + Y3 – 0. 05X3 (staff on Nov. 1) X5= X4 + Y4 – 0. 05X4 (staff on Dec. 1) All Xi, Yi ( 0 b. The computer-generated results are: | |Trained | | | |Technicians |Trainees | |Month |Available |Beg inning | |Aug. 350 |13. 7 (actually 14) | |Sept. |346. 2 |0 | |Oct. |328. 8 |72. 2 (actually 72) | |Nov. |384. 6 |0 | |Dec. |365. 4 |0 | Total salaries paid over the five-month period = $3,627,279. 8-15. a. Let Xij = acres of crop i planted on parcel j wherei = 1 for wheat, 2 for alfalfa, 3 for barley = 1 to 5 for SE, N, NW, W, and SW parcels Irrigation limits: 1. 6X11 + 2. 9X21 + 3. 5X31( 3,200 acre-feet in SE 1. 6X12 + 2. 9X22 + 3. 5X32( 3,400 acre-feet in N 1. 6X13 + 2. 9X23 + 3. 5X33( 800 acre-feet in NW 1. 6X14 + 2. 9X24 + 3. 5X34( 500 acre-feet in W 1. 6X15 + 2. 9X25 + 3. 5X35( 600 acre-feet in SW [pic] water acre-feet total Sales limits: X11 + X12 + X13 + X14 + X15 ( 2,200 wheat in acres (= 110,000 bushels) X21 + X22 + X23 + X24 + X25 ( 1,200 alfalfa in acres (= 1,800 tons) X31 + X32 + X33 + X34 + X35 ( 1,000 barley in acres (= 2,200 tons) Acreage availability: X11 + X21 + X31( 2,000 acres in SE parcel X12 + X22 + X32( 2,300 acres in N parcel X13 + X23 + X33( 600 acres in NW parcel X14 + X24 + X34( 1,100 acres in W parcel X15 + X25 + X35( 500 acres in SW parcel Objective function: maximize profit [pic] b. The solution is to plant X12= 1,250 acres of wheat in N parcel X13= 500 acres of wheat in NW parcel X14= 312[pic] acres of wheat in W parcel X15= 137[pic] acres of wheat in SW parcel X25= 131 acres of alfalfa in SW parcel X31= 600 acres of barley in SE parcel X32= 400 acres of barley in N parcel Profit will be $337,862. 10. Multiple optimal solutions exist. c. Yes, need only 500 more water-feet. 8-16. Amalgamated’s blending problem will have eight variables and 11 constraints. The eight variables correspond to the eight materials available (three alloys, two irons, three carbides) that can be selected for the blend. Six of the constraints deal with maximum and minimum quality limits, one deals with the 2,000 pound total weight restriction, and four deal with the weight availability limits for alloy 2 (300 lb), carbide 1 (50 lb), carbide 2 (200 lb), and carbide 3 (100 lb). Let X1 through X8 represent pounds of alloy 1 through pounds of carbide 3 to be used in the blend. Minimize cost = 0. 12X1 + 0. 13X2 + 0. 15X3 + 0. 09X4 + 0. 07X5 + 0. 10X6 + 0. 12X7 + 0. 09X8 subject to manganese quality: 1  Ã‚  0. 70X1 + 0. 55X2 + 0. 12X3 + 0. 01X4 + 0. 05X5 ( 42 (2. 1% of 2,000) 2  Ã‚  0. 70X1 + 0. 55X2 + 0. 12X3 + 0. 01X4 + 0. 05X5 ( 46 (2. 3% of 2,000) silicon quality: 3  Ã‚  0. 15X1 + 0. 30X2 + 0. 26X3 + 0. 10X4 + 0. 025X5 + 0. 24X6 + 0. 25X7 + 0. 23X8 ( 86 (4. 3% of 2,000) 4  Ã‚  0. 15X1 + 0. 30X2 + 0. 26X3 + 0. 10X4 + 0. 025X5 + 0. 24X6 + 0. 25X7 + 0. 23X8 ( 92 (4. 6% of 2,000) carbon quality: 5  Ã‚  0. 03X1 + 0. 01X2 + 0. 03X4 + 0. 18X6 + 0. 20X7 + 0. 25X8 ( 101 (5. 5% of 2,000) 6  Ã‚  0. 03X1 + 0. 01X2 + 0. 03X4 + 0. 18X6 + 0. 20X7 + 0. 25X8 ( 107 (5. 35% of 2,000) Availability by weight: 7  Ã‚  X2 ( 300 8  Ã‚  X6 ( 50 9  Ã‚  X7 ( 200 10  Ã‚  X8 ( 100 One-ton weight: 11  Ã‚  X1 + X2 + X3 + X4 + X5 + X6 + X7 + X8 = 2,000 The solution is infeasible. 8-17. This problem refers to Problem 8-16’s infeasibility. Some investigative w ork is needed to track down the issues. The two issues are: 1. Requiring at least 5. 05% carbon is not possible. 2. Producing 1 ton from the materials is not possible. If constraints 5 and 11 are relaxed (or removed), one solution is X2 = 83. lb (alloy 2), X6 = 50 lb (carbide 1), X7 = 83. 6 lb (carbide 2), and X8 = 100 lb (carbide 3). Cost = $34. 91. Each student may take a different approach and other recommendations may result. 8-18. X1= number of medical patients X2= number of surgical patients Maximize revenue = $2,280X1 + $1,515X2 subject to 8X1 + 5X2( 32,850 (patient-days available = 365 days ( 90 new beds) 3. 1X1 + 2. 6X2 ( 15,000 (lab tests) 1X1 + 2X2( 7,000 (x-rays) X2( 2,800 (operations/surgeries) X1, X2( 0 Problem 8-18 solved by computer: X1= 2,791 medical patients X2= 2,105 surgical patients revenue= $9,551,659 per year To convert X1 and X2 to number of medical versus surgical beds, find the total number of hospital days for each type of patient: medical= (2,791 patients)(8 days/patient) = 22,328 days surgical= (2,105 patients)(5 days/patient) = 10,525 days total= 32,853 days This represents 68% medical days and 32% surgical days, which yields 61 medical beds and 29 surgical beds. (Note that an alternative approach would be to formulate with X1, X2 as number of beds. ) See the printout on the next page for the solution and sensitivity analysis. 8-19. This problem, suggested by Professor C. Vertullo, is an excellent exercise in report writing. Here is a chance for students to present management science results in a management format. Basically, the following issues need to be addressed in any report: (a)  Ã‚  As seen in Problem 8-18, there should be 61 medical and 29 surgical beds, yielding $9,551,659 per year. (b)  Ã‚  Referring to the QM for Windows printout, there are no empty beds because the slack for constrain 1 has a value of 0.. (c)  Ã‚  There are 876 (the slack for constraint 2) lab tests of unused capacity. (d)  Ã‚  The x-ray is used to its maximum (slack for constraint 3 is 0) and has a $65. 5 dual price. The revenue would increase by this amount for each additional x-ray. (e)  Ã‚  The operating room still has 695 operations available (the slack for constraint 4). [pic] [pic] 8-20. For the Low Knock Oil Company example it was originally assumed that a one to one ratio of raw materials (crude oil) to finished goods (gasoline). In reality, that ratio is closer to 46%. Hence, the example problem needs to be modified with 0. 46 as the coefficient throughout the first two constraints as follows: Minimize 30X1 + 30X2 + 34. 80X3 + 34. 80X4 subject to: 0. 46X1 + 0. 46X3( 25000 0. 46X2+ 0. 46X4( 32000 0. 10 X1 + 0. 15X3 ( 0 0. 05X2 – 0. 25X4 ( 0 The rounded solution is X1 = 32609; X2 = 57971; X3 = 21739; X4 = 11594; Cost = 3877391 8-21. Minimize time = 12XA1 + 11XA2 + 8XA3 + 9XA4 + 6XA5 + 6XA6 + 6XG1 + 12XG2 + 7XG3 + 7XG4 + 5XG5 + 8XG6 + 8XS1 + 9XS2 + 6XS3 + 6XS4 + 7XS5 + 9XS6 subject to XA1+ XA2+ XA3+ XA4+ XA5+ XA6= 200 XG1+ XG2+ XG3+ XG4 + XG5+ XG6= 225 XS1+ XS2+ XS3+ XS4+ XS5+ XS6= 275 XA1+ XG1+ XS1= 80 XA2+ XG2+ XS2= 120 XA3+ XG3+ XS3= 150 XA4+ XG4+ XS4= 210 XA5+ XG5+ XS5= 60 XA6+ XG6+ XS6= 80 All variables ( 0 Solution: |Source |Destination |Number of |(Station) |(Wing) |Trays | |5A |5 |60 | |5A |6 |80 | |5A |3 |60 | |3G |1 |80 | |3G |3 |90 | |3G |4 |55 | |1S |4 |155 | |1S |2 |120 | Optimal cost = 4,825 minutes. Multiple op timal solutions exist. 8-22. Let Xi = proportion of investment invested in stock i for i = 1, 2, . . . , 5 Minimize beta = 1. 2X1 + 0. 85X2 + 0. 55X3 + 1. 40X4 + 1. 25X5 subject to X1 + X2 + X3 + X4 + X5 = 1total of the proportions must add to 1 0. 11X1 + 0. 09X2 + 0. 065X3 + 0. 15X4 + 0. 13X5 ( 0. 11return should be at least 11% X1 ( 0. 5no more than 35% in any single stock X2 ( 0. 35 X3 ( 0. 35 X4 ( 0. 35 X5 ( 0. 35 Xi ( 0 for i = 1, 2, . . . , 5 b. Solving this on the computer, we have X1 = 0 X2 = 0. 10625 X3 = 0. 35 X4 = 0. 35 X5 = 0. 19375 Minimum beta = 1. 015 Return = 0. 11(0) + 0. 09(0. 10625) + 0. 065(0. 35) + 0. 15(0. 35) + 0. 13(0. 19375) = 0. 11 8-23. Let A = 1,000 gallons of fuel to purchase in Atlanta L = 1,000 gallons of fuel to purchase in Los Angeles H = 1,000 gallons of fuel to purchase in Houston N = 1,000 gallons of fuel to purchase in New Orleans FA = fuel remaining when plane lands in Atlanta FL = fuel remaining when plane lands in Los Angeles FH = fuel remaini ng when plane lands in Houston FN = fuel remaining when plane lands in New Orleans Minimize cost = 4. 15A + 4. 25L + 4. 10H + 4. 18N subject to A + FA ( 24minimum amount of fuel on board when leaving Atlanta A + FA ( 36maximum amount of fuel on board when leaving Atlanta L + FL ( 15minimum amount of fuel on board when leaving Los Angeles L + FL ( 23maximum amount of fuel on board when leaving Los Angeles H + FH ( 9minimum amount of fuel on board when leaving Houston H + FH ( 17maximum amount of fuel on board when leaving Houston N + FN ( 11minimum amount of fuel on board when leaving New Orleans N + FN ( 20maximum amount of fuel on board when leaving New Orleans FL = A + FA – (12 + 0. 05(A + FA – 24)) This says that the fuel on board when the plane lands in Los Angeles will equal the amount on board at take-off minus the fuel consumed on that flight. The fuel consumed is 12 (thousand gallons) plus 5% of the excess above 24 (thousand gallons). This simplifies to: 0. 95A + 0. 95 FA – FL = 10. 8 Similarly, FH = L + FL – (7 + 0. 05(L + FL – 15)) becomes 0. 95L + 0. 95FL – FH = 6. 25 FN = H + FH – (3 + 0. 05(H + FH – 9)) becomes 0. 95H + 0. 95FH – FN = 2. 55 FA = N + FN – (5 + 0. 05(N + FN – 11)) becomes 0. 95N + 0. 95FN – FA = 4. 45 All variables ( 0 The optimal solution is A=18 (1,000 gallons of fuel to purchase in Atlanta) FA=6 (1,000 gallons of fuel remaining when plane lands in Atlanta) L=3 (1,000 gallons of fuel to purchase in Los Angeles) FL=12 (1,000 gallons of fuel remaining when plane lands in Los Angeles) H=1 (1,000 gallons of fuel to purchase in Houston) FH=8 (1,000 gallons of fuel remaining when plane lands in Houston) N=5 (1,000 gallons of fuel to purchase in New Orleans) FN=6 (1,000 gallons of fuel remaining when plane lands in New Orleans) Total cost = 112. 45 (( 1,000) Solutions to Internet Homework Problems 8-24. Let X1 = number of Chaunceys mixed X2= number of Sweet Italians mixed X3= number of bourbon on the rocks mixed X4= number of Russian martinis mixed Maximize total drinks = X1 + X2 + X3 + X4 subject to 1X1 +4X3 ( 52 oz (bourbon limit) 1X1 +1X2 ( 38 oz (brandy limit) 1X1 +2[pic]X4 ( 64 oz (vodka limit) X2 +1[pic]X4 ( 24 oz (dry vermouth limit) 1X1 +2X2 ( 36 oz (sweet vermouth limit) All variables ( 0 Because a Chauncey (X1) is [pic] sweet vermouth, it requires 1 oz of that resource (each drink totals 4 oz). Problem 8-27 solved by computer: Mix 25. 99 (or 26) Chaunceys (X1) Mix   5. 00 (or 5) Sweet Italians (X2) Mix   6. 50 (or 6[pic]) bourbon on the rocks (X3) Mix 14. 25 (or 14[pic]) Russian martinis (X4) This is a total of 51. 75 drinks (in five iterations). 8-25. Minimize 6X11 + 8X12 + 10X13 + 7X21 + 11X22 + 11X23 + 4X31 + 5X32 + 12X33 subject to X11 + X12 + X13( 150 X21 + X22 + X23( 175 X31 + X32 + X33( 275 X11 + X21 + X31= 200 X12 + X22 + X32= 100 X13 + X23 + X33= 300 All variables ( 0 The solution is: X11 = 25, X13 = 125, X23 = 175, X31 = 175, X32 = 100 Cost = $4,525. 8-26. Let Xi = number of BR54 produced in month i, for i = 1, 2, 3. Yi   = number of BR49 produced in month i, for i = 1, 2, 3. IXi = number of BR54 units in inventory at end of month i, for i = 0, 1, 2, 3. IYi = number of BR49 units in inventory at end of month i, for i = 0, 1, 2, 3. Minimize cost = 80(X1 + X2 + X3) + 95(Y1 + Y2 + Y3) + 0. 8(IX1 + IX2 + IX3) + 0. 95(IY1 + IY2 + IY3) Subject to: IX0 = 50initial inventory of BR54 IY0 = 50initial inventory of BR49 IX3 = 100ending inventory of BR54 IY3 = 150ending inventory of BR49 X1 + Y1 ( 1,100maximum production level in August X2 + Y2 ( 1,100maximum production level in September X3 + Y3 ( 1,100maximum production level in October X1 + IX0 = 320 + IX1  Ã‚  BR54 requirements for August X2 + IX1 = 740 + IX2  Ã‚  BR54 requirements for September X3 + IX2 = 500 + IX3  Ã‚  BR54 requirements for October Y1 + IY0 = 450 + IY1  Ã‚  BR49 requirements for August Y2 + IY1 = 420 + IY2  Ã‚  BR49 requirements for September Y3 + IY2 = 480 + IY3  Ã‚  BR49 requirements for October All variables ( 0 A computer solution to this results in IX0 = 50, IX1 = 190, IX2 = 130, IX3 = 100, IY0 = 50, IY3 = 150, X1 = 460, X2 = 680, X3 = 470, Y1 = 400, Y2 = 420, Y3 = 630. All other variables = 0. The total cost = $267,028. 50. Solution to Chase Manhattan Bank Case This very advanced and challenging scheduling problem can be solved most expeditiously using linear programming, preferably integer programming. Let F denote the number of full-time employees. Some number, F1, of them will work 1 hour of overtime between 5 p. m. and 6 p. m. each day and some number, F2, of the full-time employees will work overtime between 6 p. m. and 7 p. m. There will be seven sets of part-time employees; Pj will be the number of part-time employees who begin their workday at hour j, j = 1, 2, . . . , 7, with P1 being the number of workers beginning at 9 a. m. , P2 at 10 a. . , . . . , P7 at 3 p. m. Note that because part-time employees must work a minimum of 4 hours, none can start after 3 p. m. since the entire operation ends at 7 p. m. Similarly, some number of part-time employees, Qj, leave at the end of hour j, j = 4, 5, . . . , 9. The workforce requirements for the first two hours, 9 a. m. a nd 10 a. m. , are: F + P1( 14 F + P1 + P2 ( 25 At 11 a. m. half of the full-time employees go to lunch; the remaining half go at noon. For those hours: 0. 5F + P1 + P2 + P3( 26 0. 5F + P1 + P2 + P3 + P4 ( 38 Starting at 1 p. m. , some of the part-time employees begin to leave. For the remainder of the straight-time day: F + P1 + P2 + P3 + P4 + P5 – Q4( 55 F + P1 + P2 + P3 + P4 F + P1 + P2 + P5 + P6 – Q4 – Q5( 60 F + P1 + P2 + P3 + P4 + P5 F + P1 + P6 + P7 – Q4 – Q5 – Q6( 51 F + P1 + P2 + P3 + P4 + P5 + P6 F + P1 + P7 – Q4 – Q5 – Q6 – Q7( 29 For the two overtime hours: F1 + P1 + P2 + P3 + P4 + P5 + P6 F1 + P1 + P2 + P7 – Q4 – Q5 – Q6 – Q7 – Q8( 14 F2 + P1 + P2 + P3 + P4 + P5 + P6 + P7 F1 + P1 + P2 – Q4 – Q5 – Q6 – Q7 – Q8 – Q9( 9 If the left-hand sides of these 10 constraints are added, one finds that 7F hours of full-time labor are used in straight time (although 8F are paid for), F1 + F2 full-time labor hours are used and paid for at overtime rates, and the total number of part-time hours is 0P1 + 9P2 + 8P3 + 7P4 + 6P5 + 5P6 + 4P7 – 6Q4– 5Q5 – 4Q6 – 3Q7 – 2Q8 – Q9 ( 128. 4 which is 40% of the day’s total r equirement of 321 person-hours. This also leads to the objective function. The total daily labor cost which must be minimized is Z = 8(10. 11)F + 8. 08(F1 + F2) + 7. 82(10P1 + 9P2 + 8P3 + 7P4 + 6P5 + 5P6 + 4P7 – 6Q4 – 5Q5 – 4Q6 – 3Q7 – 2Q8 – Q9) Total overtime for a full-time employee is restricted to 5 hours or less, an average of 1 hour or less per day per employee. Thus the number of overtime hours worked per day cannot exceed the number of full-time employees: F1 + F2 ( F Since part-time employees must work at least 4 hours per day, Q4 ( P1 for those leaving at the end of the fourth hour. At the end of the fifth hour, those leaving must be drawn from the P1 – Q4 remaining plus the P2 that arrived at the start of the second hour: Q5 ( P1 + P2 – Q4 Similarly, for the remainder of the day, Q6( P1 + P2 + P3 – Q4 – Q5 Q7( P1 + P2 + P3 + P4 – Q4 – Q5 – Q6 Q8( P1 + P2 + P3 + P4 + P5 – Q4 – Q5 – Q6 – Q7 Q9( P1 + P2 + P3 + P4 + P5 + P6 – Q4 – Q5 – Q6 – Q7 – Q8 To ensure that all part-timers who began at 9 a. m. do not work more than 7 hours: Q4 + Q5 + Q6 + Q7 ( P1 Similarly, Q4 + Q5 + Q6+ Q7 + Q8 ( P1 + P2 Q4 + Q5 + Q+ Q7 + Q8 + Q9 ( P1 + P2 + P3 Finally, to ensure that all part-time employees leave at some time: P1 + P2 + P3 + P4 + P5 + P6 + P7 = Q4 + Q5 + Q6 + Q7 + Q8 + Q9 The resulting problem has 16 integer variables and 22 constraints. If integer programming software is not available, the linear programming problem can be solved and the solution rounded, making certain that none of the constraints have been violated. Note that the integer programming solution might also need to be adjusted- if F is an odd integer, 0. 5F will not be an integer and the requirement that â€Å"half† of the full-time employees go to lunch at 11 a. m. and the other half at noon will have to be altered by assigning the extra employee to the appropriate hour. 1. The least-cost solution requires 29 full-time employees, 9 of whom work two hours of overtime per day. In actuality, 18 of the full-time employees would work overtime on two different days and 9 would work overtime on one day. Fourteen of the full-time workers would take lunch at 11 a. m. and the other 15 would take it at noon. Eleven part-timers would begin at 11 a. m. , with 9 of them leaving at 3 p. m. and the other 2 at 4 p. m. Fifteen part-time employees would work from noon until 4 p. m. , and 5 would work from 2 p. m. until 6 p. m. The resulting cost of 232 hours of straight time, 18 hours of overtime, and 126 hours of part-time work is $3,476. 28 per day. This solution is not unique- other work assignments can be found that result in this same cost. 2. The same staffing would be used every day. In fact, one would expect different patterns to present themselves on different days; for example, Fridays are usually much busier bank days than the others. In addition, the person-hours required for each hour of the day are assumed to be deterministic. In a real situation, wide fluctuations will be experienced in a stochastic manner. The optimal solution results in a considerable amount of idle time, partly caused by the restriction that employees can start at the beginning of an hour and leave at the end. Eliminating this restriction might yield better results at the risk of increasing the problem size.

How to Make an Inference in 5 Easy Steps

How to Make an Inference in 5 Easy Steps We all have to take those standardized tests where youre presented with a large passage of text and must work your way through the multiple-choice problems that follow. Most of the time, youll get questions asking you to find the main idea, determine the authors purpose, understand vocabulary in context, figure out the authors tone, and, the topic at hand, make inferences. For many people, understanding how to make an inference is the toughest part of the reading passage, because an inference in real life requires a bit of guessing. On a multiple-choice test, however, making an inference comes down to honing a few reading skills like these listed below. Read them, then practice your new skills with the inference practice problems listed below. What exactly is an inference? Step 1: Identify an Inference Question First, youll need to determine whether or not youre actually being asked to make an inference on a reading test. The most obvious questions will have the words suggest, imply or infer right in the tag like these: According to the passage, we can reasonably infer...Based on the passage, it could be suggested that...Which of the following statements is best supported by the passage?The passage suggests that this primary problem...The author seems to imply that†¦ Some questions, however, will not come right out and ask you to infer. Youll have to actually infer that you need to make an inference about the passage. Sneaky, huh? Here are a few that require inferencing skills, but dont use those words exactly. With which of the following statements would the author most likely agree?Which of the following sentences would the author most likely use to add additional support to paragraph three? Step 2: Trust the Passage Now that youre certain you have an inference question on your hands, and you know exactly what an inference is, youll need to let go of your prejudices and prior knowledge and use the passage to prove that the inference you select is the correct one. Inferences on a multiple-choice exam are different from those in real life. Out in the real world, if you make an educated guess, your inference could still be incorrect. But on a multiple-choice exam, your inference will be correct because youll use the details in the passage to prove it. You have to trust that the passage offers you the truth in the setting of the test and that one of the answer choices provided is correct without stepping too far outside the realm of the passage. Step 3: Hunt for Clues Your third step is to start hunting for clues – supporting details, vocabulary, characters actions, descriptions, dialogue, and more – to prove one of the inferences listed below the question. Take this question and text, for example: Reading Passage: The widow Elsa was as complete a contrast to her third bridegroom, in everything but age, as can be conceived. Compelled to relinquish her first marriage after her husband died in the war, she married a man twice her years to whom she became an exemplary wife despite their having nothing in common, and by whose death she was left in possession of a splendid fortune, though she gave it away to the church. Next, a southern gentleman, considerably younger than herself, succeeded to her hand, and carried her to Charleston, where, after many uncomfortable years, she found herself again a widow. It would have been remarkable if any feeling had survived through such a life as Elsas; it could not but be crushed and killed by the early disappointment of her first grooms demise, the icy duty of her second marriage, and the unkindness of her third husband, which had inevitably driven her to connect the idea of his death with that of her comfort. Based on the information in the passage, it could be suggested that the narrator believes Elsas prior marriages to be:A. uncomfortable, but well-suited to ElsaB. satisfactory and dull to ElsaC. cold and damaging to ElsaD. awful, but worth it to Elsa To find clues that point to the correct answer, look for descriptions that would support those first adjectives in the answer choices. Here are some of the descriptions of her marriages in the passage: †¦she became an exemplary wife despite their having nothing in common†¦Ã¢â‚¬ ¦after many uncomfortable years, she found herself again a widow.†¦the icy duty of her second marriage and the unkindness of her third husband which had inevitably driven her to connect the idea of his death with that of her comfort. Step 4: Narrow Down the Choices The last step to making a correct inference on a multiple-choice test is to narrow down the answer choices. Using the clues from the passage, we can infer that nothing much was satisfactory to Elsa about her marriages, which gets rid of Choice B. Choice A is also incorrect because although the marriages certainly seem uncomfortable based on the clues, they were not well-suited to her as she had nothing in common with her second husband and wanted her third husband to die. Choice D is also incorrect because nothing is stated or implied in the passage to prove that Elsa believed her marriages to be worth it in some way; in fact, we can infer that it wasnt worth it to her at all because she gave away the money from her second husband. So, we have to believe that Choice C is the best – the marriages were cold and damaging. The passage states explicitly that her marriage was an icy duty and her third husband was unkind. We also know that they were damaging because her feelings had been crushed and killed by her marriages. Step 5: Practice To get really good at making inferences, youll need to practice making your own inferences first, so start with these free inference practice worksheets.

Bush Article Example | Topics and Well Written Essays - 1000 words

Bush - Article Example t this program successfully, Bush directed the Secretary of the US Department of Health and Human Services (HHS) to set up the National Health Information Technology Coordinator (Thomson, 2014). In 2005, the HHS Secretary Mike Leavitt took initiative to establish American Health Information Community, a federally chartered commission, with intent to accomplish President Bush’s aim of having majority Americans using interoperable electronic health records within 10 years. Although this initiative started off strongly during the term of Bush, it has gradually fallen off for the recent years. As per Duane Morris report (2009), privacy and security concerns were the most potential barriers to the implementation of this initiative. Issues related to unauthorized access to records and privacy concerns prevented the implementation of technology. Some other security concerns include trespassing by an outsider, theft or loss of devices like laptop or mobile phone, or theft while transmitting information through a wireless network. In order to address the General Accounting Office’s concerns regarding information privacy, HHS initiated several projects including the commission that strategically determines the certification criteria for electronic medical records. According to GAO, it is essential â€Å"to establish the high degree of public confidence and trust needed to help ensure the success of a nationwide health information network† (Psych iatric news). In addition, unresolved debates over whether to employ an individual’s Social Security number hampered HIPAA implementation standards. Issues associated with general security practices also have weaken the scope of this policy. The higher costs related to this policy also became a barrier to the implementation of the proposed change. The concerned officials indicate that hardware and software maintenance throughout the organization involves higher costs. According to the Harvard researchers’ findings (cited in

Research proposal about special education Major P.H.D program

About special education Major P.H.D program - Research Proposal Example For this purpose, the researcher has formulated the research aim and objectives that have been stated below: The research aims to state the importance of special education at the PhD level along with highlighting its importance in creating a difference in the society by supporting and guiding students with special needs. For this purpose, few research objectives have been designed stated below. The literature review is aimed to present an understanding over the literature written in the context of special education highlighting its relevance and importance along with its benefits in the social environment. The idea is form an understanding that will help in gaining knowledge about special education along with its worth and importance as adding value in the personal and professional setups. Special education is meant for students with special needs covering individual differences in a systematic manner. It involves individually or group planned objectives, teaching procedures and useful and innovative interventions designed to help students to attain higher level of understanding leading to self sufficiency (Swan, Morgan, 1993). Special education can be offered within a school, college or community with the prime motive of paying focus on special needs of students. Special needs may include challenges with learning, physical disabilities, emotional and mental disorders and developmental disorders. Education can be offered to anyone using classroom setting or sharing of knowledge. However, special education demands more of a systematic and compassionate approach as students’ special needs often reduce their ability to learn independently and thus thwarting their progress in the learning phase (Goodman, 1990). Special education requires more of a compassionate app roach that cannot be offered in a general classroom setting. With social stigma attached with special education, it is

My generation negative and postive issues Essay Example | Topics and Well Written Essays - 500 words

My generation negative and postive issues - Essay Example Even while outside perspectives on Generation Y might overemphasize technology when examining this generation, I recognize that the explosion of the Internet and the personal computer were defining characteristics. In these regards, my generation will be recognized as the last generation to emerge in an era before the Internet. When I consider the implications of such an occurrence, I recognize that it has positive and negative elements. Millennials were the last to experience the unfettered nature of existence prior to the onslaught of technological mediation that accompanied the computer, while at the same time being introduced to this technology at a formative enough period to grasp its more subtle concepts. Undoubtedly future generations growing up in this new world will build on Internet achievements, but they will always lack the more natural connection with the physical world of prior ages. Another prominent defining characteristic of my generation is experiencing the shifting economic stratosphere. This has been a unique experience as the 90s brought unparalleled economic growth and development only to result in a bubble economy that would pop in 1999 and then, as a result of the subprime mortgage crisis, collapse in 2008. I believe this experience has had a negative impact on my generation, as we had become accustomed to one way of living only to have it taken away. When I consider movements such as the Occupy Wall Street protests I recognize that although income disparity is a pressing concern, a great amount of the protestors are simply discontent at their inability to attain high paying employment. I believe growing up in a bubble economy greatly conditioned them to expect this out of life, resulting in a youth culture of entitlement. While there are negative aspects of my generation I also recognize that there is much to be

How do stock price volatility affect monetary policy Essay - 1

How do stock price volatility affect monetary policy - Essay Example Therefore they have an effect on interest rates, inflation rates and money supply. These variables are controlled by monetary policy made by the central banks of countries or federal reserves and the policy determination is therefore depended on the stock prices. This paper discusses how the movements in stock prices affect determination of monetary policy. Monetary policy is the process by which the central bank or a federal reserve regulates the money supply and interest rates in order to achieve a major economic goal. On the other hand the stock market is considered as the country’s economic strength and development since it’s a non-physical facility of economic transactions. In any particular country, the economy strongly reacts to stock prices movement and in most cases economic recession is preceded by crash in stock markets. There is a very important relationship between the central banks of countries and stock markets. This makes the monetary authorities to make monetary decisions and policies by closely monitoring the stock market volatility. This ensures the authorities maintain a macroeconomic balance. According to Rigobon and sack 2001, volatility of stock prices significantly impact macroeconomics hence an important factor in determining the monetary policy. As mentioned earlier, this paper discusses the how stock price volatility affects monetary policy. This is addressed by using simple models of data from the international monetary fund in the quarterly series as at December 2010. The data used in the research is UK data ranging from 1990 first quarter to 2010 fourth quarter. The variables contained in this data set are the real UK GDP (RGDP), the consumer price index (CPI) and the interest rates set by the Bank of England The international monetary fund has 188 member countries. These countries work to foster global monetary cooperation, financial stability security, reduce poverty around the world, and promote sustainable