Linear Programming Essays - Mathematical Optimization,

Linear Programming Linear programming is a nonstatistical mathematical technique whereby the maximization or minimization of a linear expresion of variables, call the objective function, is determined in the presence of known or assumed restrictions, call constraint. In essence, it's a procedure for solving the problems in which there are more variables than simultaneous equations in which the variables are expressed. No probability or statistics are needed to study linear programming. The mathematics involved in linear programming is relatively easy to understand and to manipulate in contrast to calculus. Linear equations and inequations form the mathematical skeleton around which linear programming is built. A linear function called the object function is to be maximized or minimized in some sense, like optimzed. Most real world problems have many possible solutions. The purpose of optimization is to choose from among many possible solutions the "best" possible solutions. Some example of "best" are highest profit, lowest cost, largest sales, lowest production time, etc. The optimization of the objective functions take place in teh presence of known or assumed restriction. The technical term constraints is used to describe the restrictions present in linear programming problem. The constraints are expressed mathemically as inequalities. In a practical real-world situation, the constraints are generated by the presence of limited resources or commodities such as capital manpower and raw material. Mathematically, inequations can be converted to equations by the introduction of slack variables. Linear programming can be dated from the year 1947 when G.B. Dantzing evolved an efficent technique call the Simplex Method, for solving linear programming problems. The following decades, the rapid development of both the theory and applications of linear programming which were aided by the simultaneous introduction of the electronic computers. One of the first probelm to be solved by the simplex method was Stigler's diet problem (1945). Here is the diet problem Protein Fat Carbohydrate Cost 100g bread 40 5 205 2.2p 100g cheese 60 380 60 12p Minimal daily requirement 300 790 1350 The problem is determine how much bread and cheese Mrs. Jones should buy each day in order to minimize the cost of the diet, whilst fulfilling the calorie requirements. Suppose shy buys x' * 100g of cheese and x'' * 100g of cheese, then the mathematical problem, known as a linear programme is as follows. Minimize z=2.2x' + 12x'' (Cost Of Diet) Subject To 40x' + 60x'' > or = 300 (At least 300 cal of protein) 5x' + 380x'' > or = 790 (At least 790 cal of fat) 205x' + 60x'' > or = 1350 (At least 1350 cal of carbo.) x' > or = 0, x2 > = 0 (quantites must be non-negative) The easiest and most illustrative method of solving problems in two unknowns is the graphical method. The value of x' and x'' satisfying 40x' + 60x'' > or = 300 lies in the upper half-plane bounded by the straight line 40x' + 60x'' = 300, so the x' and x'' satistying all the above inequalities lie in the intersection of their respective half - plane. Interger Solutions Provided the supplies and demands are positive intergers, the matrix minimum method always leads to and optimal solution with integer values as the method only involves operations on integers which results in integers. Obviously a non-integer optimal solution would be useless. Uniqueness It can happen that two or more differnet allocations of ships between ports give rise to thesame minimum cost. However, if v'=u'

Animal Farm Essay

Animal Farm Essay Animal Farm Essay Moshe Kramer Explore the ways in which Orwell changes the reader’s attitudes toward Napoleon in Animal Farm. ‘Animal Farm’ is a satirical allegory which mocks Communism and the Soviet Union. Orwell does this by subtly criticising every aspect of communism by using the parallel parable of animals on a farm. Orwell himself refers to the book as a fairy tale. This is clear from the simple, almost child-like style that the book is written in. Orwell writes in this fashion to give him license to ridicule Communism and Stalin without being too controversial and direct. Joseph Stalin is represented in ‘Animal Farm’ by the â€Å"large, rather fierce-looking Berkshire boar†: Napoleon. He â€Å"was not much of a talker but with a reputation of getting his own way.† This is how Napoleon is first introduced in the book. At first Napoleon is portrayed as a quiet but resourceful pig as he â€Å"served out a double ration of corn to everybody.† The celebrative and joyful tone of this sentence reflects the freedom and happiness that the animals felt. The repe tition of â€Å"Snowball and Napoleon† when orders are given by the pair suggest that they were the ones in charge. However Snowball being mentioned first every time suggests that he seemed destined to become the next leader of the farm (just like Trotsky- his parallel- had been in Russia). At first he was just seen as an alternative leader with different ideas as he â€Å"took no interest in Snowball’s committees†. The first allusion to Napoleon’s true motives takes place when he distracts the animals so he can take the milk and apples for the pigs. â€Å"That will be attended to† he said. The short sentence alludes to the selfish intentions that Napoleon was concealing. This is the point where the transformation of Napoleon by Orwell began; from a seemingly calm and composed potential leader to the exploitative dictator that he eventually becomes. Further negative characteristics of Napoleon are displayed in the following pages. He is not mentioned at all during â€Å"the battle of the cowshed,† which alludes to his cowardice and weakness of character. Napoleon â€Å"urinated over the plans† that Snowball had created to better the life of the animals. This shocking event in a so-far conservative and innocent book -along with the long sentence that it happens in- draws attention to the fact that Napoleon was counter-productive and power hungry rather than actually wanting to improve the animals’ quality of life. Further evidence of this is that: â€Å"Napoleon produced no schemes of his own.† This apparently solid statement is riddled with irony since all Napoleon did do was scheme- but just nothing productive. For example when he took the puppies â€Å"away from their mothers† and â€Å"the farm soon forgot of their existence.† The fate of these dogs is soon revealed as Napoleon  "uttered a high-pitched whimper† and â€Å"nine enormous dogs wearing brass-studded collars came bounding into the barn. They dashed straight for Snowball†. The powerful verbs and adjectives: â€Å"enormous,† â€Å"bounding,† and â€Å"dashed,† allude to the intensity of Napoleon’s evilness and his complete willingness to utilise force and exploitation to achieve his self-seeking aims. His expulsion of Snowball also hints to his shrewd and cunning personalities as he had been planning for this for a long time. This is the first major action that Napoleon does that confirms and exposes his exploitative and selfish tendencies. The reader’s attitude towards Napoleon is further changed and developed when he uses a combination of Squealer, the growling dogs and the sheep’s bleating chorus of â€Å"four legs good, two legs bad,† to eliminate any possible opposition to his position of power. Later â€Å"Napoleon announced that the windmill was to be built after all.† This was an endeavour that Napoleon had previously been bitterly opposed to. However Squealer justified this action by saying that â€Å"Napoleon had never in reality been opposed to the windmill,† but it had been his idea from the start. Animal Farm Essay Animal Farm Essay Orwell was born Eric Hugh Blair in 1903 to Richard and Mabel Blair in Motihari, Bengal. Orwell had two sisters but was never able to grow close to them as a result of his distant travels. About eight years later Orwell was shipped to England where he would begin what would become a rather promising foundation to his education. Orwell graduated from Eton at age eighteen only to be sent back to India as he acquired the job of an Imperial Police Officer. Following his five years of service Orwell moved to London by free will where he truly absorbed the world of the unequally impoverished. Grasping these sights would soon spark something in Orwell as they helped lay the foundation for his two well-known political satires â€Å"Animal Farm†, and â€Å"Nineteen Eighty-Four†. Not only bound to books, Orwell wrote an intricate essay â€Å"Politics and the English Language† depicting how manipulation can result from vague writing as he continued to branch out from his pri mal ideas. At the age of forty-seven unfortunately, Orwell pasted away due to an artery bursting in his lung. Luckily, his works are here to continue to entertain as well as enlighten readers. â€Å"Animal Farm† by George Orwell is a novel based on the lives of animals living on the Manor Farm. Even though the title of the book suggests the book is simply about animals, the story is a much more in depth re-creation of the workings of society in Communist Russia. The animals in the book show identical characteristics to those that were a part of the Russian Revolution. The animals of Manor Farm are unhappy, in fact, growing angry. Jones the farmer is not only a drunk, but also a terrible farmer. Led by the pigs, which are the â€Å"brain workers†, a successful revolution is carried out. They plan a future for the good of all animals, as they hope for a better life. They operate the farm themselves as they struggle through the hard times and battle to retake the farm. L ater on there are political struggles between the pigs who can’t agree who should be leader as they are filling up with greed. With greed there is always downfall. The pigs seem to be changing the rules to suit themselves while having ways of frightening those who speak out, similar to that of the Russian KGB. The one pig that really had a good heart (Leon Trotsky) is run out by the power hungry pig (Stalin). The plan turns into a nightmare, as living conditions for the animals fall even worse than before. In the end the provisions from the start are broken as pig befriends man and man befriends pig turning the sole purpose of animalism into something completely different. Disturbingly, it was â€Å"impossible to say which was which†, as the differences of both pig and man were no longer present. Animal Farm’s purpose is to shed light on the Russian Revolution by sizing down the different parties and armies to a sense where their interactions are more understand able. The characters in the story are given extremely similar characteristics to those that actually took part in the Russian Revolution. The satire in Animal Farm is not direct, but allegorical because the human beings are disguised as animals. The actual â€Å"human† beings in this story symbolize the capitalist class of society, while the animals represent Communists. The Rebellion against Mr. Jones is most likely a historical portrayal of the Russian Revolution, while the sign of the hoof and horn on the flag adopted by the animals is the hammer and sickle on the Russian flag. Orwell’s â€Å"Animal Farm† can be enlightening to readers on the subject of the Russian Revolution and its ties, as it’s basically a re-enactment. This book does have great significance as it helps the average person look past the face of communism and into the horrors that it created. Orwell’s book completely covers the topic, but only

Learn Artist Idioms in Context

Learn Artist Idioms in Context Here is a discussion of what makes an artist. The focus is on personality characteristics and youll find 15 new idioms defined below used in context in the story.  Try reading one time to understand the gist without using the idiom definitions. On your second reading, use the definitions to help you understand the text while learning new idioms. Finally, take the quiz after the reading to practice the idioms and expressions youve learned. The Artist What makes an artist an artist? Well, there probably isnt any easy answer to that question. However, there are some personality characteristics that many artists seem to have in common. First of all, artists come from all walks of life. They may have been born rich or poor, but they are all dedicated to realizing what only they can see in their minds eyes. Another common trait of artists is that they do things according to their own lights. In fact, for many of them, creating art is do or die. Of course, that also means that they are often perfectionists. Theyll lose themselves in a new creation and you might not see them for the next few weeks. Often, you might drop by to check up on how they are doing and youll discover that their apartment is anything but spick-and-span. Its no wonder because theyve sunk their teeth into their latest work and completely lost all track of time. Housework is certainly the last thing on their mind! Of course, this lifestyle often means that they can barely make ends meet. Jobs are few and far between and money comes in dribs and dabs. This is true even for up-and-coming superstars whose reputation is growing by leaps and bounds. Finally, artists see art as an end in itself. Its not about the money to them. Theyre different from normal people who mind their ps and qs. Artists challenge us with their vision. Theyd never slap something together that just looks pretty. Idiom and Expression Definitions do something according to your own lights do something your own way, follow your own inspiration rather than that of othersall walks of life from many different backgrounds, classes, etc.  an end in itself something done only for the pleasure of doing itbreak new ground create something new, innovatedo or die (used as an adjective) absolutely necessarydribs and dabs little by little, not happening continuously  in your minds eye in your imaginationby leaps and bounds grow or improve very quicklylose yourself in something become so involved that you dont notice anything elsemake ends meet earn enough money to live onmind your ps and qs be normal, not interfere with other peoplesink your teeth into something concentrate on doing a project seriously for a long timeslap something together create something without much care to detailspick-and-span extremely cleanup-and-coming soon to be famous, young talent becoming successful   Idiom and Expression Quiz Im afraid I cant follow your suggestion. I prefer to paint __________.Can you see that picture __________?Our son is very good at the piano. In fact, hes improving __________.Unfortunately, money is very tight at the moment. I dont have a steady job so the money is coming in __________.Id love to _________ my __________ a new project.Its important that your house is _________ if you want to sell it.Peter is an _________ musician. Hell soon be famous.I think this work of art ________. Its completely different from anything before.Please be quiet and __________. I dont want to be bothered.Students attending the academy come from __________. Youll find people from all over the world with different backgrounds.   Quiz Answers according to my own lightsin your minds eyeby leaps and boundsdribs and dabssink my teeth intospick-and-spanup-and-comingbreaks new groundmind your ps and qsall walks of life You can learn more idioms and expressions in context with these stories.

Methods and History and Cases under the Criminal Justice System Essay

Methods and History and Cases under the Criminal Justice System - Essay Example In the case of Panetti vs Quaterman, the Defendant Scott Louis Panetti was sentenced to death row because of the double murder he committed, after killing his wife's parents. His doctors stated that Panetti have a mental disorder and the doctors concludes that Panetti believes that he will be put to death because he is preaching the Gospels. The case of Panetti is similar to the decision of Supreme Court in 1986, for the case of Ford vs Wainwright. The idea of mental illness is fundamental, and in a due process model the Criminal justice development, it has been contended, can be characterized as a structure whereby ever growing impediments are required to be prevailed over as the suspect continues further down it. (Institute of Criminal Justice Studies, 2003, page 66). It is also contended by Gelsthorpe (2002, page 106) that those caught up in defence work are more connected with due process whereas prosecutors and the courts are more connected with a crime control model. Due process recognizes that a number of culpable individuals will be exonerated but contends that this is fair with the intention of making sure the freeing of the innocent. (Institute of Criminal Justice Studies, 2003, page 66). In... A rule which driven the accountability for crime prevention beyond onto the responsibility of private individuals seemed foolish, given that it purely bared the shortfalls of a criminal justice system which was calling for a greater fraction of public expenditure. Possibly more vital, although, were the issues regarding creating a stronghold mentality, which would consecutively produce more apprehension than the lopsided quantity and previously subsisted, and which was swiftly being distinguished as an issue in its own right. As a general rule, the threat of harm must be real and present 48 and the proof of dangerousness clear and convincing. 49 We note at the outset that dangerousness has a special, though elusive, meaning in the context of involuntary commitment. It refers not only to the likelihood of violence to oneself or to others but also to severe self-neglect, to the point where the individual is unable to survive safely in the community, as the Supreme Court was careful to explain in its landmark decision in O'Connor v. Donaldson. Although civil commitment had been practiced in the United States for over two hundred years, O'Connor was the first case in which the Supreme Court considered the constitutional boundaries of the commitment process. The case involved a fifty-five-year-old man who was committed to the Florida State Hospital at Chattahoochee in 1957 and kept there for nearly fifteen years without treatment, although he had never been dangerous to himself or others, was capable of earning a living outside the hospital, and had received offers to live in a supportive halfway house or with a former college classmate who was willing and able to provide for his welfare. The

Burial at Thebes Essay Example | Topics and Well Written Essays - 1500 words

Burial at Thebes - Essay Example Heaney’s work followed the same storyline of Sophocles’ work, but in an all new structure and sentences, giving his own interpretations to certain events and decisions of the characters. As Heaney wrote this work in 2003, the year of Iraq War, there is view that he seems to be influenced by the War to come up with his own interpretation of Antigone. â€Å"(He) wrote in 2003, believing that "with the White House and the Pentagon in cahoots, determined to bring the rest of us into line over Iraq, the passion and protest of an Antigone were all of a sudden as vital as oxygen masks". (Spencer 2007). Apart from these reflections, this work and the conflicts between the main characters seems to be relevant to the current times across different culture. As in Sophocles’s Antigone, The Burial at Thebes is about life, fight and death of Antigone and the events surrounding it, with the conflicts between the characters leading to a tragic end. The title of the play in a wa y recalls the punishment meted out to Antigone in the cave of Thebes, where she was buried alive. After her two brothers, Eteocles and Polyneices, die in the Thebes’ civil war, both were given contrasting ‘burials’, based on the allegiance. â€Å"The tragedy is multiplied when not only Polyneices is felled in the war, but also Antigone’s other brother, Eteocles, perishes on the opposing side -- Creon’s side. ... Already tainted by her heritage, Antigone wants to give some honour to his dead brother, although he was considered as the traitor of Thebes by the King Creon. This sets the stage for the major conflict between Antigone and her future father-in-law Creon. Antigone has been betrothed to Creon’s son Haemon, and that does not prevent her from fighting for her dead brother. On the other hand, Creon by placing his kingdom and his policies regarding traitors over his soon-to-be daughter-in-law’s dead brother, denies her wish. With both of them not willing to give in from their Stated positions, it leads to further deterioration of their relationship. This conflict between daughter-in-law and father-in-law, although not a common occurrence, happens in cultures all over the world. Stereotypically, mother-in-laws and daughter-in-laws are considered to be ‘sworn enemies’, who both indulge in conflicts quite often, with the father-in-law being the silent spectator. Ho wever, sometimes, conflicts could arise between them and that could come into the public domain, if anyone one of them is a public figure. This has happened in the case of Chairman of the family bench at Worcester Magistrates Court, Richard Westcott, whose daughter-in-law, Sarah complained that he physically assaulted him during a scuffle. Sarah had a fight with her husband and Richard’s son, Edward, when it was alleged that his father-in-law, wanting to protect his son, intervened and physically assaulted her although she had baby in her hand. The court heard she later told police: â€Å"I was hit on my upper body and Daniel was hit on the side. I'm a doctor and I'm worried about Daniel's arm. I was hit at least seven times.† (Dolan 2007). Her complaint against Richard

Ford Focus and Ford Motor Company Essay Example for Free

Ford Focus and Ford Motor Company Essay When Alan Mulally took over as Chief Executive Officer at Ford Motor Company in 2006 the organization was losing billions of dollars. According to Tony Schwartz (2010), â€Å"It had just come off reporting a $14. 6 billion loss for 2008, its fourth losing year in a row† (para. 1). The article Alan Mulally-Making Ford a Model for the Future illustrates the progress of Alan Mulally and the four simple principles that are making the company become profitable. Principles are important in any organization and an employee needs to feel important and motivated to come to work. These are a few of the principles that Alan Mulally have implemented since 2006: Stand for something beyond profit. Rally your employees around a shared mission. Practice a realistic optimism. Tell the truth without fear (Schwartz, 2010). The turnaround at Ford Motor Company was not overnight. He invested in the vision â€Å"One Ford† which has the idea of creating vehicles that will appeal to both American and European consumers by utilizing a common design theme that would move beyond the three-bar infatuation of the United States (Lavrinc, 2007). The transformation of the American icon was due to the One Ford vision and one year after 2008, Ford Motor Company reported a profit of $2. 7 billion. This transformation would not have happened if Alan Mulally did not take over in 2006. The ethical behavior by Ford Motor Company’s Chief Executive Officer has shown to be a true testament to future CEO’s in the global market. When the company raised $23. 5 billion to finance the restructuring and accelerate the investment in new products it shows great leadership during the Great Recession (Bartiromo, 2011). This American icon is 110 years old and recently had the strongest third quarter profit in history in 2012. This would not have happened without Alan Mulally reducing the brands of Aston Martin, Jaguar, Mazda, Land Rover, and Volvo into the two main components that a person would vision on the road today Ford and Lincoln. The leadership is beyond extraordinary and models like the Ford Focus is now one of the country’s best selling cars (Schwartz, 2010). The business environment is multifaceted with enormous challenges that face the global market. By focusing attention on a vision, the leader operates on the emotional and spiritual resources of the organization, on its values, commitment, and aspirations. The manager, by contrast, operates on the physical resources of the organization, on its capital, human skills, raw materials, and technology. The results that an individual observes currently are in direct correlation of the actions over the last five years. Ford has now paid back the $23. 5 billion that was taken out in 2006 to finance the restructuring and investment of new products. The company has started to hire and bring jobs back to the United States. According to Schwartz (2010), â€Å"Mulally is taking an old-school industrial company and turning it into a model of how modern company ought to be run† (para. 3). Using the PESTEL Analysis to capture macro-environmental forces and including part of the Ansoff Product/Market Opportunity Matrix Ford Motor Company can thrive on market penetration strategies. The following PESTEL Analysis shows the six factors that are the biggest weaknesses and strengths perceived to be the primary data in the next five years for the automotive giant.

Premonitions :: essays research papers

Gracie lives in Washington State with her Aunt Shay and cousin Diego. Her father deserted her when she was a young girl, and her mother was killed a year and a half ago. She makes no effort to listen to her â€Å"best friend† Emily, and that’s one of the reasons Gracie feels bad when Emily disappears. Another reason is because Gracie has premonitions. They’ve been with her since before her mother died. She never knows if she is seeing the past, the present, or the future. But she did see Emily. Gracie did not know where or when the premonition took place, but she felt the fear in Emily’s body. No news of Emily’s disappearance goes on for days, but as the days go on, Gracie sees a premonition here and there. A waterfall here, a passing light there, but they make no sense. Gracie goes to a computer camp where Emily was supposed to register. She has a feeling that there is some sort of connection with the camp because another girl disappeared who was a member of it. She sees more premonitions, but all they do is confuse her even more than she already is. One premonition shows her that another girl is going to be kidnapped at a park. Gracie convinces her cousin to take her there. Dora, a girl from the camp, is the girl from her vision. She tells her she is psychic and she has to leave the park before she is kidnapped. Dora leaves, and the head of the camp, Jonah Castle, believes that Gracie is Dora. Gracie plays along and she is led to a boat. She knows that somewhere in her visions, there was a boat. She feels close, and she doesn’t pick up any bad reading from Jonah. When they get to the boat, she runs on to find out that she is being kidnapped. Gracie had not seen Dora in her vision. She has seen herself. Jonah soon comes and explains his way of taking underprivileged children and putting them together in a secluded home. It has every essential a child could want, but the children are taken from their normal lives. Insid e the house, she finds Emily, along with other children. Gracie soon realizes that there is no hope of escaping. And she’s the only one who cares. Gracie quickly becomes a favorite of Jonah.