Operations research An introduction to solution methods Ecole des Mines de Nantes Master MOST 2012-2013 Olivier Péton - 1- Problem Min f ( x ) xS An optimization problem S is the solution set that represents all feasible solutions of a problem. f is the objective function that maps S to R. It evaluates each feasible solution. Also called evaluation function or cost function Minimization = maximization ! max f ( x) min ( f ( x)) xS xS - 2- Mathematical
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Most people would agree that raising the minimum wage sounds like a good idea‚ but arguments arise concerning if this increase would benefit the economy. Jared Bernstein believes that a minimum wage increase would positively affect the American economy. He argues that the economy is driven by consumer spending and lowincome workers are very likely to spend their extra earned money. On the contrary‚ Douglas HoltzEakin strives to make the point that raising the minimum wage would not be beneficial to the economy
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American Composer Leonard Bernstein In this paper we will compare two compositions by composer‚ conductor‚ pianist‚ Leonard Bernstein (1918-1990). Bernstein was born in Massachusetts to a Russian Jewish family and began playing and taking music lessons at a young age. He went on to study music at Harvard and Curtis Institute of Music (Seldes Web). In his early years Bernstein wrote several compositions. At the age of 19 he wrote a “Piano Trio” (1937) (https://www.youtube.com/watch?v=cFQtbPqwNWo
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not fit the data adequately. In such a case better description of the time series can be attained by non-linear curve rather than straight line. The methods of measuring non-linear trends are: graphic method‚ moving average method‚ second degree polynomial equation method and so on. . ( S.P.Gupta‚ M.P.Gupta: 2003). Moreover‚ the trends discussed so far were plotted on arithmetic scales. Trends may also
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Chinese remainder theorem The Chinese remainder theorem is a result about congruences in number theory and its generalizations in abstract algebra. It was first published in the 3rd to 5th centuries by Chinese mathematician Sun Tzu. In its basic form‚ the Chinese remainder theorem will determine a number n that when divided by some given divisors leaves given remainders. For example‚ what is the lowest number n that when divided by 3 leaves a remainder of 2‚ when divided by 5 leaves a remainder
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THE FRONT The Front was written by Walter Bernstein‚ directed by Martin Ritt and starring Woody Allen and Zero Mostel‚ is a film about the blacklist during the age of live television. Because of the blacklist‚ a number of artists‚ writers‚ directors and others were rendered unemployable‚ having been accused of subversive political activities in support of Communism or of actually being Communists themselves. The filmmakers — screenwriter Bernstein‚ director Ritt‚ Zero Mostel‚ Herschel Bernardi
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Linda Bernstein’s article “Gaming the Console” addresses the possible effects that video gaming has on teenagers and children. The article supports both sides of the debate: whether or not video gaming has negative consequences. Ultimately‚ Bernstein lets the reader form his or her own opinion on the subject. Some scientists and experts claim that video gaming is harmful as it may negatively affect areas of the brain‚ academic and social skills‚ and can become highly addictive. Other experts argue
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Les Misérables and West Side Story tell more serious stories and have captivated audiences with revivals and film versions. Both are based on classic literature‚ and share universal and relatable social problems. West Side Story created by Lenard Bernstein‚ Steven Sondheim‚ Arthur Laurents‚ and Jerome Robbins tell the story of Romeo and Juliet in 1950s New York. Les Misérables by Composer Claude-Michael Schonberg and lyricist Alain Boublil is based on Victor Hugo’s novel of the same title. The atypical
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According to Matthew Bernstein‚ “Grubitz and Hempf embody the way in which East German officials [deploy] surveillance and repression to serve personal ends” (Bernstein 32). Wiesler first has the hunch they should keep an eye on Dreyman. Except when he tells Grubitz his idea‚ Grubitz laughs in his face. It is only when Hempf asks Grubitz if Dreyman
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In All the President’s Men‚ Bob Woodward and Carl Bernstein investigated and reported a story that they believed the American people should have the right to know. Throughout their investigation Woodward and Bernstein are constantly challenged by Ben Bradlee‚ The Post’s executive editor. Due to the impact it could have on the reputation of The Post‚ Bradlee was initially hesitant to
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