Z00_REND1011_11_SE_MOD7 PP2.QXD 2/21/11 12:39 PM Page 1 7 MODULE Linear Programming: The Simplex Method LEARNING OBJECTIVES After completing this chapter‚ students will be able to: 1. Convert LP constraints to equalities with slack‚ surplus‚ and artificial variables. 2. Set up and solve LP problems with simplex tableaus. 3. Interpret the meaning of every number in a simplex tableau. 4. Recognize special cases such as infeasibility‚ unboundedness and degeneracy. 5
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PROBLEM NUMBER 1 A farmer can plant up to 8 acres of land with wheat and barley. He can earn $5‚000 for every acre he plants with wheat and $3‚000 for every acre he plants with barley. His use of a necessary pesticide is limited by federal regulations to 10 gallons for his entire 8 acres. Wheat requires 2 gallons of pesticide for every acre planted and barley requires just 1 gallon per acre. What is the maximum profit he can make? SOLUTION TO PROBLEM NUMBER 1 let x = the number of acres of wheat
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Rousseau‚ The Social Contract (1762) "All men are born free‚ but elsewhere they are in chains" states his belief that society "chains" people John Locke "Life‚ liberty‚ and property" Machiavelli " A prince should have only one end and one idea in mind‚ take only one subject for study‚ and it is war‚ its science and discipline; for it is the only science that deals with the ruler’s problems. ...[Success in war] not only maintains those born to princedoms but often causes men of private origin
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Problem statement. There’s this game called linear nim where 2 players who have 10 marks and so they have to figure out a strategy. Then who ever crosses out the last mark wins. You can also play it with 15 marks. But you have to figure what to do while playing this game and try to find patterns or strategies to win. Process. So what I did to attempt the problem is that I played the game a few times with my partner with the 10 marks and 15. So we can find some patterns and strategies that we can
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Love‚ Life and Solitude Life might be long or quite short‚ full of happiness or pain‚ but there is no exact answer to the question that what can make it meaningful. Someone chose love because they believed that life must be shared with the one; someone thought that life itself was amazing enough; but others chose to stay alone because they enjoyed the freedom that solitude brought for them. Even if love will hurt us occasionally for a variety of
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KENYA METHODIST UNIVERSITY END OF 3RD TRIMESTER 2012 (EVENING) EXAMINATIONS FACULTY:SCIENCE AND TECHNOLOGY DEPARTMENT:PURE AND APPLIED SCIENCES UNIT CODE: MATH 110 UNIT TITLE:LINEAR ALGEBRA 1 TIME:2 hours Instructions: Answer question one and any other two questions. Question One (30 marks) Find the determinant of the following matrices. -4 8 (2 marks) 0 1 1 -3 -2 (3 marks) 2 -4 -3 -3 6 +8 Find the values of x and y if:(5 marks) x + 2y 14 = 4
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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
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(2003) 1 OPERATIONS RESEARCH: 343 1. LINEAR PROGRAMMING 2. INTEGER PROGRAMMING 3. GAMES Books: Ð3Ñ IntroÞ to OR ÐF.Hillier & J. LiebermanÑ; Ð33Ñ OR ÐH. TahaÑ; Ð333Ñ IntroÞ to Mathematical Prog ÐF.Hillier & J. LiebermanÑ; Ð3@Ñ IntroÞ to OR ÐJ.Eckert & M. KupferschmidÑÞ LP (2003) 2 LINEAR PROGRAMMING (LP) LP is an optimal decision making tool in which the objective is a linear function and the constraints on the decision problem are linear equalities and inequalities. It is a very popular
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QUANTITATIVE METHODS II Mid-Term Examination Monday‚ October22‚ 2012 Time : 150 minutes Total No. of Pages :17 Name ________________________ Total No. of Questions: 3 Roll No. ________________________ Total marks:35 Section: _______________________ Instructions 1. This is a Closed Book Exam. You are not allowed to carry anything other than stationary and calculator. 2. Answer all questions only in the space provided following the question. 3.
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Linear Programming Tools and Approximation Algorithms for Combinatorial Optimization by David Alexander Griffith Pritchard A thesis presented to the University of Waterloo in fulfillment of the thesis requirement for the degree of Doctor of Philosophy in Combinatorics and Optimization Waterloo‚ Ontario‚ Canada‚ 2009 c David Alexander Griffith Pritchard 2009 I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis‚ including any required final revisions
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