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# assignp05 - Homework Set 5 15.053 Introduction to...

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15.053 Introduction to Optimization Officially due on Tuesday, March 19, 2002 but can be handed in Thursday, March 21, 2002 by 1:00pm and not be counted as late. (You can hand it in at class or give it to Veronica Mignott in E40-149. 1. BHM, Exercise 1 on page 192. (In class, the rules were given for finding the dual of a maximization problem. The book includes the rules for finding the dual of a minimization problem. Alternatively, for part 1a, you can find the maximization problem whose dual is the linear program given in part a. (This would use the fact that the dual of the dual is the primal.) 2. BHM, Exercise 3 on page 192. 3. Consider the following Payoff Matrix, which is similar to the one given in class, except that it has an additional column. The numbers represent payoffs to the row player R. -2 1 2 2 2 -1 0 -1 1 0 -2 -1 a. Formulate a linear program that will find an optimal mixed strategy for the row player R. b. Formulate a linear program that will find an optimal mixed strategy for the column player C. c. Verify that your linear program in part b is the dual of the linear program for part a. d. Modify the Excel spreadsheet used in class (and stored on the class web site under lecture notes) so that it can be used to find the optimal solution for the linear programs in part a and part b. Take the optimal mixed strategy for R, and then look at the payoffs for the column player. Note that the payoffs are not all the same. This is different from what happened in class. 4. (Graphical solution to game theory problems) . In the case that a 2-person 0-sum game has only two rows, the optimal randomized solution for the row player can be determined in a graphical manner. Similarly, if there are only two columns, then the optimal randomized solution for the column player can be determined using a graphical method. Consider for example, the problem based on the following payoff matrix. -1

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## This note was uploaded on 12/20/2011 for the course BUS 15.053 taught by Professor Prof.jamesorlin during the Spring '05 term at MIT.

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assignp05 - Homework Set 5 15.053 Introduction to...

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