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# rec4 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY 15.053...

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M ASSACHUSETTS I NSTITUTE OF T ECHNOLOGY 15.053 – Optimization Methods in Management Science (Spring 2007) Recitation 4, March 1 st and March 2 nd , 2007 Problem 1: More Simplex Tableau Suppose while solving a maximization problem we obtain the following tableau, with the basic variables highlighted in blue: z x 1 x 2 x 3 x 4 x 5 rhs 1 a c 0 3 0 10 0 0 d 0 4 1 5 0 1 -5 0 -1 0 b 0 0 e 1 2 0 3 Give conditions on the missing values a, b, c, d, e and required to make the each of the following statements true: Part A: What is the current solution? Part B: The current tableau represents a basic feasible solution in canonical form. Part C: The current tableau is optimal and multiple optimal solutions exist. Part D: The current basic solution is a degenerate basic feasible solution. Part E: The current basic solution is feasible, but the objective function value can be improved by bringing x 2 into the basis and pivoting x 3 out.

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Part F: There exists an extreme ray of optimal solutions Part G: The current solution is both optimal and degenerate and there exists an extreme ray of optimal solutions Part H: Suppose a=0, d=e=2, and c=-2 perform a pivot in terms of the variables. Problem 2: March Madness The NCAA is making plans for distributing tickets to the upcoming regional basketball championships. Up to 10,000 available seats will be divided between the media, the competing universities, and the general public, subject to the following conditions: o Media people are admitted free, and at least 1000 tickets must be reserved for the media. o
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rec4 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY 15.053...

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