# HW9 - 9th Homework for IEOR162 Linear Programming Semester...

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9th Homework for IEOR162 Linear Programming Semester: Fall 2010 Instructor: Dr. Sarah Drewes Due to: Thursday, December 2, 2010, (at the beginning of class) P1 For the following LP, max z = - x 1 + 5 x 2 s.t. x 1 + 2 x 2 0 . 5 - x 1 + 3 x 2 0 . 5 x 1 , x 2 0 , row 0 of the optimal simplex tableau is z + 0 . 4 s 1 + 1 . 4 s 2 =? Determine the optimal z -value for the given LP. P2 Consider max z = 4 x 1 + x 2 s.t. 3 x 1 + 2 x 2 6 6 x 1 + 3 x 2 10 x 1 , x 2 0 . Suppose that row 0 of the optimal simplex tableau is found to be z + 2 x 2 + s 2 = 20 3 . Use the Dual Theorem to prove that the computations must be incorrect. P3 Given the primal LP: min x 1 - x 3 s.t. x 1 + 2 x 2 5 x 2 + 2 x 3 = 6 x 1 , x 2 , x 3 0 . Determine the dual of this problem and formulate the complementary slackness conditions for this program. Use them to solve the primal and dual problem. 1

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P4 Submit your handwritten answers, AMPL code, commands and output for this problem Recall the Dorian Auto problem in Chapter 3.2 of the textbook: Dorian Auto plans to put on commercial advertisements. Each comedy commercial is seen
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