IOE310_PS09 (1) - IOE 310 - Problem Set 09 DUE: Monday,...

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IOE 310 - Problem Set 09 DUE: Monday, November 15, 2010 Problem 1 Given the following two math programs, min max { 2 x 1 3 x 2 , 7 x 1 +8 x 2 } s.t. x 1 3 . 5 x 2 8 9 x 1 + 15 x 2 100 x 1 ,x 2 0 This is not an LP. Formulate (only) an LP to ±nd the optimal solution. Problem 2 Section 6.5 Problem 2 (p.301) We are given the following LP: min w = y 1 y 2 s.t 2 y 1 + y 2 4 y 1 + y 2 1 y 1 +2 y 2 3 y 1 , y 2 0 Find the dual. Problem 3 Section 6.5 Problem 4 (p.301) We are given the following LP: min w =4 y 1 y 2 y 3 s.t y 1 y 2 6 y 1 y 2 y 3 =8 y 1 , y 2 0 y 3 urs Find the dual.
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IOE 310 – Problem Set 09 Page 2 of 2 Problem 4 Consider Problem 7 from PS08, the primal was: max 3x 1 + 4x 2 + 3x 3 + 7x 4 s.t. 2x 1 +x 2 + 4x 3 + 2x 4 54 3x 1 + 3x 2 3 4 37 x 1 x 2 x 3 x 4 0 You found the solution to the primal using the duality theorem (see solutions). Here is the dual. The dual solution is y 1 =3 . 4 and y 2 =0 . 2 and the optimal objective value = 191. Use complementary slackness to determine the primal solution, similar to the top of p.327 in the textbook. min 54y 1 + 37y 2 s.t. 2y 1 + 3y 2 3 y 1 + 3y 2 4 4y 1 +y 2 3 2y 1 2 7 y 1 ,y 2 0 Problem 5 Recall Problem 1 of PS06: Section 4.14 Problem 4 (p.189)
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This note was uploaded on 12/20/2010 for the course IOE 310 taught by Professor Saigal during the Fall '08 term at University of Michigan.

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IOE310_PS09 (1) - IOE 310 - Problem Set 09 DUE: Monday,...

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