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Unformatted text preview: IEOR 162, Fall 2011 Suggested Solution to Homework 07 Problem 1 (Modified from Problem 6.1.4) (a) Let c 1 be the objective coefficient of x 1 such that the optimal basis remains the same, then 7 2  c 1 100  1 6 50 3 c 1 350 . (b) Let c 2 be the objective coefficient of x 2 such that the optimal basis remains the same, then 7 2  50 c 2  1 6 100 7 c 2 300 . (c) Let b 1 be the RHS of constraint 1 such that the optimal basis remains the same, then 7 0 + 2 2 b 1 7 12 + 2 4 b 1 84 . Within this range, the new optimal solution with b 1 = 28 + is obtained by solving 7 x 1 + 2 x 2 = 28 + 2 x 1 + 12 x 2 = 24 . The new optimal solution is ( x * 1 ,x * 2 ) = 72 + 3 20 , 56 40 . (d) Let b 2 be the RHS of constraint 2 such that the optimal basis remains the same, then 2 4 + 12 b 2 2 0 + 12 14 8 b 2 168 . Within this range, the new optimal solution with b 2 = 24 + is obtained by solving 7 x 1 + 2 x 2 = 28 2 x 1 + 12 x 2 = 24 + . The new optimal solution is ( x ** 1 ,x ** 2 ) = 144 40 , 336 + 21 240 . (e) Let f ( x 1 ,x 2 ) = 50 x 1 + 100 x 2 be the objective function. The shadow price of constraint 1 is f ( x * 1 ,x * 2 ) f (3 . 6 , 1 .....
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This note was uploaded on 11/05/2011 for the course IEOR 162 taught by Professor Zhang during the Fall '07 term at University of California, Berkeley.
 Fall '07
 Zhang

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