# hw4-sol - Homework IV Deterministic Optimization ISYE 6669...

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Homework IV Deterministic Optimization ISYE 6669 Exercise 34 of Review Problems Since the initial basis is a 1 , s 2 and a 3 , B - 1 = 1 - 1 - 1 0 1 0 1 - 1 0 Also c B B - 1 = ± 0 20 10 ² 1 - 1 - 1 0 1 0 1 - 1 0 = ± 10 10 0 ² So the coeﬃcient of s 2 in row 0 = c BV B - 1 0 1 0 = ± 10 10 0 ² 0 1 0 = 10, the coeﬃcient of a 1 in row 0 = c BV B - 1 1 0 0 - ( - M ) = M + 10 and the coeﬃcient of a 3 in row 0 = c BV B - 1 0 0 1 - ( - M ) = M . The dual problem is min w = 150 y 1 +40 y 2 +20 y 3 s.t y 1 + y 2 20 y 1 + y 3 10 y 1 urs ,y 2 0 ,y 3 0 the optimal solution to the dual is w = 1900 ,y 1 = 10 ,y 2 = 10 ,y 3 = 0. 6.5.3 - Both Editions min w = 5 y 1 +7 y 2 +6 y 3 +4 y 4 s.t. y 1 +2 y 2 + y 4 4 y 1 + y 2 +2 y 3 = - 1 y 3 + y 4 = 2 y 1 0, y 2 0, y 3 0, y 4 u.r.s 6.5.4 - Both Editions 1

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max z = 6 x 1 +8 x 2 s.t. x 1 + x 2 4 2 x 1 - x 2 2 2 x 2 = - 1 x 1 0, x 2 u.r.s 6.5.5 - Both Editions (a) min w = 6 y 1 +5 y
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## This note was uploaded on 12/30/2011 for the course ISYE 6669 taught by Professor Staff during the Fall '08 term at Georgia Institute of Technology.

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hw4-sol - Homework IV Deterministic Optimization ISYE 6669...

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