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Unformatted text preview: Ad = 0, d ≥ 0. 1 P3 Consider the LP (from Homework 1, P2, problem c) ): max z =x 1 + 3 x 2 s.t. x 1x 2 ≤ 4 x 1 + 2 x 2 ≥ 4 x 1 , x 2 ≥ a) Reformulate the problem in standard form. b) Determine a direction of unboundedness for this problem. c) Express the vector x = x 1 x 2 s 1 e 1 with coordinates x 1 = 1 , x 2 = 4 in the representation of Theorem 2, i.e., determine a direction of unboundedness d ∈ R 4 and scalars σ i ≥ 0 and ∑ k i =1 σ i = 1, such that x can be written as x = d + k X i =1 σ i b i , where b 1 , . . . b k are the basic feasible solutions of the given LP. Hint: Choose one basic feasible solution b 1 and σ 1 = 1, σ i = 0 for i = 2 , . . . k . 2...
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This note was uploaded on 01/21/2011 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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