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Unformatted text preview: Assignment 2 Due: Wednesday October 12 at the BEGINNING of class 1. Convert the following linear programs into standard equality form: (a) minimize x 1 6 x 2 + 4 x 3 subject to 8 x 2 + x 3 ≤ 5 x 1 8 x 2 ≥ x 2 ≥ Solution: maximize x + 1 + x 1 + 6 x 2 4 x + 3 + 4 x 3 subject to 8 x 2 + x + 3 x 3 + x 4 = 5 x + 1 x 1 8 x 2 x 5 = 0 x + 1 ,x 1 ,x 2 ,x + 3 ,x 3 ,x 4 ,x 5 ≥ (b) maximize 5 x 1 + 2 x 2 x 3 subject to 5 x 1 + 3 x 2 + x 3 = 2 x 1 + x 2 3 x 3 ≤ 7 2 x 1 + x 3 ≥ 2 x 1 ≥ Solution: maximize 5 x 1 + 2 x + 2 2 x 2 x + 3 + x 3 subject to 5 x 1 + 3 x + 2 3 x 2 + x + 3 x 3 = 2 x 1 + x + 2 x 2 3 x + 3 + 3 x 3 + x 4 = 7 2 x 1 + x + 3 x 3 x 5 = 2 x 1 ,x + 2 ,x 2 ,x + 3 ,x 3 ,x 4 ,x 5 ≥ 2. Write a linear program in standard equality form that satisfies the following: (a) A linear program with one variable that is unbounded. Solution: maximize x 1 subject to x 1 ≥ (b) A linear program with one variable that is infeasible. Solution: maximize x 1 subject to x 1 = 1 x 1 ≥ (c) A linear program with one variable that has an optimal solution....
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This note was uploaded on 01/26/2012 for the course ECON 401 taught by Professor Burbidge,john during the Fall '08 term at Waterloo.
 Fall '08
 Burbidge,John

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