co227_a2_soln

co227_a2_soln - Assignment 2 Due: Wednesday October 12 at...

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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.

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co227_a2_soln - Assignment 2 Due: Wednesday October 12 at...

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