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IEOR162_hw05

# IEOR162_hw05 - IEOR 162 Fall 2011 Homework 05 1(Problem...

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Unformatted text preview: IEOR 162, Fall 2011 Homework 05 1. (Problem 4.5.2; 10 points) Use the simplex algorithm to solve the following LP z * = max 2 x 1 + 3 x 2 s.t. x 1 + 2 x 2 ≤ 6 2 x 1 + x 2 ≤ 8 x i ≥ ∀ i = 1 , 2 . Find an optimal solution x * = ( x * 1 ,x * 2 ) and the corresponding objective value z * . 2. (MODIFIED from Problem 4.6.1; 10 points) Use the simplex algorithm to solve the following LP z * = min 4 x 1 + x 2 s.t. 2 x 1- x 2 ≤ 8- x 2 ≤ 5 x 1 + x 2 ≤ 4 x 1 ≥ ,x 2 ≤ . Find an optimal solution x * = ( x * 1 ,x * 2 ) and the corresponding objective value z * . 3. (MODIFIED from Problem 4.7.5; 10 points) Use the simplex algorithm to solve the following LP z * = max 2 x 1 + 2 x 2 s.t. x 1 + x 2 ≤ 6 2 x 1 + x 2 ≤ 13 x i ≥ ∀ i = 1 , 2 . (a) (4 points) Find an optimal basic feasible solution x * = ( x * 1 ,x * 2 ) and the corresponding objective value z * . (b) (3 points) Write down all the optimal basic feasible solutions....
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IEOR162_hw05 - IEOR 162 Fall 2011 Homework 05 1(Problem...

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