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Unformatted text preview: IEOR 162, Spring 2012 Homework 06 1. (Modified from Problem 4.7.3; 10 points) Consider the following LP z * = max x 1 + x 2 s.t. x 1 + x 2 + x 3 ≤ 1 x 1 + 2 x 3 ≤ 1 x i ≥ ∀ i = 1 , ..., 3 . Use the simplex method to determine whether the LP is infeasible, unbounded, having a unique optimal solution, or having multiple optimal solutions. In the latter two cases, find the optimal solution if there is only one or find two if there are multiple. Note. The suggested way of checking whether there are multiple optimal solutions is to investigate the final tableau. You should not start from the initial tableau twice and try different entering variables. 2. (MODIFIED from Problem 4.8.1; 10 points) Consider the following LP z * = max 2 x 2 s.t. x 1 x 2 ≤ 4 x 1 + x 2 ≤ 1 x i ≥ ∀ i = 1 , 2 . Use the simplex method to determine whether the LP is infeasible, unbounded, having a unique optimal solution, or having multiple optimal solutions. In the latter two cases, find the optimal solution if theresolution, or having multiple optimal solutions....
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 Spring '07
 Zhang
 Linear Programming, Optimization, Simplex algorithm, Multiple Optimal Solutions

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