ORIE 3300/5300 ASSIGNMENT 8 Fall 2010 *NOT TO BE TURNED IN** Solutions will be posted 5 pm, Saturday November 6. 1. Consider the linear programming problem max 2 x 1 + 3 x 2 + 2 x 3 3 x 1 + 2 x 2 + x 3 ≤ 7 2 x 1 + x 2 + x 3 ≤ 4 x 1 , x 2 , x 3 ≥0 . Add slack variables and solve this problem by the revised simplex method, starting with the all-slack basis. Use the most positive re-duced cost rule to choose the entering index. 2. This question is concerned with the linear programming problem in Q2 of Assignment 7. (a) Write out the dual of this problem. (b) Use your answer for Q2 last week to ﬁnd the optimal solution of the dual problem you found in (a). (c) Give a short certiﬁcate that the solution you found in (b) is indeed the optimal solution of the dual problem.
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