quiz5solutions

# quiz5solutions - 640:354:01 Quiz#5 with solutions 1 Write...

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640:354:01, 04/02/2007 Quiz #5, with solutions 1. Write the dual of the following LP problem. Set up the initial simplex tableau and explain a step of the dual simplex method. Deter- mine which variable is leaving and which one is entering (justify). Do not compute the next tableau. Maximize z = - 3 x 1 - 2 x 2 - 5 x 3 subject to 2 x 1 - x 2 - 3 x 3 - 6 x 1 + x 2 - 4 x 3 10 x 1 , x 2 , x 3 0 Solution: The initial tableau is x 1 x 2 x 3 x 4 x 5 x 4 2 -1 -3 1 0 -6 x 5 1 1 -4 0 1 10 z 3 2 5 0 0 0 x 4 is the leaving variable, simply because it is the only one with negative value. The entering variable is the one where the largest ratio of the corresponding element of the objec- tive row and of the simplex tableau in the pivotal row is achieved (only for negative entries of the tableau). There are two ratios here: 2 - 1 for x 2 , and 5 - 3 for x 3 . The one for x 3 is bigger, so x 3 is the entering variable. 2. Consider the following primal-dual pair of linear programming problems.

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