assignment3_ProblemSet - ORIE 3300/5300 Individual work....

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ORIE 3300/5300 ASSIGNMENT 3 Fall 2008 Individual work. Due: 3 p.m., Friday September 26. 1. Part of next week’s recitation concerns the “Diet” linear programming model. In preparation, read pages 27–36 in the AMPL book. Also review pages 16–18. 2. Below is a picture of the feasible region for the following linear pro- gram. maximize 2 x 1 + 3 x 2 + x 3 subject to x 1 2 x 2 2 - x 1 + x 3 2 x 1 + x 2 3 x 1 , x 2 , x 3 0 . Solve the linear program using the simplex method. First introduce slack variables, and use them as the basic variables in an initial feasible tableau. Among the possible entering variables, always choose the one with the smallest index at each iteration. Plot the path taken by the simplex method on the picture. Does your final tableau imply that the optimal solution is unique? If not, can you find another optimal solution? 1
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3. The following is a tableau for a linear program in standard equality form. z
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assignment3_ProblemSet - ORIE 3300/5300 Individual work....

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