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assn4 - ORIE 3300/5300 Individual work ASSIGNMENT 4 Fall...

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ORIE 3300/5300 ASSIGNMENT 4 Fall 2010 Individual work. Due: 3 p.m., Friday October 1. 1. Part of next week’s recitation, and the next question, are concerned with the blend.mod model (in the MODELS folder). In preparation, read pages 37–38 in the AMPL book. 2. Do question 2-3 in the AMPL book. You should submit a paper copy *and* submit your AMPL model and data files online at this page. 3. Consider the following linear programming tableau: z - 3 x 2 + 2 x 4 - x 7 = 7 x 2 + x 3 - 3 x 4 + x 5 + 2 x 7 = 2 x 1 - x 2 + x 4 - 2 x 5 + 5 x 7 = 4 3 x 2 - 2 x 4 + x 5 + x 6 - x 7 = 6 . (a) List all possible pairs ( r, k ) such that k could be the entering index and r the leaving index for an iteration of the simplex method starting from this tableau. (b) For each of the following possibilities for ( r, k ), indicate whether a pivot making x k basic and x r nonbasic will give a basic infeasible solution or a basic feasible solution; a degenerate solution or a nondegenerate solution; and an increase in the objective value, no change in the objective value, or a decrease in the objective value.
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