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ass3o - ORIE 3300/5300 Individual work ASSIGNMENT 3 Fall...

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ORIE 3300/5300 ASSIGNMENT 3 Fall 2010 Individual work. Due: 3 pm, Friday September 24. 1. Next week’s recitation concerns the “Diet” linear programming model. In preparation, read pages 27–36 in the AMPL book. 2. Below is a picture of the feasible region for the following linear program. maximize x 1 + 2 x 2 + x 3 subject to x 1 3 x 2 3 x 1 + x 2 4 - x 1 + x 3 1 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, choose one with largest reduced cost at each iteration; if there is a choice, pick among these the one with the smallest index. 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? CONTINUED ON NEXT PAGE 1

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3. The following is a tableau for a linear program in standard equality form.
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