assignment3

# assignment3 - ORIE 3300/5300 Individual work ASSIGNMENT 3...

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ORIE 3300/5300 ASSIGNMENT 3 Fall 2011 Individual work. Due: 11am, Tuesday September 20. 1. Next week’s recitation concerns the “Diet” linear programming model. In preparation, read pages 27–35 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. 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? Now try solving the new problem obtained by replacing the objective function x 1 + 2 x 2 + x 3 by x 1 + x 2 + x 3 . This time, at each iteration, 1

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assignment3 - ORIE 3300/5300 Individual work ASSIGNMENT 3...

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