# [Excel spreadsheet available at http://web.mit.edu/15.053/www/Exer3.18.xls] Consider the…

[Excel spreadsheet available at http://web.mit.edu/15.053/www/Exer3.18.xls] Consider the parametric programming problem:

Letting x3, x4, and x5 be slack variables for the constraints, we write the optimal canonical form at θ = 0 as

a) Place the objective function in this tableau in canonical form for values of θ other than 0. For what values of θ is this canonical form optimal?

b) What are the variable transitions when this canonical form is no longer optimal? Does the problem become unbounded at either of the transition points?

c) Use the parametric programming algorithm to find the optimal solution for all values of θ. Plot the optimal objective value as a function of θ.

d) Graph the feasible region and interpret the parametric algorithm on the graph.

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