Consider the following problem.

Maximize Z 3x1  7x2  2x3, subject to

2x1  2x2  x3 10

3x1  x2  x3 20 and x1  0, x2  0, x3  0.

You are given the fact that the basic variables in the optimal solution are x1 and x3.

(a) Introduce slack variables, and then use the given information to find the optimal solution directly by Gaussian elimination.

(b) Extend the work in part

(a) to find the shadow prices.

(c) Use the given information to identify the defining equations of the optimal CPF solution, and then solve these equations to obtain the optimal solution.

(d) Construct the basis matrix B for the optimal BF solution, invert B manually, and then use this B1 to solve for the optimal solution and the shadow prices y*. Then apply the optimality test for the revised simplex method to verify that this solution is optimal.

(e) Given B1 and y* from part (d), use the fundamental insight presented in Sec. 5.3 to construct the complete final simplex tableau.