Consider the following convex programming problem:

Maximize Z 32x1  x1 4 4x2  x2 2

, subject to x1 2 x2 2 9 and x1  0, x2  0.

(a) Apply the separable programming technique discussed at the end of Sec. 13.8, with x1 0, 1, 2, 3 and x2 0, 1, 2, 3 as the breakpoint of the piecewise linear functions, to formulate an approximate linear programming model for this problem.

C

(b) Use the computer to solve the model formulated in part (a).

Then reexpress this solution in terms of the original variables of the problem.

(c) Use the KKT conditions to determine whether the solution for the original variables obtained in part

(b) actually is optimal for the original problem (not the approximate model).