Consider the following problem.

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

(a) Solve the problem graphically.

(b) Find the gradient of the objective function in the original x1-x2 coordinate system. If you move from the origin in the direction of the gradient until you reach the boundary of the feasible region, where does it lead relative to the optimal solution?

C

(c) Starting from the initial trial solution (x1, x2)  (1, 1), use your OR Courseware to perform 10 iterations of the interior-point algorithm presented in Sec. 7.4.

C

(d) Repeat part

(c) with  0.9.