Consider the following problem.

Maximize Z  2x1  5x2  7x3, subject to x1  2x2  3x3  6 and x1 0, x2 0, x3 0.

(a) Graph the feasible region.

(b) Find the gradient of the objective function, and then find the projected gradient onto the feasible region.

(c) Starting from the initial trial solution (x1, x2, x3)  (1, 1, 1), perform two iterations of the interior-point algorithm presented in Sec. 7.4 manually C

(d) Starting from this same initial trial solution, use your OR Courseware to perform 10 iterations of this algorithm.

C