Consider the following problem.

Maximize Z  3x1  x2, subject to x1  x2 4 and x1 0, x2 0.

(a) Solve this problem graphically. Also identify all CPF solutions.

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(b) Starting from the initial trial solution (x1, x2)  (1, 1), perform four iterations of the interior-point algorithm presented in Sec. 7.4 manually. Then use the automatic routine in your OR Courseware to check your work.

(c) Draw figures corresponding to Figs. 7.4, 7.5, 7.6, 7.7, and 7.8 for this problem. In each case, identify the basic (or cornerpoint) feasible solutions in the current coordinate system. (Trial solutions can be used to determine projected gradients.)