Consider the following problem.

Maximize Z  x1  2x2, subject to x1  x2  8 and x1 0, x2 0.

C

(a) Near the end of Sec. 7.4, there is a discussion of what the interior-point algorithm does on this problem when starting from the initial feasible trial solution (x1, x2)  (4, 4). Verify the results presented there by performing two iterations manually. Then use the automatic routine in your OR Courseware to check your work.

(b) Use these results to predict what subsequent trial solutions would be if additional iterations were to be performed.

(c) Suppose that the stopping rule adopted for the algorithm in this application is that the algorithm stops when two successive trial solutions differ by no more than 0.01 in any component.
Use your predictions from part

(b) to predict the final trial solution and the total number of iterations required to get there.
How close would this solution be to the optimal solution (x1, x2)  (0, 8)?