Consider the following nonconvex programming problem:

Maximize f(x) 3x1x2  2x1 2  x2 2

, subject to x1 2 2x2 2 4 2x1  x2 3 x1x2 2 x1 2

x2 2 and x1  0, x2  0.

(a) If SUMT were to be applied to this problem, what would be the unconstrained function P(x; r) to be maximized at each iteration?

D,C

(b) Starting from the initial trial solution (x1, x2) (1, 1), use the automatic routine in your OR Courseware to apply SUMT to this problem with r 1, 102

, 104

.