Consider the following linearly constrained optimization problem:

Maximize f(x) ln(1 x1 x2), subject to x1 2x2 5 and x1  0, x2  0, where ln denotes the natural logarithm.

(a) Verify that this problem is a convex programming problem.

(b) Use the KKT conditions to derive an optimal solution.

(c) Use intuitive reasoning to demonstrate that the solution obtained in part

(b) is indeed optimal. [Hint: Note that ln(1 x1 x2) is a monotonic strictly increasing function of 1 x1 x2.]