Consider the following linearly constrained optimization problem:

Maximize f(x) ln(x1 1)  x2 2

, subject to x1 2x2 3 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.