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.

12.6-6.* Consider the nonlinear programming problem given in Prob.