13.6-5. Consider the following linearly constrained optimization problem: Maximize f(x) = ln(X1 1) - x2^2subject to X1 2x2 ≤ 3and X1 ≤ 20, x2 ≤ 20,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.