Consider the following linearly constrained convex programming problem:

Minimize Z x1 2  6x1 x2 3  3x2, subject to x1 x2 1 and x1  0, x2  0.

(a) Obtain the KKT conditions for this problem.

(b) Use the KKT conditions to check whether (x1, x2) (
1 2 , 1 2 ) is an optimal solution.

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