Consider the following linearly constrained convex programming problem:

Maximize f(x) 8x1  x1 2 2x2 x3, subject to x1 3x2 2x3 12 and x1  0, x2  0, x3  0.

(a) Use the KKT conditions to demonstrate that (x1, x2, x3)

(2, 2, 2) is not an optimal solution.

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

Do some preliminary intuitive analysis to determine the most promising case regarding which variables are nonzero and which are zero.)