Consider the following quadratic programming problem:

Maximize f(x) 8x1  x1 2 4x2  x2 2

, subject to x1 x2 2 and x1  0, x2  0.

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

(b) Now suppose that this problem is to be solved by the modified simplex method. Formulate the linear programming problem that is to be addressed explicitly, and then identify the additional complementarity constraint that is enforced automatically by the algorithm.

I

(c) Apply the modified simplex method to the problem as formulated in part (b).

C

(d) Use the computer to solve the quadratic programming problem directly.