Consider the following quadratic programming problem.

Maximize f(x) 2x1 3x2  x1 2  x2 2

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

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

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

(c) Without applying the modified simplex method, show that the solution derived in part

(a) is indeed optimal (Z 0) for the equivalent problem formulated in part (b).
I

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

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