Operations research

Solve a, b, d

e 12.7-4. Consider the following quadratic programming problem. Maximize f(x) = 2x, + 3x2 - x - x, subject to x1 + x2 = 2 and n e D x = 0, X2 2 0. (a) Use the KKT conditions to derive an optimal solution directly (b) Now suppose that this problem is to be solved by the modi- fied simplex method. Formulate the linear programming prob- lem that is to be addressed explicitly, and then identify the ad- ditional complementarity constraint that is enforced automatically by the algorithm. (e) 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). 1 (d) Apply the modified simplex method to the problem as for- mulated in part (b). mode