Question: Consider the following quadratic programming problem: Maximize f(x) 250x1 25x1 2 100x2 100x2 2 90x1x2, subject to 20x1 5x2

Consider the following quadratic programming problem:

Maximize f(x) 250x1 25x1 2 100x2 100x2 2 90x1x2, subject to 20x1 5x2 90 10x1 10x2 60 and x1 0, x2 0.

Suppose that this problem is to be solved by the modified simplex method.

(a) 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.

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

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