# Question: Consider the following quadratic programming problem Maximize f x 20x1

Consider the following quadratic programming problem:

Maximize f(x) = 20x1 – 20x12 + 50x2 – 50x22 + 18x1x2,

subject to

x1 + x2 ≤ 6

x1 + 4x2 ≤ 18 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).

Maximize f(x) = 20x1 – 20x12 + 50x2 – 50x22 + 18x1x2,

subject to

x1 + x2 ≤ 6

x1 + 4x2 ≤ 18 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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