# Question

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).

## Answer to relevant Questions

Consider the following quadratic programming problem: Maximize f (x) = 2x1 + 3x2 – x12 – x22, subject to x1 + x2 ≤ 2 and x1 ≥ 0, x2 ≥ 0. The Dorwyn Company has two new products that will compete with the two new products for the Wyndor Glass Co. (described in Sec. 3.1). Using units of hundreds of dollars for the objective function, the linear programming ...Consider the following nonlinear programming problem: Maximize Z = 5x1 + x2, subject to 2x12 + x2 ≤ 13 x12 + x2 ≤ 9 and x1 ≥ 0, x2 ≥ 0. (a) Show that this problem is a convex programming problem. (b) Use the ...Reconsider the quadratic programming model given in Prob. 13.7-4. Consider the following function: Show that f (x) is convex by expressing it as a sum of functions of one or two variables and then showing (see Appendix 2) that all these functions are convex.Post your question

0