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Consider the following convex programming problem Maximize Z 32x1

Consider the following convex programming problem:

Maximize Z = 32x1 – x41 + 4x2 – x22,

Subject to

x21 + x22 ≤ 9 and

x1 ≥ 0, x2 ≥ 0.

(a) Apply the separable programming technique discussed at the end of Sec. 13.8, with x1 = 0, 1, 2, 3 and x2 = 0, 1, 2, 3 as the breakpoint of the piecewise linear functions, to formulate an approximate linear programming model for this problem.

Maximize Z = 32x1 – x41 + 4x2 – x22,

Subject to

x21 + x22 ≤ 9 and

x1 ≥ 0, x2 ≥ 0.

(a) Apply the separable programming technique discussed at the end of Sec. 13.8, with x1 = 0, 1, 2, 3 and x2 = 0, 1, 2, 3 as the breakpoint of the piecewise linear functions, to formulate an approximate linear programming model for this problem.

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