Solve the following problems by the fractional cut, and compare the true optimum integer solution with the solution obtained by rounding the continuous optimum *(a) Maximize z = 4x, + 6x2 + 2x3subject to4x1 - 4x,< 5-X1 + 6x,-X1 + x2 + x3< 5X1, X2, X3 2 0 and integer(b) Маximize z3x1 + x2 + 3x3subject to-x, + 2x, + x3< 44x, - 3x, < 2X1 - 3x, + 2, < 3X1, X2, Xz 2 0 and integer

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*(a) Maximize z = 4x1 + 6x2 + 2x3 subject to 4x, - 4x2 -X, + 6x2 -X1 + x2 + x35 5 X1, X2, Xz 2 (0 and integer (b) Maximize z = 3x1 + x2 + 3x3 subject to -x1 + 2x, + xz< 4 4x2 - 3x3 < 2 x1 - 3x, + 2x3< 3 X1, X2, Xz 2 0 and integer

*(a) Maximize z = 4x1 + 6x2 + 2x3 subject to 4x, - 4x2 -X, + 6x2 -X1 + x2 + x35 5 X1, X2, Xz 2 (0 and integer (b) Maximize z = 3x1 + x2 + 3x3 subject to -x1 + 2x, + xz< 4 4x2 - 3x3 < 2 x1 - 3x, + 2x3< 3 X1, X2, Xz 2 0 and integer

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter7: Nonlinear Optimization Models

Section: Chapter Questions

Problem 49P: If a monopolist produces q units, she can charge 400 4q dollars per unit. The variable cost is 60...

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Optimization Models

Optimization models are mathematical models that help organizations determine the best way to allocate scarce resources to achieve specific objectives. These models can be used to solve a wide variety of problems, from finding the most efficient route for a delivery truck to determining the optimal mix of products to stock in a store.

Question

Solve the following problems by the fractional cut, and compare the true optimum integer solution with the solution obtained by rounding the continuous optimum

*(a) Maximize z = 4x, + 6x2 + 2x3
subject to
4x1 - 4x,
< 5
-X1 + 6x,
-X1 + x2 + x3< 5
X1, X2, X3 2 0 and integer
(b) Маximize z
3x1 + x2 + 3x3
subject to
-x, + 2x, + x3< 4
4x, - 3x, < 2
X1 - 3x, + 2, < 3
X1, X2, Xz 2 0 and integer

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