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Consider the following problem: Maximize 10x, + 24x2 + 20x3 + 20x4 + 25x5 St. X1 + x2 + 2x3+ 3x4 + 5x5 < 19 2x1 + 4x2 + 3x3 + 2x4 + x5 < 57 X1, X2, X3, X4, X5 20 (a) (b) From the graphical solution of the dual found in (a), (w, W2) = (4,5) is a feasible solution and could be the optimal dual solution. i) based on the complementary slackness conditions. ii) Write the dual problem. Use the information in Part (a) and (b) to derive a corresponding primal solution Verify whether the obtained primal and dual solutions are optimal to each problem.

Consider the following problem: Maximize 10x, + 24x2 + 20x3 + 20x4 + 25x5 St. X1 + x2 + 2x3+ 3x4 + 5x5 < 19 2x1 + 4x2 + 3x3 + 2x4 + x5 < 57 X1, X2, X3, X4, X5 20 (a) (b) From the graphical solution of the dual found in (a), (w, W2) = (4,5) is a feasible solution and could be the optimal dual solution. i) based on the complementary slackness conditions. ii) Write the dual problem. Use the information in Part (a) and (b) to derive a corresponding primal solution Verify whether the obtained primal and dual solutions are optimal to each problem.

Algebra for College Students
Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter12: Algebra Of Matrices
Section12.CR: Review Problem Set
Problem 37CR
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Consider the following problem: Maximize 10x, + 24x2 + 20x3 + 20x4 + 25x5 St. X1 + x2 + 2x3+ 3x4 + 5x5 < 19 2x1 + 4x2 + 3x3 + 2x4 + x5 < 57 X1, X2, X3, X4, X5 20 (a) (b) From the graphical solution of the dual found in (a), (w,, W2) = (4,5) is a feasible solution and could be the optimal dual solution. i) based on the complementary slackness conditions. ii) Write the dual problem. Use the information in Part (a) and (b) to derive a corresponding primal solution Verify whether the obtained primal and dual solutions are optimal to each problem.
Transcribed Image Text:Consider the following problem: Maximize 10x, + 24x2 + 20x3 + 20x4 + 25x5 St. X1 + x2 + 2x3+ 3x4 + 5x5 < 19 2x1 + 4x2 + 3x3 + 2x4 + x5 < 57 X1, X2, X3, X4, X5 20 (a) (b) From the graphical solution of the dual found in (a), (w,, W2) = (4,5) is a feasible solution and could be the optimal dual solution. i) based on the complementary slackness conditions. ii) Write the dual problem. Use the information in Part (a) and (b) to derive a corresponding primal solution Verify whether the obtained primal and dual solutions are optimal to each problem.
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