Explanation Given: The primal linear programming problem is, Maximize : 2 x 1 + 3 x 2 subject t o : 3 x 1 + 2 x 2 ≤ 1200 x 1 + 2 x 2 ≤ 800 x 1 + x 2 ≤ 450 and x 1 ≥ 0 , x 2 ≥ 0. And the final tableau in the simplex method for solving the primal problem is, [ x 1 x 2 x 3 x 4 x 5 M 0 0 1 1 − 4 0 200 0 1 0 1 − 1 0 350 1 0 0 − 1 2 0 100 0 0 0 1 1 1 1250 ] . Theorem used: Theorem 7: The Duality Theorem (Continued): Let P be a (primal) linear programming problem and let P * be its dual problem. Suppose P (or P * ) has an optimal solution. If either P or P * is solved by the simplex method, then the solution of its dual is displayed in the bottom row of the final tableau in the columns associates with the slack variables. Calculation: The primal linear programming problem is, Maximize : 2 x 1 + 3 x 2 subject t o : 3 x 1 + 2 x 2 ≤ 1200 x 1 + 2 x 2 ≤ 800 x 1 + x 2 ≤ 450 and x 1 ≥ 0 , x 2 ≥ 0. The final tableau in the simplex method for solving the primal problem is as follows, [ x 1 x 2 x 3 x 4 x 5 M 0 0 1 1 − 4 0 200 0 1 0 1 − 1 0 350 1 0 0 − 1 2 0 100 0 0 0 1 1 1 1250 ]

Linear Algebra and Its Applications (5th Edition)

5th Edition

ISBN: 9780321982384

Author: David C. Lay, Steven R. Lay, Judi J. McDonald

Publisher: PEARSON

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Chapter 9.4, Problem 3PP

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To find: The marginal values of fescue, rye, and bluegrass at the optimal solution.

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Chapter 9.4, Problem 2PP

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Chapter 9 Solutions

Linear Algebra and Its Applications (5th Edition)

Ch. 9.1 - Find the optimal strategies and the value of the...Ch. 9.1 - Player R has a supply of dimes and quarters....Ch. 9.1 - Prob. 2E Ch. 9.1 - In the traditional Japanese childrens game janken...Ch. 9.1 - Prob. 4E Ch. 9.1 - Prob. 5E Ch. 9.1 - Find all saddle points for the matrix games in...Ch. 9.1 - Find all saddle points for the matrix games in...Ch. 9.1 - Find all saddle points for the matrix games in...Ch. 9.1 - Prob. 9E

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The marginal values of fescue, rye, and bluegrass at the optimal solution.

Solution Summary: The author explains that the marginal values of fescue, rye and bluegrass at the optimal solution are 0,1,mathrmand1 respectively.

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To find: The marginal values of fescue, rye, and bluegrass at the optimal solution.

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Chapter 9 Solutions