a) Write the dual of the following linear programming problem: Maximize Ζ = 3x1 + 5x2 + 4x3, Subject to 2x1 + 3x2 ≤ 8, 2x2 + 5x3 ≤10 3x1 + 2x2 + 4x3 ≤15 x1 , x2 , x3 ≥ 0 (b) Find the optimal solution to the given problem in (a) above, using the simplex method. (c) From the final optimal table in (b) above, find the solution to the dual problem.
a) Write the dual of the following linear programming problem: Maximize Ζ = 3x1 + 5x2 + 4x3, Subject to 2x1 + 3x2 ≤ 8, 2x2 + 5x3 ≤10 3x1 + 2x2 + 4x3 ≤15 x1 , x2 , x3 ≥ 0 (b) Find the optimal solution to the given problem in (a) above, using the simplex method. (c) From the final optimal table in (b) above, find the solution to the dual problem.
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter11: Simulation Models
Section: Chapter Questions
Problem 68P
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(a) Write the dual of the following linear programming problem:
Maximize Ζ = 3x1 + 5x2 + 4x3,
Subject to 2x1 + 3x2 ≤ 8,
2x2 + 5x3 ≤10
3x1 + 2x2 + 4x3 ≤15
x1 , x2 , x3 ≥ 0
(b) Find the optimal solution to the given problem in (a) above, using the simplex method.
(c) From the final optimal table in (b) above, find the solution to the dual problem.
(d) Give the economic interpretation to the solution in (c) above.
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