Minimize Z = 2x1 - 2x2 + 3x3, subject to - x1 + x2 + x3  ≤ 4 (resource 1) 2x1 - x2 + x3  ≤ 2 (resource 2) x1 + x2 + 3x3  ≤ 12 (resource 3) x1 , x2 , x3 are non-negative (a) Work through the simplex method step by step to solve the problem. (b) Identify the shadow prices for the three resources and describe their significance

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter6: Optimization Models With Integer Variables
Section: Chapter Questions
Problem 53P
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Minimize Z = 2x1 - 2x2 + 3x3,

subject to - x1 + x2 + x3  ≤ 4 (resource 1)

2x1 - x2 + x3  ≤ 2 (resource 2)

x1 + x2 + 3x3  ≤ 12 (resource 3)

x1 , x2 , x3 are non-negative

(a) Work through the simplex method step by step to solve the problem.

(b) Identify the shadow prices for the three resources and describe their significance

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ISBN:
9781337406659
Author:
WINSTON, Wayne L.
Publisher:
Cengage,