*4-12. Consider the following LP:Maximize z = 5x1 + 2x2 + 3¤3subject toX1 + 5x2 + 2x3 = 30X1 – 5x2 – 6x3 < 40X1, X2, X3 > 0Given that the artificial variable x4 and the slack variable x5 form the starting basicvariables and that M was set equal to 100 when solving the problem, the optimal tableauis given as:BasicX1X2X3X4X5Solution237105150X1151300 -10-1 1X5-810Write the associated dual problem, and determine its optimal solution in two ways.

Answered: Image /qna-images/answer/56f242f5-954e-4346-bfaa-81397cad6be2.jpg

Answered: Maximize z = 5æ, + 2æ2 + 3æz x1 +5x2 +…

Business

Operations Management

Maximize z = 5æ, + 2æ2 + 3æz x1 +5x2 + 2xz = 30 x1 – 5x2 – 6x3 < 40 X1, X2, X3 > 0

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

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Concept explainers

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

*4-12. Consider the following LP:
Maximize z = 5x1 + 2x2 + 3¤3
subject to
X1 + 5x2 + 2x3 = 30
X1 – 5x2 – 6x3 < 40
X1, X2, X3 > 0
Given that the artificial variable x4 and the slack variable x5 form the starting basic
variables and that M was set equal to 100 when solving the problem, the optimal tableau
is given as:
Basic
X1
X2
X3
X4
X5
Solution
23
7
105
150
X1
1
5
1
30
0 -10
-1 1
X5
-8
10
Write the associated dual problem, and determine its optimal solution in two ways.

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