11. The computer output below is a product mix problem of a manufacturing company. Use the output to answer the following questions. Assume that the company wishes to maximize the profit. Variable Value Reduced Cost 0 20 X3 0 Constraint Dual Value Slack/Surplus X₁ X₂ Resource A Resource B Resource C 40 0 10 20 10 0 0 0 30 Original Lower Bound Upper Bound Value 50 20 30 Original Value 90 50 80 30 - Infinity 25 60 40 50 Lower Bound Upper Bound 50 45 50 100 80 Infinity a) What is the optimal solution and the total profit for this problem? b) Determine the marginal value of an additional pound of Resource A. Over what range is this value valid?

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter7: Nonlinear Optimization Models
Section7.3: Pricing Models
Problem 2P
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11.
The computer output below is a product mix problem of
a manufacturing company. Use
the output to answer the following questions. Assume that
the company wishes to
maximize the profit.
Variable Value Reduced Cost
X₁
0
X₂
20
X3
0
Constraint Dual Value Slack/Surplus
Resource A
Resource B
Resource C
40
0
10
20
10
0
0
0
30
Original Lower Bound Upper Bound
Value
50
20
30
Original
Value
90
50
80
30
Infinity
25
60
40
50
Lower Bound Upper Bound
50
45
50
100
80
Infinity
a) What is the optimal solution and the total profit for this
problem?
b) Determine the marginal value of an additional pound of
Resource A. Over what range is this value valid?
Transcribed Image Text:11. The computer output below is a product mix problem of a manufacturing company. Use the output to answer the following questions. Assume that the company wishes to maximize the profit. Variable Value Reduced Cost X₁ 0 X₂ 20 X3 0 Constraint Dual Value Slack/Surplus Resource A Resource B Resource C 40 0 10 20 10 0 0 0 30 Original Lower Bound Upper Bound Value 50 20 30 Original Value 90 50 80 30 Infinity 25 60 40 50 Lower Bound Upper Bound 50 45 50 100 80 Infinity a) What is the optimal solution and the total profit for this problem? b) Determine the marginal value of an additional pound of Resource A. Over what range is this value valid?
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