Practical Management Science
6th Edition
ISBN: 9781337406659
Author: WINSTON, Wayne L.
Publisher: Cengage,
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Question
Transcribed Image Text:c. Which constraint shows extra capacity? How much? constraint shows no extra capacity, enter 0 as number of
units. If required, round your answers to the nearest whole number.
Constraints
Fan motors
Cooling coils
Manufacturing time
The optimal solution
solution changing.
d. If the profit for the deluxe model were increased to $152 per unit, would the optimal solution change?
change because the profit of the deluxe model can vary from
$152 is
this range without the optimal
The optimal solution
Extra capacity
$0
$12
$125
$137
$149
Yes
†No
d. If the profit for the deluxe model were increased to $152 per unit, would the optimal sc
change because the profit of the deluxe mo
$152 is
this rang
solution changing.
would
would not
to
d. If the profit for the deluxe model were increased to $152 per unit, would the optimal sol
The optimal solution
change because the profit of the deluxe mod
$152 is
this range
solution changing.
Number of units
to
$12
$125
$137
$149
linfinitv
d. If the profit for the deluxe model were increased to $152 per unit, would the optimal solution change?
The optimal solution
change because the profit of the deluxe model can vary from
$152 is (
this range without the optimal
to
in
not in
Transcribed Image Text:Quality Air Conditioning manufactures three home air conditioners: an economy model, a standard model, and a
deluxe model. The profits per unit are $59, $89, and $137, respectively. The production requirements per unit are as
follows:
Economy
Standard
Deluxe
Max
s.t.
Number of
Fans
1
1
1
59E+ 895 + 137D
1E +
1E +
For the coming production period, the company has 250 fan motors, 380 cooling coils, and 2600 hours of
manufacturing time available. How many economy models (E), standard models (S), and deluxe models (D) should
the company produce in order to maximize profit? The linear programming model for the problem is as follows:
15 +
25 +
Optimal Objective Value =
Variable
E
S
D
250 Fan motors
380 Cooling coils
8E + 125 + 14D ≤ 2600 Manufacturing time
E, S, D 20
Constrainal
1
2
3
The computer solution is shown in the figure below.
Variable
D
Constraint
1D S
4D S
Fan motors:
Cooling coils:
Manufacturing time:
Number of
Cooling Coils
b. Which constraints are binding?
1
2
4
Economy models (E)
Standard models (S)
Deluxe models (D)
Value of the objective function $
Binding
Non binding
18650.00000
Manufacturing
Time (hours)
Slack/Surplus
Objective
Coefficient
RIIS
Value
Value
120.00000
130.00000
0.00000
59.00000
89.00000
137.00000
Optimal Solution
8
12
14
0.00000
0.00000
80.00000
250.00000
380.00000
2600.00000
Allowable
Increase
6.00000
29.00000
12.00000
Allowable
Increase
20.00000
20.00000
Infinite
Reduced Cost
0.00000
0.00000
12.00000
Dual Value
29.00000
30.00000
0.00000
a. What is the optimal solution, and what is the value of the objective function? If required, round your answers to
the nearest whole number. If your answer is zero, enter "0".
Allowable
Decrease
14.50000
4.00000
Infinite
Allowable
Decrease
60.00000
130.00000
80.00000
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