The computer solution is shown in Figure 3.17. a. What is the optimal solution, and what is the value of the objective function? b. Which constraints are binding? Which constraint shows extra capacity? How much? d. If the profit for the deluxe model were increased to $150 per unit, would the optimal solution change? Use the information in Figure 3.17 to answer this question. c.
The computer solution is shown in Figure 3.17. a. What is the optimal solution, and what is the value of the objective function? b. Which constraints are binding? Which constraint shows extra capacity? How much? d. If the profit for the deluxe model were increased to $150 per unit, would the optimal solution change? Use the information in Figure 3.17 to answer this question. c.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 28EQ
Related questions
Question
100%
![12. Quality Air Conditioning manufactures three home air conditioners: an economy model, a
standard model, and a deluxe model. The profits per unit are $63, $95, and $135, respec-
tively. The production requirements per unit are as follows:
Number of
Fans
Manufacturing
Time (hours)
Number of
Cooling Coils
Economy
Standard
Deluxe
1
8
1
2
1
12
1
4
14
For the coming production period, the company has 200 fan motors, 320 cooling coils,
and 2400 hours of manufacturing time available. How many economy models (E), stan-
dard 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:
Max 63E + 95S + 135D
s.t.
1E + 1S +
1D< 200
Fan motors
1E + 2S +
Cooling coils
Manufacturing time
4D < 320
8E + 12S + 14D < 2400
E, S, D 0](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd7451af8-c677-4bc1-8ff0-c69e4b49e989%2F97979551-239d-4aaf-bc6f-6af78be55650%2Fmwb3iwj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:12. Quality Air Conditioning manufactures three home air conditioners: an economy model, a
standard model, and a deluxe model. The profits per unit are $63, $95, and $135, respec-
tively. The production requirements per unit are as follows:
Number of
Fans
Manufacturing
Time (hours)
Number of
Cooling Coils
Economy
Standard
Deluxe
1
8
1
2
1
12
1
4
14
For the coming production period, the company has 200 fan motors, 320 cooling coils,
and 2400 hours of manufacturing time available. How many economy models (E), stan-
dard 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:
Max 63E + 95S + 135D
s.t.
1E + 1S +
1D< 200
Fan motors
1E + 2S +
Cooling coils
Manufacturing time
4D < 320
8E + 12S + 14D < 2400
E, S, D 0
![FIGURE 3.17 THE SOLUTION FOR THE QUALITY AIR CONDITIONING PROBLEM
Optimal Objective Value =
16440.00000
Variable
Value
Reduced Cost
E
80.00000
0.00000
120.00000
0.00000
0.00000
-24.00000
Constraint
Slack/Surplus
Dual Value
1
0.00000
31.00000
0.00000
32.00000
3
320.00000
0.00000
Objective
Allowable
Allowable
Variable
Coefficient
Increase
Decrease
E
63.00000
12.00000
15.50000
95.00000
31.00000
8.00000
135.00000
24.00000
Infinite
RHS
Allowable
Allowable
Constraint
Value
Increase
Decrease
1
200.00000
80.00000
40.00000
320.00000
80.00000
120.00000
3
2400.00000
Infinite
320.00000
The computer solution is shown in Figure 3.17.
a. What is the optimal solution, and what is the value of the objective function?
b. Which constraints are binding?
c. Which constraint shows extra capacity? How much?
d. If the profit for the deluxe model were increased to $150 per unit, would the optimal
solution change? Use the information in Figure 3.17 to answer this question.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd7451af8-c677-4bc1-8ff0-c69e4b49e989%2F97979551-239d-4aaf-bc6f-6af78be55650%2Fge4g2z_processed.jpeg&w=3840&q=75)
Transcribed Image Text:FIGURE 3.17 THE SOLUTION FOR THE QUALITY AIR CONDITIONING PROBLEM
Optimal Objective Value =
16440.00000
Variable
Value
Reduced Cost
E
80.00000
0.00000
120.00000
0.00000
0.00000
-24.00000
Constraint
Slack/Surplus
Dual Value
1
0.00000
31.00000
0.00000
32.00000
3
320.00000
0.00000
Objective
Allowable
Allowable
Variable
Coefficient
Increase
Decrease
E
63.00000
12.00000
15.50000
95.00000
31.00000
8.00000
135.00000
24.00000
Infinite
RHS
Allowable
Allowable
Constraint
Value
Increase
Decrease
1
200.00000
80.00000
40.00000
320.00000
80.00000
120.00000
3
2400.00000
Infinite
320.00000
The computer solution is shown in Figure 3.17.
a. What is the optimal solution, and what is the value of the objective function?
b. Which constraints are binding?
c. Which constraint shows extra capacity? How much?
d. If the profit for the deluxe model were increased to $150 per unit, would the optimal
solution change? Use the information in Figure 3.17 to answer this question.
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