Economy Standard Deluxe Number of Fans Number of Cooling Colls Manufacturing Time (hours) 8 12 14
Economy Standard Deluxe Number of Fans Number of Cooling Colls Manufacturing Time (hours) 8 12 14
Cornerstones of Cost Management (Cornerstones Series)
4th Edition
ISBN:9781305970663
Author:Don R. Hansen, Maryanne M. Mowen
Publisher:Don R. Hansen, Maryanne M. Mowen
Chapter16: Cost-volume-profit Analysis
Section: Chapter Questions
Problem 2CE
Related questions
Question
![(a) What is the optimal solution, and what is the value of the objective function?
E
140
x
S
110
X
D
0
✓.
x
profit
$19430
(b) which constraints are binding? (Select all that apply.)
fan motors
cooling coils
manufacturing time
(c) Which constraint shows extra capacity?
Ofan motors
O cooling coils
O manufacturing time
How much extra capacity (in hr) is available?
160
xhr
(d) If the profit for the deluxe model were increased to $145 per unit, would the optimal solution change? Use the information in the output to answer this question,
The optimal solution would not
✓change because the new profit is within
the range of optimality](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcf7428e1-3114-4898-86bf-7061418e8923%2Ff53c4e43-7f48-4c89-b914-dd29ec8f0151%2F0ph1nca_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(a) What is the optimal solution, and what is the value of the objective function?
E
140
x
S
110
X
D
0
✓.
x
profit
$19430
(b) which constraints are binding? (Select all that apply.)
fan motors
cooling coils
manufacturing time
(c) Which constraint shows extra capacity?
Ofan motors
O cooling coils
O manufacturing time
How much extra capacity (in hr) is available?
160
xhr
(d) If the profit for the deluxe model were increased to $145 per unit, would the optimal solution change? Use the information in the output to answer this question,
The optimal solution would not
✓change because the new profit is within
the range of optimality
![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, respectively. The
production requirements per unit are as follows:
Number of
Number of
Fans
Manufacturing
Time (hours)
Cooling Colls
Economy
A
1
8
Standard
1
2
12
Deluxe
1
4
14
For the coming production period, the company has 260 fan motors, 340 cooling colls, and 2,600 hours of manufacturing time available. How many economy models (6), 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:
Max 63E+ 955 +
1350
s.t.
Fan motors
18+ 15 +
LE+ 25 +
85+ 125+
10 260
40 s 340
140 s 2,600
Cooling coils
Manufacturing time
The sensitivity report is shown below.
Variable Cells
Final Value Reduced Cost Objective Coefficient Allowable Increase Allowable Decrease
0.000
63.000
12.000
15.500
180.000
80.000
0.000
95.000
31.000
8.000
0.000
24.000
135.000
24.000
1E+30
Final Value Shadow Price Constraint R.H. Side Allowable Increase
Allowable Decrease
260.000
31.000
260.000
50.000
90.000
32.000
340.000
50.000
80.000
340.000
2,400.000
0.000
2,600,000
18+30
200.000
E,S, DO
Name
Economy Models
Standard Models
Deluxe Models
Model Variable
E
S
D
Constraints
Constraint Number
1
2
3
Name
Fan Motors
Cooling Colls
Manufacturing Time](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcf7428e1-3114-4898-86bf-7061418e8923%2Ff53c4e43-7f48-4c89-b914-dd29ec8f0151%2Fvjezvoa_processed.jpeg&w=3840&q=75)
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 $63, $95, and $135, respectively. The
production requirements per unit are as follows:
Number of
Number of
Fans
Manufacturing
Time (hours)
Cooling Colls
Economy
A
1
8
Standard
1
2
12
Deluxe
1
4
14
For the coming production period, the company has 260 fan motors, 340 cooling colls, and 2,600 hours of manufacturing time available. How many economy models (6), 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:
Max 63E+ 955 +
1350
s.t.
Fan motors
18+ 15 +
LE+ 25 +
85+ 125+
10 260
40 s 340
140 s 2,600
Cooling coils
Manufacturing time
The sensitivity report is shown below.
Variable Cells
Final Value Reduced Cost Objective Coefficient Allowable Increase Allowable Decrease
0.000
63.000
12.000
15.500
180.000
80.000
0.000
95.000
31.000
8.000
0.000
24.000
135.000
24.000
1E+30
Final Value Shadow Price Constraint R.H. Side Allowable Increase
Allowable Decrease
260.000
31.000
260.000
50.000
90.000
32.000
340.000
50.000
80.000
340.000
2,400.000
0.000
2,600,000
18+30
200.000
E,S, DO
Name
Economy Models
Standard Models
Deluxe Models
Model Variable
E
S
D
Constraints
Constraint Number
1
2
3
Name
Fan Motors
Cooling Colls
Manufacturing Time
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