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: Economy Standard Deluxe Number of Fans 1 1 1 Number of Cooling Coils 1 2 4 Manufacturing Time (hours) 8 12 14 For the coming production period, the company has 240 fan motors, 340 cooling coils, and 2,600 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: Max 63E+ 95S + 135D

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 33P: Assume the demand for a companys drug Wozac during the current year is 50,000, and assume demand...
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E
S
D
Variable
E
HSD
E
S
D
profit
~ 3
Constraint
1
NH
2
3
Objective Allowable
Coefficient
Increase
12.00000
31.00000
24.00000
to
0.00000
280.00000
to
to
63.00000
95.00000
135.00000
(a) Identify the range of optimality for each objective function coefficient. (If there is no upper or lower limit, enter NO LIMIT.)
RHS
Value
240.00000
340.00000
2600.00000
32.00000
0.00000
Allowable
Increase
70.00000
70.00000
Infinite
units
units
units
Allowable
Decrease
15.50000
8.00000
Infinite
Allowable
Decrease
70.00000
100.00000
280.00000
(b) Suppose the profit for the economy model is increased by $6 per unit, the profit for the standard model is decreased by $2 per unit, and the profit for the deluxe
model is increased by $4 per unit. What will the new optimal solution be?
Transcribed Image Text:E S D Variable E HSD E S D profit ~ 3 Constraint 1 NH 2 3 Objective Allowable Coefficient Increase 12.00000 31.00000 24.00000 to 0.00000 280.00000 to to 63.00000 95.00000 135.00000 (a) Identify the range of optimality for each objective function coefficient. (If there is no upper or lower limit, enter NO LIMIT.) RHS Value 240.00000 340.00000 2600.00000 32.00000 0.00000 Allowable Increase 70.00000 70.00000 Infinite units units units Allowable Decrease 15.50000 8.00000 Infinite Allowable Decrease 70.00000 100.00000 280.00000 (b) Suppose the profit for the economy model is increased by $6 per unit, the profit for the standard model is decreased by $2 per unit, and the profit for the deluxe model is increased by $4 per unit. What will the new optimal solution be?
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:
Economy
Standard
Deluxe
Max
s.t.
Number of
Fans
1
1
1
63E+ 95S +
Variable
E
S
D
1E + 1S +
1E + 2S +
8E+12S +
Constraint
1
2
The computer solution is shown below.
Number of
Cooling Coils
135D
For the coming production period, the company has 240 fan motors, 340 cooling coils, and 2,600 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:
Value
140.00000
100.00000
0.00000
1
1D ≤ 240
4D ≤ 340
14D ≤ 2,600
E, S, D≥ 0
2
Optimal Objective Value = 18320.00000
4
Slack/Surplus
0.00000
0.00000
Reduced Cost
0.00000
0.00000
-24.00000
Manufacturing
Time (hours)
8
12
Fan motors
Cooling coils
Manufacturing time
Dual Value
31.00000
32.00000
14
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: Economy Standard Deluxe Max s.t. Number of Fans 1 1 1 63E+ 95S + Variable E S D 1E + 1S + 1E + 2S + 8E+12S + Constraint 1 2 The computer solution is shown below. Number of Cooling Coils 135D For the coming production period, the company has 240 fan motors, 340 cooling coils, and 2,600 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: Value 140.00000 100.00000 0.00000 1 1D ≤ 240 4D ≤ 340 14D ≤ 2,600 E, S, D≥ 0 2 Optimal Objective Value = 18320.00000 4 Slack/Surplus 0.00000 0.00000 Reduced Cost 0.00000 0.00000 -24.00000 Manufacturing Time (hours) 8 12 Fan motors Cooling coils Manufacturing time Dual Value 31.00000 32.00000 14
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