Quality Air Conditioning manufactures three home air conditioners: an economy model, a standard model, and a deluxe model. The p
rofits per unit are $57, $93, and $141, respectively. The production requirements per unit are as follows:
Number of
Fans Number of
Cooling Coils Manufacturing
Time (hours)
Economy 1 1 8
STandard 1 2 12
Deluxe 1 4 14
For the coming production period, the company has 320 fan motors, 380 cooling coils, and 3200 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 57E + 93S + 141D
s.t.
1E + 1S + 1D ≤ 320 Fan motors
1E + 2S + 4D ≤ 380 Cooling coils
8E + 12S + 14D ≤ 3200 Manufacturing time
E, S, D ≥ 0
The sensitivity report is shown in the figure below.
Optimal Objective Value = 20400.00000
Variable Value Reduced Cost
E 260.00000 0.00000
S 60.00000 0.00000
D 0.00000 24.00000
Constraint Slack/Surplus Dual Value
Fan motors 0.00000 21.00000
Cooling coils 0.00000 36.00000
Manufacturing time 400.00000 0.00000
Variable Objective
Coefficient Allowable
Increase Allowable
Decrease
E 57.00000 12.00000 10.50000
S 93.00000 21.00000 8.00000
D 141.00000 24.00000 Infinite
Constraint RHS
Value Allowable
Increase Allowable
Decrease
Fan motors 320.00000 60.00000 130.00000
Cooling coils 380.00000 100.00000 60.00000
Manufacturing time 3200.00000 Infinite 400.00000
a. Identify the range of optimality for each objective function coefficient. If there is no limit, then enter the text "NA" as your answer. If required, round your answers to one decimal place.
Objective Coefficient Range
Variable lower limit upper limit
E
S
D
b. Suppose the profit for the economy model (E) is increased by $6 per unit, the profit for the standard model (S) is decreased by $2 per unit, and the profit for the deluxe model (D) is increased by $4 per unit. What will the new optimal solution be? If required, round your answers to three decimal places. If your answer is zero, enter "0".
Optimal Solution
E
S
D
If required, round your answer for Total Profit to two decimal places.
Total Profit: $
c. Identify the range of feasibility for the right-hand-side values. If there is no limit, then enter the text "NA" as your answer. If required, round your answers to one decimal place.
Right-Hand-Side-Range
Constraints lower limit upper limit
Fan motors
Cooling coils
Manufacturing time
d. If the number of cooling coils available for production is increased by 120, will the dual value for that constraint change?
YES because the allowable increase for cooling coils is _____ without changing the optimal solution.
Number of
Fans Number of
Cooling Coils Manufacturing
Time (hours)
Economy 1 1 8
STandard 1 2 12
Deluxe 1 4 14
For the coming production period, the company has 320 fan motors, 380 cooling coils, and 3200 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 57E + 93S + 141D
s.t.
1E + 1S + 1D ≤ 320 Fan motors
1E + 2S + 4D ≤ 380 Cooling coils
8E + 12S + 14D ≤ 3200 Manufacturing time
E, S, D ≥ 0
The sensitivity report is shown in the figure below.
Optimal Objective Value = 20400.00000
Variable Value Reduced Cost
E 260.00000 0.00000
S 60.00000 0.00000
D 0.00000 24.00000
Constraint Slack/Surplus Dual Value
Fan motors 0.00000 21.00000
Cooling coils 0.00000 36.00000
Manufacturing time 400.00000 0.00000
Variable Objective
Coefficient Allowable
Increase Allowable
Decrease
E 57.00000 12.00000 10.50000
S 93.00000 21.00000 8.00000
D 141.00000 24.00000 Infinite
Constraint RHS
Value Allowable
Increase Allowable
Decrease
Fan motors 320.00000 60.00000 130.00000
Cooling coils 380.00000 100.00000 60.00000
Manufacturing time 3200.00000 Infinite 400.00000
a. Identify the range of optimality for each objective function coefficient. If there is no limit, then enter the text "NA" as your answer. If required, round your answers to one decimal place.
Objective Coefficient Range
Variable lower limit upper limit
E
S
D
b. Suppose the profit for the economy model (E) is increased by $6 per unit, the profit for the standard model (S) is decreased by $2 per unit, and the profit for the deluxe model (D) is increased by $4 per unit. What will the new optimal solution be? If required, round your answers to three decimal places. If your answer is zero, enter "0".
Optimal Solution
E
S
D
If required, round your answer for Total Profit to two decimal places.
Total Profit: $
c. Identify the range of feasibility for the right-hand-side values. If there is no limit, then enter the text "NA" as your answer. If required, round your answers to one decimal place.
Right-Hand-Side-Range
Constraints lower limit upper limit
Fan motors
Cooling coils
Manufacturing time
d. If the number of cooling coils available for production is increased by 120, will the dual value for that constraint change?
YES because the allowable increase for cooling coils is _____ without changing the optimal solution.
1 answer:
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