Problem 3-13 (Algorithmic) Quality Air Conditioning manufactures three home air
ID: 3073440 • Letter: P
Question
Problem 3-13 (Algorithmic)
Quality Air Conditioning manufactures three home air conditioners: an economy model, a standard model, and a deluxe model. The profits per unit are $63, $97, and $133, respectively. The production requirements per unit are as follows:
For the coming production period, the company has 350 fan motors, 340 cooling coils, and 2000 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:
The sensitivity report is shown in the figure below.
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.
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".
If required, round your answer for Total Profit to two decimal places.
Total Profit: $
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.
If the number of manufacturing time available for production is increased by 740, will the dual value for that constraint change?
Yes because the allowable increase for manufacturing time is without changing the optimal solution.
Fans Number of
Cooling Coils Manufacturing
Time (hours) Economy 1 1 8 Standard 1 2 12 Deluxe 1 4 14
Explanation / Answer
Q - What is the optimal solution, and what is the value of the objective function? If required, round your answers to the nearest whole number.
Answer - Refer the first table of computer solution (Variable, Value, Reduced Cost)
Optimal Solution
Economy models (E)
80
Standard models (S)
120
Deluxe models (D)
0
Value of the objective function
$ 16440
Q - Which constraints are binding?
Answer - Constraints having slack/surplus equal to 0 are binding, otherwise non-binding
Fan motors:
Binding
Cooling coils:
Binding
Manufacturing time:
Non binding
Q - Which constraint shows extra capacity? How much? If constraint shows no extra capacity, enter 0 as number of units. If required, round your answers to the nearest whole number.
Answer – Refer table (Constraint, Slack/Surplus, Dual Value)
Slack/Surplus is the number of units
Constraints
Extra capacity
Number of units
Fan motors
No
0
Cooling coils
No
0
Manufacturing time
Yes
320
Q - If the profit for the deluxe model were increased to $150 per unit, would the optimal solution change?
Answer - Refer table (variable, objective coefficient, allowable increase, allowable decrease)
Allowable increase in coefficient of Variable D is 24, which means it be increased up to 159 (=135+24) without changing the optimal solution. 150 is within the limit, so changing the coefficient to 150 will not change the optimal solution.
Optimal Solution
Economy models (E)
80
Standard models (S)
120
Deluxe models (D)
0
Value of the objective function
$ 16440
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