Quality Air Conditioning manufactures three home air conditioners: an economy mo
ID: 467912 • Letter: Q
Question
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:
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), 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 computer solution is shown in the figure below.
Optimal Objective Value = 16440.00000
Variable
Value
Reduced Cost
E
80.00000
0.00000
S
120.00000
0.00000
D
0.00000
-24.00000
Constraint
Slack/Surplus
Dual Value
Fan motors
0.00000
31.00000
Cooling coils
0.00000
32.00000
Manufacturing time
320.00000
0.00000
Variable
Objective
Coefficient
Allowable
Increase
Allowable
Decrease
E
63.00000
12.00000
15.50000
S
95.00000
31.00000
8.00000
D
135.00000
24.00000
Infinite
Constraint
RHS
Value
Allowable
Increase
Allowable
Decrease
Fan motors
200.00000
80.00000
40.00000
Cooling coils
320.00000
80.00000
120.00000
Manufacturing time
2400.00000
Infinite
320.00000
What is the optimal solution, and what is the value of the objective function? If required, round your answers to the nearest whole number.
Optimal Solution
Economy models (E)
Standard models (S)
Deluxe models (D)
Value of the objective function
$
Which constraints are binding?
Fan motors:
Binding
Cooling coils:
Binding
Manufacturing time:
Non binding
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.
Constraints
Extra capacity
Number of units
Fan motors
No
?
Cooling coils
No
?
Manufacturing time
Yes
?
If the profit for the deluxe model were increased to $150 per unit, would the optimal solution change?
The optimal solution would not change because the profit of the deluxe model can vary from $0 to $159 . $150 is in this range without the optimal solution changing.
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