Quality Air Conditioning manufactures three home air conditioners: an economy mo
ID: 467855 • 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: Number of Number of Manufacturing Cooling Coils Time (hours) Fans Economy Standard Deluxe 14 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: Max 63E 95s 135D s.t 1E 1s 10 s 200 Fan motors 1E 2S 4D s 320 Cooling coils 8E 12S 14D s 2400 Manufacturing time E, S, D 20 The computer solution is shown in the figure below. Optimal objective Value 16440.00000 Variable Value Reduced Cost 0.00000 80.00000 120.00000 0.00000 0.00000 24.00000Explanation / Answer
a.
Optimal Solution:
Economy models
80 units
Standards models
120 units
Deluxe models
0 unit
Value of the objective function
$16440
b.
The resource constraints that have slack/surplus value equal to zero are assumed be completely satisfied or consumed. Thus, such resource constraints are binding or limiting the optimal solution.
Fan motors
Binding
Cooling coils
Binding
Manufacturing Time
Non-binding
c.
The resource constraints those are binding or limiting the optimal solution, there is no extra capacity. Whereas, the non-binding constraints are not completely utilized, for such constraints there are balance amount remained.
Constraints
Extra Capacity
Number of units
Fan motors
Binding
No
0
Cooling coils
Binding
No
0
Manufacturing Time
Non-binding
Yes
320
d.
The allowable increase and decrease values for the decision variables, represents the range of cost or profit coefficient f decision variable, beyond which the variable will be in optimal solution. For the variable D, allowable increase is 24, thus, when the profit coefficient of the D is increased to 135 + 24 = $159, the variable is included in the optimal solution.
The optimal solution will not change because the profit of the deluxe can vary from $0 to $159. $150 is within this range without the optimal solution changing.
Economy models
80 units
Standards models
120 units
Deluxe models
0 unit
Value of the objective function
$16440