Assignment 2 Problem 3-12 (Algorithmic) Quality Air Conditioning manufactures th
ID: 3072528 • Letter: A
Question
Assignment 2 Problem 3-12 (Algorithmic) Quality Air Conditioning manufactures three home air conditioners: an economy model, a standard model and a deluxe model. The profits per unit are $59, $89, and $137, respectively. The production requirements per unit are as follows: Number of Fans Number of Manufacturing Time (hours) Cooling Coils Economy Standard 12 Deluxe 14 For the coming production period, the company has 250 fan motors, 380 cooling cails, and 2600 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 59E+895+1370 s.t. 1E 1S+ 1D s 250 Fan motors E 25+ 4D 380 Cooling coils BE 12S 14D s 2600 Manufacturing time E, S, D 20 The computer solution is shown in the figure belovw Optimal Objective Value-18650.00000 Variable Value Reduced Cost 130.00000 0.00000 0.00000 0.00000 12.00000 Constraint Fan motors Cooling coils Manufacturing time Slack/Surplus Dual Value 0.00000 0.00000 80.00000 29.00000 30.00000 0.00000 Objective Coefficient Allowable Increase Variable 59.00000 89.00000 137.00000 6.00000 29.00000 12.00000 14.50000 4.00000 RHS value 250.00000 Increase Fan motors 20.00000 60.00000Explanation / Answer
a)
E = 120 {see column value and row E in first table}
S = 130
D = 0
value of objective function = 18650 {see optimal objective value}
b)
fan motors- yes {see column slack/surplus and row Fan moter , it is 0 }
cooling coils - yes
manufacturing time - no {non -zero value }
c)
fan motors- no , 0
cooling coils - no , 0
manufacturing time - yes ,80
d)
optimal solution will change
profit can change from 0 to 137 +12 = 149 {see allowable increas and decrease in last table }
152 is not in this range