Quality Air Conditioning manufactures three home air conditioners: an economy mo

Question

Quality Air Conditioning manufactures three home air conditioners: an economy model, a standard model, and a deluxe model. The profits per unit are $65, $97, and $139, respectively. The production requirements per unit are as follows: Number of Number of Manufacturing Time (hours) 8 12 14 Fans Cooling Coils Economy Standard Deluxe 4 For the coming production period, the company has 350 fan motors, 360 cooling coils, and 3000 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 65E 97S + 139D s.t. 1E 1S 1D s 350 Fan motors 1E 2S4D 360 Cooling coils 8E 12S14D s 3000 Manufacturing time E,S, D2 0

Explanation / Answer

a) What is the optimal solution

Economy Models(E)= 340

Standard Models(S)= 10

Deluxe models(D) = 0

Objective Value =$23070

b) To know which constraints are binding if the LHS value = RHS value of the constraints they are binding or Non-binding otherwise

Constraint 1 Fan Motors LHS = 340+10+0 =350=RHS (Binding)

Constraint 2 Cooling Coils LHS= 340+20+0=360=RHS(Binding)

Constraint 3 Manufacturing time LHS= 8*340+12*10+0= 2840< RHS (Non Binding)

C) Fan Motors No extra capcity as the constraint is binding Number of units =0

Cooling Coils No extra capacity as the constraint is binding Number of units =0

Manufacturing time is having extra capacity Number of units = 3000-2840 = 160 units

d.) No the optimal solution wont change as the allowable increase is 22 means 139+22= $161

and the allwable decerease is -infinity

Range is -infinity to 161 and 154 lies within this range

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