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:

$\backslash$table$[[,\backslash$table$[[$Number of$],[$Fans$]],\backslash$table$[[$Number of$],[$Cooling Coils$]],\backslash$table$[[$Manufacturing$],[$Time $($hours$)]]],[$Economy$,1,1,8],[$Standard$,1,2,12],[$Deluxe$,1,4,14]]$

For the coming production period, the company has $240$ fan motors, $360$ cooling coils, and $2,600$ 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 $63E+95S+135D$

$s.t.$

$1E+1S+1D240$ Fan motors

$1E+2S+4D360$ Cooling coils

$8E+12S+14D2,600$ Manufacturing time

$E,S,D0$

The computer solution is shown below.

Variable

Objective

Allowable

Allowable

E

Coefficient

Increase

Decrease