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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 $$65,$ $$97,$ and $$139,$ 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 $350$ fan motors, $360,$ Eooling 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 $65E+975+1390$

$s.t.$

$1E+15+10350$ Fan motors

$1E+25+4D360$ Cooling coils

$8E+125+14D3000$ Manufacturing time

$E,S,D0$

The computer solution is shown in the flgure below.

Optimal Objective value $=,23070\mathrm{.}00000$

Variabie

value

Reduced cost