Textbook Question $12-$ 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: 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 $63$ E$+95$ S$+135$ D s$.$t$.1$ E$+1$ S$+1$ D $<=200$ Fan motors $1$ E$+2$ S$+4$ D $<=320$ Cooling coils $8$ E$+12$ S$+14$ D $<=2400$ Manufacturing time E$,$ S$,$ D $>=0$The Solution for the Quality Air Conditioning Problem Identify the range of optimality for standard models $($S$)?47\mathrm{.}5$ to $7587$ to $126$ No lower limit to $159$