Please answer all the following questions. I$\text{'}$m having difficulty getting the correct answers.

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 $220$ fan motors, $340$ cooling coils, and $2,500$ 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 $63E+95S+135D$

$s.t.$

$1E+1S+1D220$ Fan motors

$1E+2S+4D340$ Cooling coils

$8E+12S+14D2,500$ Manufacturing time

$E,S,D0$

The computer solution is shown below.

Optimal Objective Value $=17700\mathrm{.}00000$

Variable

E

S

Objective

Coefficient

$63\mathrm{.}00000$

$95\mathrm{.}00000$

Allowable

Increase

$12\mathrm{.}00000$

$31\mathrm{.}00000$

Allowable

Decrease

$15\mathrm{.}50000$

$8\mathrm{.}00000($a$)$ What is the optimal solution, and what is the value of the objective function?

E

$S$

$D$

profit $

$($b$)$ Which constraints are binding? $($Select all that apply.$)$

fan motors

cooling coils

manufacturing time

$($c$)$ Which constraint shows extra capacity?

fan motors

cooling coils

manufacturing time

How much extra capacity $($in hr$)$ is available?

hr

$($d$)$ If the profit for the deluxe model were increased to $$140$ per unit, would the optimal solution change? Use the information in the output to answer this question.

The optimal solution

change because the new profit is

the