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 $195$S $1135$D s$.$t$\mathrm{.}1$E$11$S$11$D# $200$ Fanmotors$1$E$12$S$14$D # $320$ Cooling coils$8$E $112$S $114$D # $2400$ Manufacturing timeE, S$,$ D $ $0$The computer solution is shown in Figure $3\mathrm{.}17.$a$.$ What is the optimal solution, and what is the value of the objective function?b$.$ Which constraints are binding?c$.$ Which constraint shows extra capacity? How much?d$.$ If the profit for the deluxe model were increased to $$150$ per unit, would the optimalsolution change? Use the information in Figure $3\mathrm{.}17$ to answer this question.