Please give the step $by$ step solution

The Porsche Club $of$ America sponsors driver education events that provide high$-$performance driving instruction $on$ actual racetracks. Because safety $is$ a primary consideration $at$ such events, many owners elect $to$ install roll bars $in$ their cars. Deegan Industries manufactures two types $of$ roll bars for Porsches. Model $DRBis$ bolted $to$ the car using existing holes $in$ the car$s$ frame. Model $DRWis$ a heavier roll bar that must $be$ welded $to$ the car$s$ frame. Model $DRB$ requires $20$ pounds $of$ a special high$-$alloy steel, $40$ minutes $of$ manufacturing time, and $60$ minutes $of$ assembly time. Model $DRW$ requires $25$ pounds $of$ the special high$-$alloy steel, $100$ minutes $of$ manufacturing time, and $40$ minutes $of$ assembly time. Deegan$s$ steel supplier indicated that $at$ most $40,000$ pounds $of$ the high$-$alloy steel will $be$ available next quarter. $In$ addition, Deegan estimates that $2000$ hours $of$ manufacturing time and $1600$ hours $of$ assembly time will $be$ available next quarter. The profit contributions are $$200$ per unit for model $DRB$ and $$280$ per unit for model $DRW.$ The linear programming model for this problem $isas$ attached.

FigurWhat are the optimal solution and the total profit contribution?

Another supplier offered $to$ provide Deegan Industries with $an$ additional $500$ pounds $of$ the steel alloy $at$ $$2$ per pound. Should Deegan purchase the additional pounds $of$ the steel alloy? Explain.

Deegan $is$ considering using overtime $to$ increase the available assembly time. What would you advise Deegan $todo$ regarding this option? Explain.

Because $of$ increased competition, Deegan $is$ considering reducing the price $of$ model $DRB$ such that the new contribution $to$ profit $is$ $$175$ per unit. How would this change $in$ price affect the optimal solution? Explain.

$If$ the available manufacturing time $is$ increased $by500$ hours, will the shadow price for the manufacturing time constraint change? Explain.$e8\mathrm{.}21$ Sensitivity Report for the Deegan Industries