$$200$ per unit for model DRB and $$280$ per unit for model DRW$.$ The linear programming model for this problem is as follows:

Max $200DRB+280DRW,$

$s.t.$

$,20DRB+25DRW,38,000$ Steel available

$,40DRB+100DRW,120,000$ Manufacturing minutes

$60DRB+40DRW,102,000$ Assembly minutes

$,DRB,DRW,0,$

The computer solution is shown $in$ picture.

$($a$)$ What is the optimal solution and the total profit contribution $($in $$)?$

DRB$-?$

DRW$-?$

total profit contribution$-?$ $

$($b$)$ 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.

a$)$ Yes, there is no surplus of steel so any additional steel that becomes available should be purchased.

b$)$ Yes, the dual value for steel available is $8\mathrm{.}8.$ Each pound of steel will increase profits more than the $$2$ per pound that the supplier is offering. c$)$ No$,$ the dual value for steel available is $0\mathrm{.}6.$ Each pound of steel will not increase profits enough to justify the $$2$ per pound that the supplier is offering.

d$)$ No$,$ there is a slack value of $4,273,$ so additional pounds of steel will not increase profits.

e$)$ No$,$ the allowable increase for steel is only $24$ pounds, so the additional profits are not applicable for $500$ pounds.

$($c$)$Deegan is considering using overtime to increase the available assembly time. What would you advise Deegan to do regarding this option?

Constraint $(1,2,3?)$ has a slack. Increasing the number of hours of assembly time will $($improve$/$not improve$)$ profits.

$($d$)$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.

The objective coefficient range for model DRB shows a lower limit of $$-?$ Thus, the optimal solution $($will$/$will not$)$ change and the new value will be $$-?$

$($e$)$ If the available manufacturing time is increased by $500$ hours, will the dual value for the manufacturing time constraint change? Explain.

The allowable increase is $?$ minutes so the dual value for this constraint $($will$/$will not$)$ change.