Problem $3-17$ DRB and $$280$ per unit for model DRW$.$ The linear programming model for this problem is as follows: Max $200$DRB$+280$DRW s$.$t$.20$DRB$+25$DRW Steel available $40$DRB$+100$DRW Manufacturing minutes $60$DRB$+40$DRW Assembly minutes DRB$,$DRW$>=0$ The sensitivity report is shown in the figure below. Optimal Objective Value $=424000\mathrm{.}00000$ Variable Value Reduced Cost DRB $1000\mathrm{.}000000\mathrm{.}00000$follows:

Max $200DRB+280DRW$

$s.t.$

$20DRB+25DRW32,000$ Steel available

$40DRB+100DRW120,000$ Manufacturing minutes

$60DRB+40DRW108,000$ Assembly minutes

The computer solution is shown below.

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

DRB

DRW

total profit contribution $

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 suplier is

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

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

No$,$ there is a slack value of $11,636,$ so additional pounds of steel will not increase profits.

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.

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

Constraint $]$ has a slack. Increasing the number of hours of assembly time will $--$Select$---vv$ profits.

The objective coefficient range for model DRB shows a lower limit of $

$.$ Thus, the optimal solution $---$ Select$---vv$ 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

$]$ change.