VariableValueReduced CostAM$100\mathrm{.}000000\mathrm{.}00000$BM$60\mathrm{.}000000\mathrm{.}00000$AP$0\mathrm{.}000001\mathrm{.}75000$BP$90\mathrm{.}000000\mathrm{.}00000$

ConstraintSlack$/$SurplusDual Value$10\mathrm{.}0000012\mathrm{.}2500020\mathrm{.}000009\mathrm{.}00000320\mathrm{.}000000\mathrm{.}0000040\mathrm{.}000000\mathrm{.}37500$

VariableObjective

CoefficientAllowable

IncreaseAllowable

DecreaseAM$10\mathrm{.}000001\mathrm{.}75000$InfiniteBM$6\mathrm{.}000003\mathrm{.}000002\mathrm{.}33333$AP$14\mathrm{.}00000$Infinite$1\mathrm{.}75000$BP$9\mathrm{.}000002\mathrm{.}333333\mathrm{.}00000$

ConstraintRHS

ValueAllowable

IncreaseAllowable

Decrease$1100\mathrm{.}0000011\mathrm{.}42857100\mathrm{.}000002150\mathrm{.}00000$Infinite$90\mathrm{.}000003600\mathrm{.}00000$Infinite$20\mathrm{.}0000041,080\mathrm{.}0000053\mathrm{.}33333480\mathrm{.}00000$

$($a$)$

Interpret the ranges of optimality for the objective function coefficients.

If a single change to the injection molding time or assembly time for either model case is within the allowable range, the optimal solution will not change.If a single change to the manufacturing cost or purchase cost for either model case is within the allowable range, the optimal solution will not change.$$If multiple changes are made to the manufacturing or purchase costs for either model case within their respective allowable ranges, the optimal solution will not change.If multiple changes are made to the injection molding time or assembly time for either model case within their respective allowable ranges, the optimal solution will not change.

$($b$)$

Suppose that the manufacturing cost increases to $$11\mathrm{.}30$ per case for model A$.$ Would the optimal solution change?

Yes, it is necessary to solve the model again.No$,$ the optimal solution remains the same.$$

What is the new optimal solution?

at

$($AM$,$ BM$,$ AP$,$ BP$)=$

$$

$($c$)$

Suppose that the manufacturing cost increases to $$11\mathrm{.}30$ per case for model A and the manufacturing cost for model B decreases to $$5$ per unit. Would the optimal solution change?

Yes, it is necessary to solve the model again.No$,$ the optimal solution remains the same.$$

What is the new optimal solution?

at

$($AM$,$ BM$,$ AP$,$ BP$)=$