$($a$)$ Formulate and solve for the recommended production quantities.

component $1$

$($b$)$ What are the objective coefficient ranges for the three components? $($If there is no upper or lower limit$,$ enter NO LIMIT. Round your answers to the nearest integer.$)$

Interpret these ranges for company management.

Changes in the profit coefficients within these ranges will not cause a change in the optimal number of components to produce.

Changes in the profit coefficients outside these ranges will not cause a change in the optimal number of components to produce.

Changes in the profit coefficients within these ranges will cause changes in the optimal number of components to produce.

$($c$)$ What are the right$-$hand$-$side ranges? $($Use minutes for time. If there is no upper or lower limit$,$ enter NO LIMIT. Round your answers to the nearest integer.$)$

shaper availability

grinder availability

max units of component $3$

max units of component $1$

max units of component $2$

existing orders for component $1$

Interpret these ranges for company management.

These are the ranges over which the reduced costs for the associated constraints are applicable.

These are the ranges over which the reduced costs for the associated constraints are not applicable.

These are the ranges over which the dual values for the associated constraints are not applicable.

These are the ranges over which the dual values for the associated constraints are applicable.

$($d$)$ If more time could be made available on the grinder, how much would it be worth?

Nothing, since there are $300$ minutes of slack time on the grinder at the optimal solution.

Every additional minute on the grinder decreases profits by $$1.$

Every additional minute on the grinder increases profits by $$3.$

Every additional minute on the grinder increases profits by $$1\mathrm{.}50.$

$($e$)$ If more units of component $3$ can be sold by reducing the sales price by $$4,$ should the company reduce the price?

Yes. At that price, it would be profitable to produce $700$ units of component $3.$

Yes. Every additional unit of component $3$ increases profits by $$3.$

No$.$ At that price, it would not be profitable to produce any of component $3.$

No$.$ There is a slack of $300$ units so selling more would not improve profits.