$($a$)$ For each component, calculate the profit margin $($in dollars, profit margin $=$ selling price $-$ material cost $-$ labor cost$).$

component $1,$$

component $2$$

component $3$$$.,$$

Formulate and solve for the recommended production quantities that will maximize contribution to profit.

component $1$

units

component $2\text{'}$ units

component $3,$ units

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

component $1$$

to $

component $2$

to $

component

$

to $

Interpret these ranges for company management.

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

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

Individual 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.$)$

to

shaper availability

grinder availability

to

Interpret these ranges for company management.

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

These are the ranges over which the shadow prices for the associated constraints are not applicable.

These are the ranges over which the shadow prices for the associated constraints are applicable.

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

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

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

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

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

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

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

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

Yes. At that price, the optimal solution would produce $700$ units of component $3.$

No$.$ At that price, the optimal solution would not produce any of component $3.$

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