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

Component $1$: $

Component $2$: $

Component $3$:

Formulate and solve the model to determine the maximum profit. If the constant is $"1",$ it must be entered in the box. If an amount is zero, enter $"0".$

Let $C_1=$ units of component $1$ manufactured

$C_2=$ units of component $2$ manufactured

$C_3=$ units of component $3$ manufactured

Maximum profit: $

$($b$)$ What are the objective coefficients ranges for the three components? If required, round your answers to two decimal places.

Interpret these ranges for company management.

Individual changes in the profit coefficients $-$ Select your answer $-$ these ranges will not cause a change in the optimal number of components to produce.

$($c$)$ What are the right$-$hand$-$side ranges?

Interpret these ranges for company management.

These are the ranges over which the shadow prices for the associated constraints $-$ Select your answer $-$ applicable.

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

Select your answer $-$

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

$,$ because the production of component $3$ would be $-$ Select your answer $-$

profitable than the production of the other two components and at the reduced price $-$ Select your answer $-$ of component $3$ would be produced.