Borges Machine$$ Shop, Inc., has a$1-$year contract for the production of $250$ comma $000$ gear housings for a new$$ off$-$road vehicle. Owner Luis Borges hopes the contract will be extended and the volume increased next year. Borges has developed costs for three alternatives. They are$$ general$-$purpose equipment$($GPE$),$ flexible manufacturing system$($FMS$),$ and$$ expensive, but$$ efficient, dedicated machine$($DM$).$ The cost data$$ follow:

$$General$-$Purpose Equipment$($GPE$)$

Flexible Manufacturing System$($FMS$)$

Dedicated Machine$($DM$)$

Annual contracted units

$250$ comma $000$

$250$ comma $000$

$250$ comma $000$

Annual fixed cost

$ $150$ comma $000$

$ $225$ comma $000$

$ $525$ comma $000$

Per unit variable cost

$ $18\mathrm{.}00$

$ $14\mathrm{.}00$

$ $13\mathrm{.}00$

Part $2$

To determine the effective volumes for each of the manufacturing$$ processes, one needs to determine the$$ break$-$even point$($BEP$)$ by comparing two$$ processes:

BEP Subscript x comma y Baseline equals StartFraction left parenthesis Fixed Cost Subscript y Baseline minus Fixed Cost Subscript x Baseline right parenthesis Over left parenthesis Variable Cost Subscript x Baseline minus Variable Cost Subscript y Baseline right parenthesis EndFraction

$,$ where x and y are the processes being compared.

Part $3$

The option GPE is best when the contracted volume is below

$$

$18,750$ units $($enter your response as a whole$$ number$).$

Part $4$

The option FMS is best when the contracted volume is between

$$

$18,750$ and

$$

$300,000$ units $($enter your respon