for three alternatives. They are general$-$purpose equipment $($GPE$),$ flexible manufacturing system $($FMS$),$ and expensive, but efficient, dedicated machine $($DM$).$ The cost data follow:

$\backslash$table$[[,\backslash$table$[[$General$-$Purpose$],[$Equipment $($GPE$)]],\backslash$table$[[$Flexible Manufacturing$],[$System $($FMS$)]],\backslash$table$[[$Dedicated$],[$Machine $($DM$)]]],[$Annual contracted units,$200,000,200,000,200,000],[$Annual fixed cost,$$125,000,$$$225,000,$$$525,000$Borges Machine$$ Shop, Inc., has a$1-$year contract for the production of $200$ 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

$200$ comma $000$

$200$ comma $000$

$200$ comma $000$

Annual fixed cost

$ $125$ comma $000$

$ $225$ comma $000$

$ $525$ comma $000$

Per unit variable cost

$ $18\mathrm{.}00$

$ $14\mathrm{.}00$

$ $13\mathrm{.}00$

If the contract for the second and third years is$$ pending, for demand below $25$ comma $000$units$,$ option

$$

is the best alternative for Luis.

Part $2$

For demand above $300$ comma $000$units$,$ option

$$

FMS

GPE

DM

is the best alternative for Luis.