Question

Borges Machine​ Shop, Inc., has a​ 1-year contract for the production of 225 comma 000225,000 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

225 comma 000225,000         

225 comma 000225,000              

225 comma 000225,000      

Annual fixed cost

$ 125 comma 000$125,000         

$ 250 comma 000$250,000              

$ 525 comma 000$525,000      

Per unit variable cost

$ 18.00$18.00         

$ 14.00$14.00              

$ 13.00$13.00      

The option GPE is best when the contracted volume is below ___ units.

The option FMS is best when the contracted volume is between ___ and ___ units.

The option DM is best when the contracted volume is over ____ units.

Answer 1

Total cost = fixed cost + variable cost per unit * volume

For GPE is to be the best:

The cost of GPE is to be less than the other two

Let the volume be x

Cost of GPE = 125000 + 18*x

Cost of FMS = 250000 + 14*x

Cost of DM = 525000 + 13*x

So,

125000 + 18*x <= 525000 + 13*x

5*x <= 400000

x <= 400000/5 = 80000

125000 + 18*x <= 250000 + 14*x

x <= 31250

Answer is: below 31250 (as 31250 < 80000)

For FMS to be the best:

Let the volume be x

Cost of GPE = 125000 + 18*x

Cost of FMS = 250000 + 14*x

Cost of DM = 525000 + 13*x

250000 + 14*x <= 125000 + 18*x

x >= 31250

250000 + 14*x <= 525000 + 13*x

x <= 275000

Answer is: between 31250 and 275000

DM is best:

125000 + 18*x >= 500000 + 13*x

5*x >= 400000

x >= 80000

250000 + 14*x >= 525000 + 13*x

x >= 275000

Answer is: above 275000

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