Meile Machine Shop, Inc., has a 1-year contract for the production of 225,000 ge
ID: 402952 • Letter: M
Question
Meile Machine Shop, Inc., has a 1-year contract for the production of 225,000 gear housings for a new off-road vehicle. Owner Larry Meile hopes the contract will be extended and the volume increased next year. Meile 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:
GPE FMS DM
Annual contracted units 225,000 225,000 225,000
Annual fixed cost $150,000 $225,000 $500,000
Per unit variable cost $15.00 $14.00 $13.00
a) The option GPE is best when the contracted volume is below __________ units.
b) The option Gms is best when the contracted volume is between ________ and _________ units.
c) The option DM is best when the contracted volume is over _________ units.
Explanation / Answer
Total cost of each machine is
Fixed cost + variable cost * number of units.
a) Low cost option: 150000 + 15 * x
b) Middle: 225000 + 14 * x
c) High: 500000 + 13 * x
You want to see where those lines cross
and then the range(s) where one or the other is lowest.
The best way to do it is by graphing them, but that's not practical here.
a = b:
150000 + 15x = 225000 + 14x
x = 75000
So first two options are equal at 75000
and since first has higher per unit cost, it's better below that,
and the other above it.
a = c:
150000 + 15x = 500000 + 13x
x = 175000
Same deal: a better below that point, c better above it
(This turns out to unnecessary, but best to include it just to be sure.)
b = c:
225000 + 14 x = 500000 + 13x
x = 275,000
b better below, c better above
So we have:
a best below 75000
b best from 75000 to 275000
c best over 275000