Borges Machine Shop, Inc., has a 1-year contract for the production of 250 comma

Question

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 $ 125 comma 000 $ 250 comma 000 $ 525 comma 000 Per unit variable cost $ 16.00 $ 14.00 $ 13.00 The option GPE is best when the contracted volume is below nothing units

Explanation / Answer

Total cost of manufacturing can be expressed as :

Total cost = Fixed cost + Variable cost / unit x Number of units

Let , number of untis = N

Therefore ,

Total cost of manufacturing for N units :

Using Option GPE = $125,000 + $16.N

Using Flexible manufacturing = $250,000 + $14.N

Using Dedicated machine = $525,000 + $13.N

For GPE to be the best option :

Total cost under GPE < Total cost using flexible manufacturing

Or, 125,000 + 16.N < 250,000 + 14.N

Or, 2N < 125,000

Or, N < 62500

Total cost under GPE < Total cost using Dedicated machine

Or,

125,000 + 16.N < 525,000 + 13.N

Or, 3.N < 400,000

Or, N < 133333.33

Taking into consideration above two constraints N < 62500 and N < 133333.33 simultaneously, we can conclude that N < 62,500

Therefore GPE is best option when contracted volume is less than 62,500

For FMS to be the best option :

Total cost under FMS < Total cost under GPE

Or, 250,000 + 14.N < 125,000 + 16.N

Or, 2N > 125,000

Or, N > 62500

Total cost under FMS < Total cost under Dedicated Machine

Or, 250,000 + 14.N < 525,000 + 13.N

Or, N < 275,000

Taking into consideration above two constraints i.e. N > 62.500 and N < 275,000 simultaneously , we can conclude that     : 62,500 < N < 275,000

Thus, option FMS is best when contracted value is between 62,500 and 275,000

For DM to be the best option :

Total cost under DM < Total cost under GPE

Or, 525,000 + 13.N < 125,000 + 16.N

Or, 3.N > 400,000

Or, N > 133333.33

Total cost under DM < Total cost under FMS

525,000 + 13.N < 250,000 + 14.N

Or, N > 275000

Taking into consideration above two constraints i.e. N > 133333.33 and N > 275,000 , we can conclude that N > 275,000

THE OPTION GPE IS BEST WHEN CONTRACTED VOLUME IS BELOW 62,500 UNITS

THE OPTION GMS IS BEST WHEN CNTRACTED VOLUME IS BETWEEN 62,500 AND 275,000 UNITS

THE OPTION DM IS BEST WHEN CONTRACTED VLUME IS OVER 275,000 UNITS

THE OPTION GPE IS BEST WHEN CONTRACTED VOLUME IS BELOW 62,500 UNITS

THE OPTION GMS IS BEST WHEN CNTRACTED VOLUME IS BETWEEN 62,500 AND 275,000 UNITS

THE OPTION DM IS BEST WHEN CONTRACTED VLUME IS OVER 275,000 UNITS

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