Borges Machine Shop, Inc., has a 1-year contract for the production of 250,000 g

Question

Borges Machine Shop, Inc., has a 1-year contract for the production of 250,000 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 altermatives. They are general-purpose equipment (GPE), flexible manufacturing system (FMS), and expensive, but efficient, dedicated machine (DM). The cost data follow: General-Purpose Flexible Manufacturing Annual contracted units Annual fixed cost Per unit variable cost Equipment (GPE) 250,000 $100,000 $15.00 System (FMS) 250,000 $200,000 $14.00 Dedicated Machine (DM) 250,000 S500,000 $13.00 The option GPE is best when the contracted volume is below units (enter your response as a whole number). The option FMS is best when the contracted volume is between and units (onter your responses as whole numbors). The option DM is best when the contracted volume is over units (ontor your response as a whole number).

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 = $100,000 + $15.N

Using Flexible manufacturing = $200,000 + $14.N

Using Dedicated machine = $500,000 + $13

For GPE to be the best option :

Total cost under GPE < Total cost using flexible manufacturing

Or, 100,000 + 15.N < 200,000 + 14.N

Or, N < 100,000

Total cost under GPE < Total cost using Dedicated machine

Or,

100,000 + 15.N < 500,000 + 13.N

Or, 2.N < 400,000

Or, N < 200,000

Taking into consideration above two constraints N < 100,000 and N < 200,000 simultaneously, we can conclude that N < 100,000

Therefore GPE is best option when contracted volume is less than 100,000

For FMS to be the best option :

Total cost under FMS < Total cost under GPE

Or, 200,000 + 14.N < 100,000 + 15.N

Or, N > 100,000

Total cost under FMS < Total cost under Dedicated Machine

Or, 200,000 + 14.N < 500,000 + 13.N

Or, N < 300,000

Taking into consideration above two constraints i.e. N > 100,000 and N < 300,000 simultaneously , we can conclude that     : 100,000 < N < 300,000

Thus, option FMS is best when contracted value is between 100,000 and 300,000

For DM to be the best option :

Total cost under DM < Total cost under GPE

Or, 500,000 + 13.N < 100,000 + 15.N

Or, 2.N > 400,000

Or, N > 200,000

Total cost under DM < Total cost under FMS

500,000 + 13.N < 200,000 + 14.N

Or, N > 300,000

Taking into consideration above two constraints i.e. N > 200,000 and N > 300,000 , we can conclude that N > 300,000

THE OPTION GPE IS BEST WHEN CONTRACTED VOLUME IS BELOW 100,000 UNITS

THE OPTION GMS IS BEST WHEN CNTRACTED VOLUME IS BETWEEN 100,000 AND 300,000 UNITS

THE OPTION DM IS BEST WHEN CONTRACTED VLUME IS OVER 300,000 UNITS

THE OPTION GPE IS BEST WHEN CONTRACTED VOLUME IS BELOW 100,000 UNITS

THE OPTION GMS IS BEST WHEN CNTRACTED VOLUME IS BETWEEN 100,000 AND 300,000 UNITS

THE OPTION DM IS BEST WHEN CONTRACTED VLUME IS OVER 300,000 UNITS

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