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Borges Machine​ Shop, Inc., has a​ 1-year contract for the production of 200,000 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

200,000         

200,000              

200,000      

Annual fixed cost

$100,000         

$200,000              

$500,000      

Per unit variable cost

$15.00         

$14.00              

$13.00      

The option GPE is best when the contracted volume is below nothing units ​(enter your response as a whole​ number).

The option FMS is best when the contracted volume is between nothing and nothing units ​(enter your responses as whole​ numbers).

The option DM is best when the contracted volume is overunits ​(enter your response as a whole​ number).

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Answer:

Task 1:

GPE is best when the contracted volume is below 25,000 units.

Task 2:

FMS is best when the contracted volume is between 25,000 and 300,000 units.

Task 3:

DM is best when the contracted volume is over 300,000 units.

Explanation:

The schedule for total cost is attached.

Task 1:

The option GPE is best when the contracted volume is below nothing units ​(enter your response as a whole​ number).

Answer:

GPE is best when the contracted volume is below 25,000 units.

Working:

GPE is best when cost for GPE is less than other two.

Difference between the variable cost per unit of GPE and FMS = $18 per unit - $14 per unit = $4 per unit.

Difference between the fixed cost of GPE and FMS = $200,000 - $100,000 = $100,000

The difference of cost between GPE and FMS can be found by (assuming n units produced)

GPE-FMS: 4n – $100,000

The cost difference has to be zero in order to lower the cost for GPE

Hence 4n-$100,000=0

Hence n = 25,000

GPE is best when the contracted volume is below 25,000 units.

Task 2:

The option FMS is best when the contracted volume is between nothing and nothing units ​(enter your responses as whole​ numbers).

Answer:

FMS is best when the contracted volume is between 25,000 and 300,000 units.

Working:

To compare FMS:

The cost has to be in between GPE and FMS

Considering difference between GPE and FMS

n = 25,000 (from above calculation)

Considering FMS and DM:

Difference in variable cost per unit of FMS and DM = $14 - $13 = $1 per unit

Difference in fixed cost of FMS and DM = $500,000 - $200,000 = $300,000

Difference = n – $300,000

n-300,000=0

n = 300,000

Hence FMS is best when the contracted volume is between 25,000 and 300,000 units.

Task 3:

The option DM is best when the contracted volume is over units ​(enter your response as a whole​ number).

Solution:

DM is best when the contracted volume is over 300,000 units.

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