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Borges Machine​ Shop, Inc., has a​ 1-year contract for the production of 225,000 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:
GPE FMS 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
Which process is best for this contract?
The option GPE is best when the contracted volume is______units
The option FMS is best when the contracted volume is______units
The option DM is best when the contracted volume is_______.units

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Answer:

The option GPE is best when the contracted volume is below 100,000 units

The option FMS is best when the contracted volume is between 100,000 and 300,000 units (enter you response as a whole number)

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

Explanation:

To calculate the total cost for each of the options we would have to use the following formula:

Total Cost (TC) = Fixed Cost (FC) + [Variable Cost (VC) x Annual Contract Units (ACU)]

For GPE: TC  = $100,000 + ($15.00 x 200,000)= $3,100,000

For FMS:TC  = $200,000 + ($14.00 x 200,000)= $3,000,000

For DM:TC = $500,000 + ($13.00 x 200,000)= $3,100,000

For 225,000 units FMS is the best alternative.

For 0 units GPE has the lowest TC. The next lowest cost is of FMS. Comparing these plans, let x be the no of units when cost of both plans is same.

x = ($200,000-$100,000)/($15-$14) = 100,000

Therefore, for 0 to 100,000 units GPE is the best alternative

Similarly comparing FMS and DM to find x, we get

x= ($ 500,000-$ 200,000)/($14-$13) = 300,000

So, for 225,000 and 300,000 range FMS is the best alrernative.

For greater than 300,000 DM is the best alternative.

The option GPE is best when the contracted volume is below 100,000 units

The option FMS is best when the contracted volume is between 100,000 and 300,000 units (enter you response as a whole number)

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

The option GPE is best when the contracted volume is below 100,000 units, FMS is best when the contracted volume is between 100,000 and 300,000 units and DM is best when the contracted volume is over 300,000 units.

What is Total Cost?

Total cost is the sum of all the costs incurred by a company in producing a certain level of product.

Calculation of the total cost for each of the options we would have to use the following formula:

[tex]\rm\,Total \;Cost \;(TC) = Fixed \;Cost \;(FC) + [Variable Cost \; (VC) \times \;Annual \;Contract \; Units \; (ACU)]\\\\For \;GPE: TC = \$100,000 + (\$15.00 \times 200,000) = \$3,100,000\\\\For \;FMS:TC = \$200,000 + (\$14.00 \times 200,000) = \$3,000,000\\\\\rm\, For \; DM:TC \;= \$500,000 + (\$13.00 \times 200,000)= \$3,100,000[/tex]

FMS is the best alternative for 225,000 units.

GPE has the lowest Total Cost for 0 units. The next lowest cost is FMS. For comparing these plans, let Y be the no of units when the cost of both plans is the same.

[tex]\rm\,Y = \frac{(\$200,000-\$100,000)}{(\$15-\$14)} \\\\\rm\,Y = 100,000 \,Units[/tex]

GPE is the best alternative for 0 to 100,000 units.

Similarly, When we compare FMS and DM to find Y, we get

[tex]\rm\,Y= \frac{(\$ 500,000- \$ 200,000)}{(\$14 - \$13)} \\\\rm\,Y= 300,000\,Units[/tex]

So, FMS is the best alternative for the 225,000 and 300,000 range,

DM is the best alternative for greater than 300,000.

Hence, The option GPE is best when the contracted volume is below 100,000 units, option FMS is best when the contracted volume is between 100,000 and 300,000 units. The option DM is best when the contracted volume is over 300,000 units.

To learn more about Total Cost, refer to the link:

https://brainly.com/question/25109150

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