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: ​ General-Purpose Equipment​ (GPE) Flexible Manufacturing System​ (FMS) Dedicated Machine​ (DM)
Annual contracted units 225,000 225,000 225,000
Annual fixed cost $125,000 $225,000 $480,000
Per unit variable cost $15.00 $14.00 $13.00

The option GPE is best when the contracted volume is below:

For 225,000 units FMS is the best alternative.

For GPE: TC  

GPE  

For 0 units GPE has the lowest TC. The next lowest cost is FMS.

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

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

Explanation:  

Formula used:-

For 225,000 units FMS is the best alternative.

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

For GPE: TC  

GPE  

For FMS: TC  

FMS  

For DM: TC  

DM  

For 0 units GPE has the lowest TC. The next lowest cost is FMS. Comparing these two plans, let x be the no of units when the cost of both plans is the 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= ($ 480,000-$ 200,000)/($14-$13) = 280,000  

So, for the 225,000 and 280,000 range, FMS is the best alrernative.  

For greater than 280,000 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 280,000 units (enter your response as a whole number)  

The option DM is best when the contracted volume is over 280,000 units (enter your response as a whole number)

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explanation: