Problem 8-3 A small producer of machine tools wants to move to a larger building

Question

Problem 8-3 A small producer of machine tools wants to move to a larger building, and has identified two alternatives. Location A has annual fixed costs of $100,000 and variable costs of $13,000 per unit, location B has annual fixed costs of $300,000 and variable costs of $8,000 per unit. The finished items sell for $18,000 each. a. At what volume of output would the two locations have the same total cost? Volume of output units b-1. For what range of output would location A be superior? (Enter your answer as a whole number. Do not include the indifference point in your answer.) Range of output to b-2. For what range would B be superior? (Enter your answer as a whole number. Do not include the indifference point in your answer.) Range of output or more

Explanation / Answer

Answer to question a :

Let the volume at which 2 locations have the same total cost = N

Total cost of locationA = $100,000 + $13,000.N

Total cost of location B = $300,000 + $ 8000.N

Therefore ,

100,000 + 13,000.N = 300,000 + 8000.N

Or , 5000.N = 200,000

Or, N = 40

VOLUME OF OUTPUT = 40 UNITS

Answer to question b1 :

Let the quantum of output for which A be superior = N1

That means total cost at location A < Total cost at Location B

Total cost at location A = $100,000 + $13,000.N1

Total cost at location B = $300,000 + $8000.N1

Therefore ,

100,000 + 13,000.N1 < 300,000 + 8000.N1

Or, 5000.N1 < 200,000

Or, N1 < 40

RANGE OF OUTPUT =0 TO 40

Answer to question b2:

Let the quantum of output for which B be superior = N2

That means total cost at location B < Total cost at Location A

Total cost at location A = $100,000 + $13,000.N2

Total cost at location B = $300,000 + $8000.N2

Therefore ,

300,000 + 8000.N2< 100,000 + 13,000.N2

Or, 5000.N2 > 200,000

Or, N1 > 40

RANGE OF OUTPUT =41 OR MORE

VOLUME OF OUTPUT = 40 UNITS

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