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. At what volume of output would the two locations have the same total cost?

Question

Cassandra

Business

20 August, 19:48

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. At what volume of output would the two locations have the same total cost?

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Answers (1)

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Hadassah Garrett · Answer 1

The two location will have the same total cost for a volume of 40 items.

Explanation:

The cost function C for the alternatives in terms of the variable cost V and the fixed cost F, being x the selling items, can be expressed as:

C = F + V. x

Thus for the alternatives A and B the corresponding cost function Ca and Cb will be:

Ca = Fa + Va. x

Cb = Fb + Vb. x

Replacing the fixed and variables values for eahc alternatives:

Ca = 100,000 + 13,000x

Cb = 300,000 + 8,000x

By equalling the cost:

Ca = Cb

100,000 + 13,000*x = 300,000 + 8,000*x

13,000x - 8,000x = 300,000 - 100,000

5,000x = 200,000

x = 200,000 / 5,000 = 40

The cost functions will be equal for a 40 volume of items.