Asmall 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?

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.