Question

A company is considering two designs for a machine in its manufacturing line. The first, called machine A, will cost $200000 in fixed costs and will cost $80 per unit in variable costs, for each unit it produces. The second, called B, will cost $270000 in fixed costs and will cost $1 per unit in variable costs, for each unit it produces.
1. At what volume of production will the two machines cost the same? (In other words, what is the break-even point of the two machines?)

Answer 1

Answer:

Explanation:

Let x represent the volume of production for which the two machines cost the same.

The first, called machine A, will cost $200000 in fixed costs and will cost $80 per unit in variable costs, for each unit it produces. This means that the total cost of producing x units would be

200000 + 80x

The second, called B, will cost $270000 in fixed costs and will cost $1 per unit in variable costs, for each unit it produces. This means that the total cost of producing x units would be

270000 + x

Therefore, for the costs to be the same,

200000 + 80x = 270000 + x

270000 - 200000 = 80x - x

70000 = 79x

x = 70000/79 = 886.1 units