Question

A small publishing company is planning to publish a new book. The production costs will include one-time fixed costs (such as editing) and variable costs (such as printing). There are two production methods it could use. With one method, the one-time fixed costs will total $18,853 , and the variable costs will be $19.75 per book. With the other method, the one-time fixed costs will total $64,853 , and the variable costs will be $8.25 per book. For how many books produced will the costs from the two methods be the same?

Answer 1

Production cost = one time cost + variable costs

Let the number of published books for equal production costs be n.

Using the first method:
production cost = 18,853 + 19.75n
Using the second method:
production cost = 64,853 + 8.25n

Now, we need the two production costs to be equal:
18,853 + 19.75n = 64,853 + 8.25n

Solve for n as follows:
18,853 + 19.75n = 64,853 + 8.25n
19.75n - 8.25n = 64,853 - 18,853
11.5n = 46000
n = 46000/11.5
n = 4000 books