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$65,054, and the variable costs will be$8.25per book. With the other method, the one-time fixed costs will total$12,539, and the variable costs will be$19.50per book. For how many books produced will the costs from the two methods be the same?

Answer 1

The number of books produced at which the costs from the two methods be the same is 4668 books

Explanation:

Here, we have

For the first production method

Fixed cost = $65,054 and variable cost per book = $8.25

For the second production method

Fixed cost = $12,539 and variable cost per book = $19.50

Therefore, let the number of books at which the to methods cost the same be M, we then have

$65,054 + $8.25 × M = $12,539 + $19.50× M

Which gives

$65,054 - $12,539 = $19.50× M - $8.25 × M

$52515 = $11.25 × M

M = $52515/$11.25 = 4668 books.