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). The one-time fixed costs will total $66,978. The variable costs will be $9.75 per book. The publisher will sell the finished product to bookstores at a price of $25 per book. How many books must the publisher produce and sell so that the production costs will equal the money from sales?

Answer 1

4,392 books

Explanation:

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). The one-time fixed costs will total $66,978. The variable costs will be $9.75 per book. The publisher will sell the finished product to bookstores at a price of $25 per book. How many books must the publisher produce and sell so that the production costs will equal the money from sales?

You are looking for the break even point (BEP) of sales. This is where sales equals fixed and variable costs.This is illustrated by the equation:

9.75x + 66,978 = 25x

subtract 9.75x from both sides:

9.75x + 66,978 - 9.75x = 25x - 9.75x

66,978 = 15.25x

divide both sides by 15.25:

66,978 /15.25 = 15.25x/15.25

x = 4,392 books

CHECK: when x = 4,392

9.75x + 66,978 = 25x

9.75(4,392) + 66,978 = 25(4,392)

42,822 + 66,978 = 109,800

109,800 = 109,800