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 $43,400. The variable costs will be $10 per book. The publisher will sell the finished product to bookstores at a price of $22.50 per book. How many books must the publisher produce and sell so that the production costs will equal the money from sales?

Answer 1

Let x be the number of books. The cost of printing x books is given by:

$C=10x+43400$

The revenue for selling x books is given:

$R=22.5x$

Equating the expressions and solving for x we have:

$\begin{gathered} 10x+43400=22.5x \\ 22.5x-10x=43400 \\ 12.5x=43400 \\ x=\frac{43400}{12.5} \\ x=3472 \end{gathered}$

Therefore, the publisher needs to produce and sell 3472 books to break even