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 $21,053 . The variable costs will be $9.50 per book. The publisher will sell the finished product to bookstores at a price of $18.75 per book. How many books must the publisher produce and sell so that the production costs will equal the money from sales?

Answer 1

2,276

Explanation:

The problem statement tells us that for b books, ...

production cost = 21053 +9.50b

sales = 18.75b

For these to be equal, we must have ...

production cost = sales

21053 +9.50b = 18.75b . . . . . substitute the expressions

21053 = 9.25b . . . . . . . . . . . . subtract 9.50*

21053/9.25 = b = 2276

The publisher must produce and sell 2,276 books to break even.

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* The value 9.25 is sometimes called the "contribution margin" of the book. It is the excess of the marginal sales over the marginal cost. As we see, dividing the fixed costs by this amount tells the number of sales required to break even, earn a total profit of zero, cover costs.