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 $50,052. The variable costs will be $9.75 per book. The publisher will sell the finished product to bookstores at a price of $20.50 per book. How many books must the publisher produce and sell so that the production costs will equal the money from sales?

Answer 1

To break even, the publishing company must produce and sell approximately 4,654 books, calculated by dividing the fixed costs by the difference between the selling price and the variable cost per book.

Step-by-step explanation:

The student is tasked with determining the break-even point for a publishing company's new book. To compute this, we will use the given fixed costs and variable costs per book. We know that the fixed costs are $50,052, which are incurred regardless of the number of books produced. The variable cost per book is $9.75, and the selling price per book is $20.50.

To find out how many books must be sold to cover all costs, we can set up the equation where total costs equal total sales. Let's use 'x' to represent the number of books.

Equation for the break-even point:

50,052 + 9.75x = 20.50x

Now, let's solve for 'x' to find the break-even quantity.

20.50x - 9.75x = 50,052
10.75x = 50,052
x = 50,052 / 10.75
x = 4,654 (rounded to the nearest book)

Therefore, the publisher must produce and sell approximately 4,654 books to break even.