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 $41,870 The variable costs will be $12.50 per book The publisher will sell the finished product to bookstores at a price of $25.75 per book. How many books must the publisher produce and sell so that the production costs will equal the money from sales?

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 $41,870 The variable costs will be $12.50 per book  The publisher will sell the finished product to bookstores at a price of $25.75 per book. How many books must the publisher produce and sell so that the production costs will equal the money from sales?

GPT 3.5 · Answer

Let's represent the number of books the publisher must produce and sell as "x".

The one-time fixed costs total $41,870.

The variable costs are $12.50 per book, so the total variable costs will be 12.50x.

The publisher will sell each book to bookstores for $25.75, so the total revenue from sales will be 25.75x.

To find the number of books the publisher must produce and sell to break even, we need to find the value of "x" that satisfies the equation:

41,870 + 12.50x = 25.75x

To solve for "x", let's isolate the variable terms on one side:

41,870 = 25.75x - 12.50x

Combine like terms:

41,870 = 13.25x

Divide both sides by 13.25:

x = 41,870 / 13.25

Simplify the expression:

x ≈ 3,159.25

Since the publisher cannot produce and sell a fraction of a book, the publisher must produce and sell at least 3,160 books in order for the production costs to equal the money from sales.