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This problem is about finding the break-even point, where the production costs equal the sales revenue.

### Variables:
- **Fixed Costs (F)** = $21,629
- **Variable Cost per book (V)** = $12.75
- **Price per book (P)** = $23.50

### Let $ x $ represent the number of books that need to be sold to break even.

### Equation for total cost:
\[ \text{Total Cost} = \text{Fixed Costs} + (\text{Variable Cost per book} \times x) \]
\[ \text{Total Cost} = 21,629 + 12.75x \]

### Equation for total revenue:
\[ \text{Total Revenue} = \text{Price per book} \times x \]
\[ \text{Total Revenue} = 23.50x \]

### Break-even condition:
At break-even, Total Cost = Total Revenue:
\[
21,629 + 12.75x = 23.50x
\]

### Solving for $ x $:
\[
21,629 = (23.50 - 12.75)x
\]
\[
21,629 = 10.75x
\]
\[
x = \frac{21,629}{10.75}
\]
Let me calculate this value.

The publisher must produce and sell **2,012 books** to break even, meaning the production costs will equal the money from sales.

Would you like further details or have any questions? 

Here are some related questions you might find useful:
1. What happens if the price per book increases?
2. How does a change in variable costs affect the break-even point?
3. How would the break-even point change with additional fixed costs?
4. What if the publisher wants to make a profit? How many books would they need to sell?
5. How can the publisher reduce the break-even point?

**Tip**: Reducing either fixed or variable costs can lower the break-even point, helping the publisher reach profitability sooner.

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 $21,629. The variable costs will be $12.75 per book. The publisher will sell the finished product to bookstores at a price of $23.50 per book. How many books must the publisher produce and sell so that the production costs will equal the money from sales?

Learn how to calculate the break-even point for a publishing company planning to publish a new book. The fixed costs are $21,629, variable costs per book are $12.75, and the selling price per book is $23.50. This step-by-step guide helps you determine how many books must be sold to break even.

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