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We need to determine the number of books that must be sold for the publisher to break even. To do this, we use the break-even point formula:

\[
\text{Total Revenue} = \text{Total Costs}
\]

### Definitions:
- **Fixed Costs (FC):** The one-time fixed cost is $44,256.
- **Variable Costs (VC):** The variable cost per book is $8.50.
- **Price per book (P):** The selling price per book is $20.50.

### Let $ x $ be the number of books to be produced and sold.

### Total Costs:
\[
\text{Total Costs} = \text{Fixed Costs} + \text{Variable Costs} \times x
\]
\[
\text{Total Costs} = 44,256 + 8.50x
\]

### Total Revenue:
\[
\text{Total Revenue} = \text{Price per book} \times x
\]
\[
\text{Total Revenue} = 20.50x
\]

### Break-even condition:
\[
\text{Total Revenue} = \text{Total Costs}
\]
\[
20.50x = 44,256 + 8.50x
\]

### Solve for $ x $:
\[
20.50x - 8.50x = 44,256
\]
\[
12x = 44,256
\]
\[
x = \frac{44,256}{12} = 3,688
\]

### Conclusion:
The publisher must produce and sell **3,688 books** to break even.

Would you like more details or have any questions about this solution?

Here are 5 related questions:
1. What happens if the fixed costs increase?
2. How would a change in the selling price affect the break-even point?
3. Can the break-even point be lowered by reducing variable costs?
4. What is the profit if the publisher sells 5,000 books?
5. How would a discount on the books affect overall revenue?

**Tip:** When calculating the break-even point, always separate fixed and variable costs clearly for easier adjustments.

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 $44,256. The variable costs will be $8.50 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?

Learn how to calculate the break-even point for a publishing company that incurs fixed costs of $44,256 and variable costs of $8.50 per book. The company sells each book for $20.50. This problem involves algebraic calculations for determining the number of books needed to cover total production costs.

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