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.