This problem asks for the break-even point, where total costs equal total revenue. Let's break it down:

Given:

• Fixed costs = $71,946
• Variable cost per book = $9.25
• Selling price per book = $25

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

1. Total Costs: Total costs include both fixed and variable costs. The total cost is given by: $\text{Total Cost} = \text{Fixed Cost} + (\text{Variable Cost per book} \times x)$ Substituting values: $\text{Total Cost} = 71,946 + 9.25x$

2. Total Revenue: The total revenue is given by the selling price per book times the number of books sold: $\text{Total Revenue} = 25x$

3. Break-even Point: To find the break-even point, we set total revenue equal to total costs: $25x = 71,946 + 9.25x$

4. Solve for $x$: First, subtract $9.25x$ from both sides: $25x - 9.25x = 71,946$ Simplify: $15.75x = 71,946$ Now, divide both sides by 15.75: $x = \frac{71,946}{15.75} = 4,569.27$

Since the number of books must be a whole number, the publisher needs to sell 4,570 books to break even.

Would you like further explanation or clarification on any part? Here are 5 related questions to expand on this:

1. How does the fixed cost affect the break-even point?
2. What would happen if the variable cost per book increased?
3. How many books would need to be sold if the selling price changed to $30 per book?
4. Can the break-even point be reduced by lowering the fixed costs? How?
5. How does a change in both fixed and variable costs impact the break-even point?

Tip:

To minimize the break-even point, consider either increasing the selling price or reducing production costs (fixed or variable).