To determine the break-even point for the publisher, we need to use the break-even formula:

$\text{Break-even point (in units)} = \frac{\text{Fixed Costs}}{\text{Price per Unit} - \text{Variable Cost per Unit}}$

Given dataTo determine the break-even point for the publisher, we need to use the break-even formula:

$\text{Break-even point (in units)} = \frac{\text{Fixed Costs}}{\text{Price per Unit} - \text{Variable Cost per Unit}}$

Given

• Fixed Costs: $\$54,000$
• Variable Costs per unit: $\$1.30$
• Price per unit (selling price): $\$15.00$

Now, we can plug these values into the formula:

$\text{Break-even point} = \frac{54,000}{15.00 - 1.30}$

Let's calculate this.

$\text{Break-even point} = \frac{54,000}{13.70} \approx 3,942.34$

Since the number of books must be a whole number, the publisher needs to produce and sell at least 3,943 books to break even.

Would you like a detailed breakdown or have further questions? Here are 5 related questions to explore:

1. What happens to the break-even point if the price per unit increases to $20?
2. How much profit will the publisher make if they sell 5,000 books?
3. What is the total cost for producing 3,943 books?
4. How does a change in fixed costs impact the break-even point?
5. What if variable costs increase to $2.00 per book?

Tip: Always factor in both fixed and variable costs when estimating the break-even point for a business.