A publisher for a promising new novel figures fixed costs​ (overhead, advances,​ promotion, copy​ editing, typesetting, and so​ on) at ​$54,000​, and variable costs​ (printing, paper,​ binding, shipping) at ​$1.30 for each book produced. If the book is sold to distributors for ​$15 ​each, how many must be produced and sold for the publisher to break​ even?

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.

A publisher for a promising new novel figures fixed costs (overhead, advances, promotion, copy editing, typesetting, and so on) at $54,000, and variable costs (printing, paper, binding, shipping) at $1.30 for each book produced. If the book is sold to distributors for $15 each, how many must be produced and sold for the publisher to break even?

Discover how to calculate the break-even point for a publisher with fixed costs of $54,000 and variable costs of $1.30 per book. Learn the formula to determine the number of books that must be sold at $15 each to cover all costs. This problem illustrates key concepts in algebra and business math, suitable for high school students.

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