Question 14

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

$46,966

. The variable costs will be

$11.50

per book. The publisher will sell the finished product to bookstores at a price of

$23

per book. How many books must the publisher produce and sell so that the production costs will equal the money from sales?

To solve this problem, we need to find the number of books the publisher must sell to break even, which means the total costs will equal the total revenue.

### Let:
- $ x $ = number of books sold.

### The total cost consists of:
1. **Fixed costs** = $46,966
2. **Variable costs per book** = $11.50

Thus, the total cost $ C(x) $ is given by:

\[
C(x) = 46,966 + 11.50x
\]

### The total revenue is the money earned from selling the books, where each book is sold at $23. Therefore, the total revenue $ R(x) $ is:

\[
R(x) = 23x
\]

### To find the break-even point, set the total cost equal to the total revenue:

\[
46,966 + 11.50x = 23x
\]

Now, solve for $ x $.

1. Subtract $ 11.50x $ from both sides:

\[
46,966 = 23x - 11.50x
\]

\[
46,966 = 11.50x
\]

2. Divide both sides by 11.50:

\[
x = \frac{46,966}{11.50} = 4083.13
\]

Since the number of books must be a whole number, the publisher must sell **4,084 books** to break even.

### Conclusion:
The publisher must sell **4,084 books** to cover all the production costs.

---

Would you like a more detailed explanation or have any further questions?

Here are 5 questions related to this problem:
1. What is the concept of fixed costs and variable costs in business?
2. How would the break-even point change if the variable costs per book increased?
3. What happens if the selling price per book decreases?
4. How can the publisher increase profits after reaching the break-even point?
5. How does the formula for break-even analysis apply in other industries?

**Tip:** Always separate fixed and variable costs when calculating the break-even point. It helps in understanding how different factors influence the overall cost.

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 $46,966. The variable costs will be $11.50 per book. The publisher will sell the finished product to bookstores at a price of $23 per book. How many books must the publisher produce and sell so that the production costs will equal the money from sales?

Discover how to calculate the break-even point for a small publishing company with fixed costs of $46,966 and variable costs of $11.50 per book. Learn how to set up the necessary equations and find out that the publisher needs to sell 4,084 books to cover all production costs.

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