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.

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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.