To determine the break-even point for the bookstore, we need to understand the costs and revenues involved. The break-even point is the number of books that must be sold so that the total revenue matches the total cost (i.e., the bookstore does not make a loss or a profit).
Here's a detailed, step-by-step solution:
1. Fixed Cost:
The bookstore has a fixed cost of \[tex]$80 per day, which is the cost just to keep it open.
2. Variable Cost:
The bookstore spends \$[/tex]15 per book sold.
3. Selling Price:
Each book is sold for \[tex]$23.
4. Net Revenue per Book:
The profit made on each book sold is given by subtracting the cost per book from the selling price.
\[
\text{Profit per book} = \text{Selling Price} - \text{Cost per Book} = 23 - 15 = \$[/tex]8
\]
5. Break-even Calculation:
To find the break-even point, we need to find the number of books sold (denoted by [tex]\( n \)[/tex]) such that the total profit from selling these books equals the fixed cost of \$80.
The equation representing this is:
[tex]\[
\text{Fixed Cost} = \text{Profit per Book} \times n
\][/tex]
Plugging in the known values:
[tex]\[
80 = 8 \times n
\][/tex]
6. Solve for [tex]\( n \)[/tex]:
[tex]\[
n = \frac{80}{8} = 10
\][/tex]
Therefore, the break-even point is at [tex]\( n = 10 \)[/tex]. This means the bookstore must sell 10 books to cover all its costs and start making a profit.
The correct answer is:
A. [tex]\( n = 10 \)[/tex]
