Question

A club wants to sell a shirt for $15, the fixed cost is $400 and the variable cost is $9. How many shirts would the club need to sell to break even

Answer 1

To calculate the break-even point, we need to determine how many shirts need to be sold such that total revenue equals total costs.

1. **Define the costs and revenues:**
- Fixed Costs (FC) = $400
- Variable Cost per shirt (VC) = $9
- Selling Price per shirt (SP) = $15

2. **Calculate the profit per shirt:**
\[
\text{Profit per shirt} = \text{Selling Price} - \text{Variable Cost} = 15 - 9 = 6
\]

3. **Set up the break-even equation:**
At break-even, total revenue equals total costs:
\[
\text{Total Revenue} = \text{Total Costs}
\]
\[
(\text{Selling Price} \times \text{Number of Shirts}) = \text{Fixed Costs} + (\text{Variable Cost} \times \text{Number of Shirts})
\]
Substituting the values:
\[
15x = 400 + 9x
\]
where \( x \) is the number of shirts sold.

4. **Solve for \( x \):**
\[
15x - 9x = 400
\]
\[
6x = 400
\]
\[
x = \frac{400}{6} \approx 66.67
\]

Since you cannot sell a fraction of a shirt, round up to the nearest whole number. Therefore, the club needs to sell at least **67 shirts** to break even.