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. What selling price should the club set to break even after selling just 50 shirts
Answers
GPT-4o mini
To determine how many shirts the club needs to sell to break even, we first need to identify the total cost and the revenue from selling shirts.
**Break-even analysis:**
1. **Fixed Costs (FC)**: $400
2. **Variable Cost per Shirt (VC)**: $9
3. **Selling Price per Shirt (SP)**: $15
The total cost (TC) for selling \( x \) shirts can be calculated as:
\[
\text{Total Cost} = \text{Fixed Costs} + (\text{Variable Cost per Shirt} \times \text{Number of Shirts})
\]
So,
\[
\text{Total Cost} = 400 + 9x
\]
The total revenue (TR) from selling \( x \) shirts is:
\[
\text{Total Revenue} = \text{Selling Price per Shirt} \times \text{Number of Shirts}
\]
Thus,
\[
\text{Total Revenue} = 15x
\]
To break even, total revenue must equal total cost:
\[
15x = 400 + 9x
\]
Now, subtract \( 9x \) from both sides:
\[
15x - 9x = 400
\]
\[
6x = 400
\]
Now, divide both sides by 6:
\[
x = \frac{400}{6} \approx 66.67
\]
Since you cannot sell a fraction of a shirt, the club would need to sell **at least 67 shirts** to break even.
**Selling Price for Breakeven After Selling 50 Shirts:**
To find out what selling price the club should set to break even after selling just 50 shirts, we need to set the total revenue equal to the total cost for 50 shirts.
Total Cost for 50 shirts:
\[
\text{Total Cost} = 400 + 9 \times 50 = 400 + 450 = 850
\]
Total Revenue for 50 shirts, denoted as \( x \):
\[
\text{Total Revenue} = x \times 50
\]
Setting total revenue equal to total cost for breakeven:
\[
50x = 850
\]
Dividing both sides by 50:
\[
x = \frac{850}{50} = 17
\]
Therefore, the selling price to break even after selling just 50 shirts should be set at **$17**.
In summary, the club needs to sell **67 shirts** to break even, and to break even after selling just **50 shirts**, the selling price should be **$17**.
**Break-even analysis:**
1. **Fixed Costs (FC)**: $400
2. **Variable Cost per Shirt (VC)**: $9
3. **Selling Price per Shirt (SP)**: $15
The total cost (TC) for selling \( x \) shirts can be calculated as:
\[
\text{Total Cost} = \text{Fixed Costs} + (\text{Variable Cost per Shirt} \times \text{Number of Shirts})
\]
So,
\[
\text{Total Cost} = 400 + 9x
\]
The total revenue (TR) from selling \( x \) shirts is:
\[
\text{Total Revenue} = \text{Selling Price per Shirt} \times \text{Number of Shirts}
\]
Thus,
\[
\text{Total Revenue} = 15x
\]
To break even, total revenue must equal total cost:
\[
15x = 400 + 9x
\]
Now, subtract \( 9x \) from both sides:
\[
15x - 9x = 400
\]
\[
6x = 400
\]
Now, divide both sides by 6:
\[
x = \frac{400}{6} \approx 66.67
\]
Since you cannot sell a fraction of a shirt, the club would need to sell **at least 67 shirts** to break even.
**Selling Price for Breakeven After Selling 50 Shirts:**
To find out what selling price the club should set to break even after selling just 50 shirts, we need to set the total revenue equal to the total cost for 50 shirts.
Total Cost for 50 shirts:
\[
\text{Total Cost} = 400 + 9 \times 50 = 400 + 450 = 850
\]
Total Revenue for 50 shirts, denoted as \( x \):
\[
\text{Total Revenue} = x \times 50
\]
Setting total revenue equal to total cost for breakeven:
\[
50x = 850
\]
Dividing both sides by 50:
\[
x = \frac{850}{50} = 17
\]
Therefore, the selling price to break even after selling just 50 shirts should be set at **$17**.
In summary, the club needs to sell **67 shirts** to break even, and to break even after selling just **50 shirts**, the selling price should be **$17**.