Erica wants to start a business printing custom logo T-shirts. The required equipment costs $2,560 and that each shirt will require $9.97 in materials. She estimates that she can sell 320 shirts in her first month of operations, and is hoping to recoup her equipment costs over that period.
For full marks your answer(s) should be rounded to the nearest cent.
a. What must her contribution margin be to achieve this?
Contribution Margin: 
$8.00
b. What selling price does this correspond to?
Selling Price: 
$17.97


Let's go through each part of the question to verify and confirm the calculations.

### Part (a): Contribution Margin

The **contribution margin** is the difference between the selling price per unit and the variable cost per unit (cost of materials in this case). The contribution margin helps cover fixed costs, such as the equipment cost.

The fixed cost for Erica's business is:
\[
\text{Fixed cost (equipment)} = \$2,560
\]
She estimates selling **320 shirts** in the first month, so she hopes to recover the equipment cost during this period. 

We are given that the **contribution margin per shirt** must be $8.00. To determine the total contribution margin from selling 320 shirts, we multiply:
\[
\text{Total contribution margin} = 320 \times 8.00 = 2,560
\]
Since the total contribution margin is equal to the fixed cost of the equipment, Erica will be able to cover her equipment cost if the contribution margin is $8.00 per shirt.

Thus, the contribution margin needed is **$8.00**.

### Part (b): Selling Price

We are asked to find the **selling price** that corresponds to this contribution margin. The selling price can be found by adding the contribution margin to the cost of materials per shirt.

The cost of materials per shirt is:
\[
\text{Cost of materials} = \$9.97
\]
The contribution margin is:
\[
\text{Contribution margin} = \$8.00
\]
The selling price is the sum of the cost of materials and the contribution margin:
\[
\text{Selling price} = 9.97 + 8.00 = 17.97
\]

Therefore, the selling price corresponds to **$17.97**.

### Summary:
- **Contribution Margin**: $8.00
- **Selling Price**: $17.97

Would you like further details or have any additional questions?

Here are 5 related questions to think about:
1. What if the estimated sales were 400 shirts instead of 320? How would that affect the contribution margin?
2. How would a reduction in the cost of materials affect the selling price to maintain the same contribution margin?
3. What selling price would Erica need if she wanted to recover the equipment cost in two months instead of one?
4. How would an increase in fixed costs affect the contribution margin requirement?
5. What would be the selling price if the contribution margin was increased to $10.00 per shirt?

**Tip**: Understanding contribution margin is key to determining how changes in costs or sales volume affect profitability.

Erica wants to start a business printing custom logo T-shirts. The required equipment costs $2,560 and that each shirt will require $9.97 in materials. She estimates that she can sell 320 shirts in her first month of operations, and is hoping to recoup her equipment costs over that period. For full marks your answer(s) should be rounded to the nearest cent.

a. What must her contribution margin be to achieve this?
Contribution Margin: $8.00

b. What selling price does this correspond to?
Selling Price: $17.97

Learn how to determine the contribution margin and selling price for a custom T-shirt business. This problem covers cost analysis, profit calculation, and contribution margin concepts. Suitable for students in Grades 9-12.

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