To determine the minimum number of shirts the retailer needs to sell to cover all its costs in a month, we need to take the following steps:
1. Understand the costs and revenues:
- Fixed monthly cost: \[tex]$500
- Marginal cost per shirt: \$[/tex]5
- Marginal benefit per shirt: \[tex]$10
2. Calculate the net profit per shirt:
- Net profit per shirt = Marginal benefit per shirt - Marginal cost per shirt
- Net profit per shirt = \$[/tex]10 - \[tex]$5 = \$[/tex]5
3. Find the minimum number of shirts that need to be sold to cover the fixed monthly cost:
- Let [tex]\( x \)[/tex] be the number of shirts that need to be sold.
- Total profit from selling [tex]\( x \)[/tex] shirts should equal the fixed cost.
- Net profit from [tex]\( x \)[/tex] shirts = Fixed monthly cost
- [tex]\( 5x = 500 \)[/tex]
4. Solve for [tex]\( x \)[/tex]:
- [tex]\( x = \frac{500}{5} \)[/tex]
- [tex]\( x = 100 \)[/tex]
Therefore, the retailer needs to sell a minimum of 100 shirts to cover all its costs in a month.
The correct answer is:
C. 100
