To find the cost function for Jenna's clothing store per month, we need to consider both the variable costs and the fixed costs associated with her business.
1. Variable Costs: These are costs that change with the number of T-shirts produced.
- Cost per shirt: [tex]$\$[/tex]7[tex]$
- Ink per shirt: $[/tex]\[tex]$2$[/tex]
- Bag per shirt: [tex]$\$[/tex]0.10[tex]$
To find the total variable cost per T-shirt, we sum these costs:
\[
\text{Total variable cost per shirt} = 7 + 2 + 0.10 = 9.10
\]
2. Fixed Costs: These costs do not change with the number of T-shirts produced. They remain constant each month.
- Rent: $[/tex]\[tex]$500$[/tex]
- Electricity: [tex]$\$[/tex]40[tex]$
- Advertising: $[/tex]\[tex]$30$[/tex]
To find the total fixed costs per month, we sum these costs:
[tex]\[
\text{Total fixed costs} = 500 + 40 + 30 = 570
\][/tex]
Combining these, the total cost function [tex]\(C\)[/tex] for Jenna's store, where [tex]\(n\)[/tex] represents the number of T-shirts sold, is given by the sum of the variable costs per shirt multiplied by the number of shirts sold and the total fixed costs:
[tex]\[
C = 9.10n + 570
\][/tex]
So, the correct option is:
A. [tex]\( C = 9.10n + 570 \)[/tex]
