Let's determine the cost function for Jenna's clothing store. The cost function is a mathematical expression that represents all costs incurred by Jenna, both fixed and variable, as a function of the number of T-shirts [tex]\(n\)[/tex] she sells.
1. Variable Costs:
- The cost per shirt is [tex]\(\$ 7\)[/tex].
- The cost for ink per shirt is [tex]\(\$ 2\)[/tex].
- The cost for a bag per shirt is [tex]\(\$ 0.10\)[/tex].
To find the total variable cost per shirt, we need to add these costs together:
[tex]\[
7 + 2 + 0.10 = 9.10
\][/tex]
So, the variable cost per shirt is [tex]\(\$ 9.10\)[/tex].
2. Fixed Costs:
- The rent is [tex]\(\$ 500\)[/tex] per month.
- The electricity cost is [tex]\(\$ 40\)[/tex] per month.
- The advertising cost is [tex]\(\$ 30\)[/tex] per month.
Adding these fixed costs together, we get:
[tex]\[
500 + 40 + 30 = 570
\][/tex]
So, the total fixed costs per month are [tex]\(\$ 570\)[/tex].
3. Cost Function:
The total cost function combines the fixed costs and the variable costs, which depend on the number of T-shirts sold. The cost function [tex]\(C\)[/tex] is given by:
[tex]\[
C = (\text{variable cost per shirt} \times n) + \text{fixed costs}
\][/tex]
Substituting in the values we calculated, the cost function is:
[tex]\[
C = 9.10n + 570
\][/tex]
Therefore, the correct cost function for Jenna's clothing store per month is:
[tex]\[
\boxed{C = 9.10n + 570}
\][/tex]
So, the correct answer is A. [tex]\(\mathbf{C=9.10n + 570}\)[/tex].
