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Jenna is opening a clothing store. She plans to start by selling T-shirts. It costs her [tex]$7 for each shirt, $[/tex]2 for ink per shirt, and [tex]$0.10 a bag. Jenna also spends $[/tex]500 on rent, [tex]$40 on electricity, and $[/tex]30 on advertising each month.

What is the cost function for Jenna's clothing store per month?

A. [tex]\(C = 7.00n + 500\)[/tex]
B. [tex]\(C = 570n + 9.10\)[/tex]
C. [tex]\(C = 7.00n + 570\)[/tex]
D. [tex]\(C = 9.10n + 570\)[/tex]



Answer :

GinnyAnswer
To find the cost function for Jenna's clothing store per month, we need to account for both the variable costs (the costs that depend on the number of [tex]$T$[/tex]-shirts sold) and the fixed costs (the costs that do not depend on the number of [tex]$T$[/tex]-shirts sold).

Let's break down the costs:

1. Variable costs per [tex]$T$[/tex]-shirt:
- Cost per shirt: [tex]$\$[/tex]7[tex]$ - Cost for ink per shirt: $[/tex]\[tex]$2$[/tex]
- Cost for a bag per shirt: [tex]$\$[/tex]0.10[tex]$ Adding these together, the total variable cost per shirt is: \[ 7 + 2 + 0.10 = 9.10 \] 2. Fixed costs per month: - Rent: $[/tex]\[tex]$500$[/tex]
- Electricity: [tex]$\$[/tex]40[tex]$ - Advertising: $[/tex]\[tex]$30$[/tex]

Adding these together, the total fixed costs per month are:
[tex]\[ 500 + 40 + 30 = 570 \][/tex]

Now, the cost function, [tex]\( C \)[/tex], which gives the total monthly cost depending on the number of [tex]$T$[/tex]-shirts sold [tex]\( n \)[/tex], can be constructed as follows:
[tex]\[ C(t) = (\text{variable cost per shirt} \times \text{number of shirts}) + \text{fixed costs} \][/tex]
[tex]\[ C(t) = (9.10n) + 570 \][/tex]

So, the correct answer is:

D. [tex]\( C = 9.10n + 570 \)[/tex]

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