At Westonci.ca, we make it easy to get the answers you need from a community of informed and experienced contributors. Get immediate and reliable answers to your questions from a community of experienced experts on our platform. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.
Sagot :
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]
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]
Thank you for visiting our platform. We hope you found the answers you were looking for. Come back anytime you need more information. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.