Question

Suppose the total cost of producing T-shirts can be represented as 2+10q². What is the average cost when producing 8 T-shirts?

Answer 1

The average cost of producing 8 T-shirts, using the cost function 2+10q², is calculated by substituting q with 8 to find the total cost, which is then divided by the quantity produced, resulting in an average cost of $80.25 per T-shirt.

Step-by-step explanation:

To calculate the average cost of producing T-shirts when 8 T-shirts are made, we'll use the given cost function 2+10q², where q is the quantity of T-shirts produced. We plug in 8 for q to get the total cost for producing 8 T-shirts:

1. Substitute q with 8 in the cost function: Total Cost = 2 + 10(8)².
2. Calculate the value of 8², which is 64.
3. Multiply 10 by 64 to get 640.
4. Add the constant term 2 to 640, getting a total cost of 642.
5. To find the average cost, divide the total cost of 642 by the number of T-shirts produced (8): Average Cost = 642 / 8.
6. Calculate the division to get the average cost per T-shirt, which is 80.25.

The average cost of producing 8 T-shirts is therefore $80.25 per T-shirt.