Question

At a small clothing company, the estimated average cost function for producing a new line of t-shirts is where x is the number of t-shirts produced, in thousands. is measured in dollars.

a) calculate the average cost of a t-shirt at a production level of 3000 pairs.
b) estimate the rate at which the average cost is changing at a production level of 3000 t-shirts.

Answer 1

Average total cost is calculated by dividing total cost by the quantity of output. To find the average cost for the production of 3000 t-shirts, divide the total production cost by 3000. Estimating the rate of change of the average cost at a production level of 3000 t-shirts requires the cost function and its derivative.

Step-by-step explanation:

To answer the student's question regarding average total cost and the rate of change of this cost at a specified production level, we need to apply some key economic principles. Average total cost is calculated by dividing the total cost by the quantity of output. For example, if a company has a total cost of $320 to produce 40 haircuts, the average total cost per haircut would be $8, calculated by dividing $320 by 40. These average costs often form a U-shaped curve on a graph. Understanding this concept, a company will profit if its average cost of production is lower than the market price.

To calculate the average cost of a t-shirt at a production level of 3000 t-shirts, you would divide the total cost of producing 3000 t-shirts by 3000. To estimate the rate at which the average cost is changing at that production level, would require knowing the specific cost function to find the derivative and then evaluate it at 3000 t-shirts.