Suppose the total cost function for manufacturing a certain product C (x) is given by the function below, where C (x) is measured in dollars and x represents the number of units produced. Find the level of production that will minimize the average cost. (Round your answer to the nearest whole number.)

C (x) = 53 $

Step-by-step explanation: Incomplete question. From google the question is (paste)

Suppose the total cost function for manufacturing a certain product C (x) is given by the function below, where C (x) is measured in dollars and x represents the number of units produced. Find the level of production that will minimize the average cost. (Round your answer to the nearest whole number.)

C (x) = 0.2 (0.01x^2+133)

If C (x) = 0.2 (0.01x^2+133); and x numbers of produced units, the average cost is

Ca (x) = (0,002*x² + 26,6) / x ⇒ Ca (x) = 0.002*x + 26.6/x

Taking derivatives on both sides of the equation

Ca' (x) = 0.002 - 26.6/x² Ca' (x) = 0

0.002 - 26.6/x² = 0 ⇒ 0.002x² - 26.6 = 0

x² = 26.6 / 0.002

x = 115,33 ⇒ x = 115 units

And the level of production will be

C (x) = 0.2 (0.01x^2+133)

C (x) = 0.002*x² + 26,6

C (x) = 26.45 + 26,60

C (x) = 53.05 $

C (x) = 53 $