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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.)

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Answer:

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 $

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