math

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)

? units

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1. average cost = totalcost/number of units

a(x) = C(x)/x
= 0.2(0.01x + 133/x)

minimum avg cost is where a'(x) = 0
a'(x) = .02(.01 - 133/x^2)
x = 10√133 = 115.3, so 115

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