posted by Renee on .
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.)
How many units?
C(x) is the total cost for x units, so the average cost is C(x)/x per unit.
A(x) = C(x)/x = 0.2(0.01x + 132/x)
to minimize A(x), find where dA/dx = 0
dA/dx = 0.2(0.01 - 132/x^2)
dA/dx = 0 when x = 20√33 = 114.89 = 115