A small manufacturing company estimates that the total cost in dollars of producing x radios per day is given by the formula $C = 0.1 x ^ { 2 } + 20 x + 500$ . Find the number of units that will minimize the average cost.
A) 100
B) 147
C) 36
D) 71

Question

Quizplus · Accepted Answer

The average cost function is $ \frac{C}{x} = 0.1x + 20 + \frac{500}{x} $. To minimize it, take the derivative, set it to zero, and solve for $ x $. This yields $ x = 71 $.

A Small Manufacturing Company Estimates That the Total Cost in Dollars