Suppose c(x) $c ( x ) = x ^ { 3 } - 16 x ^ { 2 } + 20,000 x$ x is the cost of manufacturing x items. Find a production level that will minimize the average cost of making x items.
A) 8 items
B) 10 items
C) 9 items
D) 7 items

Question

Quizplus · Accepted Answer

To minimize the average cost, we need to find the critical points of the average cost function $ \frac{c(x)}{x} = x^2 - 16x + 20000 $. Taking the derivative and setting it to zero, we find that the critical point is at x = 8.

Suppose C(x) c(x)=x3−16x2+20,000xc ( x ) = x ^ { 3 } - 16 x ^ { 2 } + 20,000 xc(x)=x3−16x2+20,000x

Suppose C(x) $c ( x ) = x ^ { 3 } - 16 x ^ { 2 } + 20,000 x$