Suppose that the cost function for a product is given by C(x) =.002^3 -9x + 4000.?

Suppose that the cost function for a product is given by C(x) =.002^3 -9x + 4000.


Find the production level that will produce the minimum average cost per unit.





If you could show your work so I can get a better understanding of this problem it would help me.

Suppose that the cost function for a product is given by C(x) =.002^3 -9x + 4000.?
average cost: A(x) = C(x)/x.





minimum: A'(x) = [xC'(x) - C(x)] / x^2 = 0





then xC'(x) - C(x) = 0


C'(x) = C(x)/x


it occurs when the marginal cost equals the average cost.


solve for x .... x is the desired production level.


There is a problem with your function... it is not expressed properly... §





It is better to solve the equation: xC'(x) = C(x)


x *(.006x^2 - 9) = .002x^3 -9x + 4000





anyway... i believe its at x = 100.