Question

For the cost function in problem 2, find the value of x which minimized the average cost.

Answer 1

this was problme # 2


2) The cost of manufacturing x items is given by C(x) = 0.02x2 + 20x + 1800. Find the marginal cost function. Compuare the marginal cost at x = 20 to the actual cost of producing the 20th item.

Answer 2

and this is what i got for #2

C’(x) = 0.04x + 20
C’(20) = 0.04(20) + 20 = 20.8
and the actual cost of producing the 20th item.
c(20)-c(19) = 2208 - 2187,22 = 20.78
20.8 is very close to 20.78

Answer 3

@dumbcow @RadEn can u help?

Answer 4

to minimize avg cost , set derivative equal to 0
\[\frac{d}{dx}\frac{C(x)}{x} = \frac{d}{dx} (.02x +20+\frac{1800}{x}) = .02-\frac{1800}{x^{2}} = 0\]
\[\rightarrow .02x^{2} = 1800\]
\[x=300\]