Minimum average cost
the cost of producing x units of a product is modeled by
c = 500 + 300x - 300 ln x, x ≥ 1.
(a) find the average cost function ć.
(b) find the minimum average cost analytically. use a graphing utility to confirm your result.

a)

b)

Step-by-step explanation:

Given the cost function as C(x):

a) Find the average cost function,

if C is the cost of selling x units, The Average can be denoted by:

this is the average cost function

b) The minimum average cost:

To find the minimum average cost, we'll have to differentiate the average cost function . and equate it to zero. (like finding the stationary point of any function)

now just simplify:

we've found the derivative of C(x), now to find the minimum we'll equate this derivative to zero.

and now solve for x

at this value of x the average cost is minimum.

This is the minimum average cost!

3

step-by-step explanation: