Question

The total revenue received for the sale of x items is given by R(x) =25 ln (4x+3), while the total cost to produce x items is c(x)=x/3. Find the approx # of items that should be manufactured so profit, r(x)-c(x) is a max.

(round answer to nearest integer)

Answer 1

just my guess but wouldn't it be where rx and cx intersect?

Answer 2

or would it be profit =rx-cx and find the max of profit?

Answer 3

I'm not to sure...Would this help? How many items should be manufactured to maximize the profit?

Answer 4

create a profit function

P(x) = R(x) - C(x)

\[P(x) = 25 \ln(4x + 3) - \frac{x}{3}\]

differentiate

\[P'(x) = \frac{ 100}{4x + 3} - \frac{1}{3}\]

let P'(x) = 0

\[\frac{100}{4x + 3} - \frac{ 1}{3} = 0\]

\[\frac{100}{4x + 3} = \frac{1}{3} ....... 300 = 4x + 3\]

solve for x.