A company estimates that the cost in dollars of producing x units of a certain product is given by the model
C = 800 + 0.4x + 0.02x^2 + 0.0001x^3
Find the production level that minimizes the average cost per unit.
I first divided the equation by X in order to get
_
C = C/x = .0001x^2 + .02x +.4 + 800/x
I then took the first derivitave of this equation and got
f'(x) = .0002x + .02 + -800/x^2
I set the equation to zero and this is where I am having trouble. I couldn't find the zeros so I decided to try Newton's Method but I seem to be unable to find an answer. I'm not sure if I did something wrong in setting up my equations or if I am doing Newton's Method wrong. THanks!
C = 800 + 0.4x + 0.02x^2 + 0.0001x^3
Find the production level that minimizes the average cost per unit.
I first divided the equation by X in order to get
_
C = C/x = .0001x^2 + .02x +.4 + 800/x
I then took the first derivitave of this equation and got
f'(x) = .0002x + .02 + -800/x^2
I set the equation to zero and this is where I am having trouble. I couldn't find the zeros so I decided to try Newton's Method but I seem to be unable to find an answer. I'm not sure if I did something wrong in setting up my equations or if I am doing Newton's Method wrong. THanks!
