The cost function for the manufacture of mp3 players is Dollars.
a) How many mp3 players should be manufactures to minimize the cost?
b) What is the resulting average cost of an mp3 player?
Note: X= number of mp3 manufactures
I'm stumped. This question was given to me by my Finite Maths teacher under the topic of 'Application of Derivatives', and I don't seem to be making any progress. I'd appreciate it if you guys could help me out
EDIT: Correction in the problem
When Massachusetts Cowboy say "divide it by x", he is referring to C(x) for the value of x you found in (a). Find the cost of manufacturing that number of mpe players and divide by that value of x.
A friend of mine told me to do this:
The cost function tells you the overall cost of making the units. What you need is the cost per unit function, which is (25000+20x+0.001x^2)/x.
That has a derivative (20 + 0.002 x)/x - (25000 + 20 x + 0.001 x^2)/x^2 which has solutions at -5000 and 5000.
So to minimise costs, manufacture 5000. And if you plug 5000 back into the equation then the overall cost is 25000 + (20 * 5000) + (0.001*(5000^2)) = 25000 + 100000 + 25000 = 150000, or cost per unit of 30.
What do you guys think?