Given C=.02x^3+55x^2+1250, find the number of units, x, that produces the min avg cost per unit.

Question

anonymous · Answer

are you looking for the minimum value of that function, or is there something else going on?

anonymous · Answer

oh minimum "average value" not sure what that means

aum · Answer

I think you need to minimize C(x) / x

anonymous · Answer

ooh

anonymous · Answer

This is exactly how the question was phrased. I'm confused because I thought that in order to find the cost per unit (which I thought would be the first step), I would have to divide the equation by x.

aum · Answer

$$
C = .02x^3+55x^2+1250 \
\text{Cost per unit is: } \frac{C}{x}.  \text{  Let } U = \frac{C}{x}. \
U = 0.02x^2 + 55x + \frac{1250}{x} \
U' = 0.04x + 55 - \frac{1250}{x^2} = 0 \
$$

aum · Answer

Solve for x.

anonymous · Answer

I am so dreadfully horrible at math in general and these calculus topics are killing me. :) I need to see the steps, I think. If anyone can show me.

anonymous · Answer

Oh wow, aum! Thanks! So, I wasn't far off in my approach! That is reassuring. Seeing the steps REALLY helps! Thank you so much!

aum · Answer

You are welcome.  But you need to solve the above for x.
Are you allowed to use graphing/online calculators?

anonymous · Answer

Yes. I have a TI-89 Plus that I'm able to use.

anonymous · Answer

I knew I needed to solve for x, I just was unsure of how to get to that point and that is what threw me off.

aum · Answer

http://www.wolframalpha.com/input/?i=0.04x+%2B+55+-+1250%2Fx^2+%3D+0 Do you have answer choices or answer to this question?

aum · Answer

Since x is the number of units, it has to be rounded to the nearest whole number.