average cost

[bord3]

I need to find the average cost per item as function of q given that the Cost is C(q)=.04q^3-3q^2+75q+96. the 96 is throwing me off since i have to find the value of q that the average cost per item is smallest and what it is at that point (when i find a'(q) thanks

 

[tkhunny]

The '96' does not change the calculation of average cost. It remains Total Cost divided by Number of Units. C(q)/q.

As for the minimum, do you get to use calculus?

 

[bord3]

Yep I can use caculus for that. I guess what I'm lost on is when i take C(q)/q I get stuck with 96/q in my a(q) equation

 

[JeffM]

Yep I can use caculus for that. I guess what I'm lost on is when i take C(q)/q I get stuck with 96/q in my a(q) equation

I am a little confused about what a(q) is, but I PRESUME it is the function for average cost whereas C(q) is the function for total cost. Btw, if we are going to use capitals to represent functions, (a non-standard convention that I happen to like), let's make the average cost function A(q).

OK C(q) = .04q^3 - 3q^2 + 75q + 96.

So A(q) = [C(q) / q] = .04q^2 -3q + 75 + (96 / q). You are doing fine so far. (96 / q) BELONGS there.

Now to find the minimum of A(q) using calculus you do what? Can you do it?

And then what do you do?

PS What units are q in. Are they divisible or integers?

 

[tkhunny]

Have you considered rewriting as a negative exponent and applying the power rule, like all the rest of the tems?

\(\displaystyle \frac{96}{q}\;=\;96\cdot q^{-1}\)

Now what?