Total Cost Function

yoursource · Jun 4, 2008

Not sure how to go about this problem, I got started a little bit. It's for practice, but I'm sure it will show up on my assignment and then test too.

A total cost function is given (in thousands of dollars) by C(q)= 1.1^3 - 5q^2 + 20q, where q is in thousands and 0 is less than or equal to q which is less than or equal to 5.

a) Find the average cost function and determine when it is minimized.
I believe the answer to this is AC(q) =(1.1^3 - 5q^2 + 20q)/q (is that much right?) then I don't know how to determine when it is minimized.

b.) If the revenue function is given by R(q) =14q, determine what values of q (if any) will maximize the profit.

c.) Repeat part (b) with R(q) = .01^2 + 11q

Hopefully somebody will be able to walk me through this entire problem to the answer. It will help come assignment and test time. I have a few more assignments and tests left to graduate from college and I'm trying very hard (and getting discouraged). Thanks for the assistance!

stapel · Jun 4, 2008

yoursource said:
Hopefully somebody will be able to walk me through this entire problem to the answer.

So neither your book nor your instructor covered this at all?!? Ouch! :shock:

It will help if you can provide at least some context. Are you familiar with algebra at all? Have you ever taken any calculus at all? If so, are you familiar with "derivatives"? And so forth.

yoursource said:
A total cost function is given (in thousands of dollars) by C(q)= 1.1^3 - 5q^2 + 20q, where q is in thousands and 0 is less than or equal to q which is less than or equal to 5.

a) Find the average cost function and determine when it is minimized.

Assuming that the average cost function AC measures the average cost of one unit, given a production run of "q" units, the average (per-unit) cost would be found by dividing the total cost A by the number of units q. If this function is defined to mean something else, then naturally it would probably be found by some other method.

The method(s) available for finding the minimum will depend upon what the function is, and what topics you have studied (or whether you're just supposed to work from a picture on a graphing calculator). Did your instructor provide any direction on this?

yoursource said:
b.) If the revenue function is given by R(q) =14q, determine what values of q (if any) will maximize the profit.

If the revenue function measures the total income R from "q" units sold (as we're assuming all units produced are then sold), then the existance of any max/min point is fairly clear -- if you've ever done any graphing at all. Have you, or do you need lessons on this topic?

yoursource said:
c.) Repeat part (b) with R(q) = .01^2 + 11q

I'm not sure why they wrote "0.01[sup:3mvlbwlq]2[/sup:3mvlbwlq]", instead of just "0.0001"...? But, since this is just a straight line, exactly as in part (b), the solution "method" would be the same. :wink:

Eliz.

yoursource · Jun 4, 2008

stapel said:
yoursource said:

Hopefully somebody will be able to walk me through this entire problem to the answer.

Click to expand...

So neither your book nor your instructor covered this at all?!? Ouch! :shock:

It will help if you can provide at least some context. Are you familiar with algebra at all? Have you ever taken any calculus at all? If so, are you familiar with "derivatives"? And so forth. Yes I"m familar with some derivatives, but have problems when they're too complicated

yoursource said:

A total cost function is given (in thousands of dollars) by C(q)= 1.1^3 - 5q^2 + 20q, where q is in thousands and 0 is less than or equal to q which is less than or equal to 5.

a) Find the average cost function and determine when it is minimized.

Click to expand...

Assuming that the average cost function AC measures the average cost of one unit, given a production run of "q" units, the average (per-unit) cost would be found by dividing the total cost A by the number of units q. If this function is defined to mean something else, then naturally it would probably be found by some other method.

The method(s) available for finding the minimum will depend upon what the function is, and what topics you have studied (or whether you're just supposed to work from a picture on a graphing calculator). Did your instructor provide any direction on this? We aren't working from a picture on a calculator, we're not allowed graphing calculators. This is a calc course I'm in and we've studied derivatives inflection, maxima and minima, and the like.

yoursource said:

b.) If the revenue function is given by R(q) =14q, determine what values of q (if any) will maximize the profit.

Click to expand...

If the revenue function measures the total income R from "q" units sold (as we're assuming all units produced are then sold), then the existance of any max/min point is fairly clear -- if you've ever done any graphing at all. Have you, or do you need lessons on this topic? I have but I'm not really sure where you're going with this, I'm so rusty.

yoursource said:

c.) Repeat part (b) with R(q) = .01^2 + 11q

Click to expand...

I'm not sure why they wrote "0.01[sup:2qhif8fb]2[/sup:2qhif8fb]", instead of just "0.0001"...? But, since this is just a straight line, exactly as in part (b), the solution "method" would be the same. :wink: I messed this up, it should be 0.01q^2, not .01^2

Eliz.

stapel · Jun 4, 2008

yoursource said:
I"m familar with some derivatives, but have problems when they're too complicated

To help solve this problem, try working through all of the exercises whose answers are in the back of the book, and perhaps working with a personal tutor who can watch you as you work. With that sort of "on the spot" guidance, you can learn how to do the algebra related to applying the various plug-n-chug formulas in calculus, such as the Product Rule. :idea:

yoursource said:
This is a calc course I'm in and we've studied derivatives inflection, maxima and minima, and the like.

Okay; then use derivatives and the First and Second Derivative Tests to find the information requested.

stapel said:
the existance of any max/min point is fairly clear -- if you've ever done any graphing at all.

yoursource said:
I have but I'm not really sure where you're going with this

Graph the linear function y = 16x, just like you learned back in algebra. What does this graph tell you about max or min points? :wink:

yoursource said:
I messed this up, it should be 0.01q^2, not .01^2

Okay; then find the vertex, like they taught you back in algebra; or else find the derivative (using the Power Rule) and then the max/min point (using the derivative tests, and/or the graph), like they've shown you in calculus.

Eliz.

Total Cost Function

yoursource

New member

stapel

Super Moderator

yoursource

New member

stapel

Super Moderator