Results 1 to 4 of 4

Math Help - Min average cost

  1. #1
    Newbie
    Joined
    Apr 2012
    From
    Texas
    Posts
    5

    Min average cost

    The cost function for a company is C(x)=2000+96x+4x3/2 where x represents thousands of units. Is there a production level that minimizes average cost?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member ignite's Avatar
    Joined
    Apr 2012
    From
    Kanpur,India
    Posts
    54
    Thanks
    12

    Re: Min average cost

    Average cost is defined by AC(x)=\frac{C(x)}{x}.
    In order to minimise AC(x) , find x_0 such that AC'(x_0)=0 and AC''(x_0)>0

    You will find that x_0=100 satisfies these conditions.
    Last edited by ignite; April 24th 2012 at 02:03 PM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Apr 2012
    From
    Texas
    Posts
    5

    Re: Min average cost

    I'm not sure I understand how to do that. I know its a simple problem I'm just lost.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member ignite's Avatar
    Joined
    Apr 2012
    From
    Kanpur,India
    Posts
    54
    Thanks
    12

    Re: Min average cost

    AC(x)=\frac{2000}{x}+96+4x^\frac{1}{2}
    Differentiating wrt x,
    AC'(x)=\frac{-2000}{x^2}+2x^\frac{-1}{2}
    AC'(x)=0 \Rightarrow 2x^\frac{-1}{2}=\frac{2000}{x^2} \Rightarrow x_0=100
    Similarly find AC''(x) and show that it's value at x_0=100 is greater than 0.

    If you are new to Differentiation,please read Derivative - Wikipedia, the free encyclopedia
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Finding minimum of average cost
    Posted in the Calculus Forum
    Replies: 2
    Last Post: January 7th 2011, 04:50 PM
  2. average cost
    Posted in the Business Math Forum
    Replies: 1
    Last Post: July 13th 2010, 10:42 AM
  3. Marginal and Average cost functions
    Posted in the Calculus Forum
    Replies: 2
    Last Post: December 14th 2009, 06:06 PM
  4. Average Cost - Limits!
    Posted in the Calculus Forum
    Replies: 2
    Last Post: November 15th 2009, 04:56 PM
  5. [SOLVED] Average minimum cost?
    Posted in the Calculus Forum
    Replies: 2
    Last Post: December 11th 2008, 08:35 PM

Search Tags


/mathhelpforum @mathhelpforum