Results 1 to 3 of 3

Math Help - minimizing marginal cost help

  1. #1
    Member
    Joined
    Dec 2009
    Posts
    97

    minimizing marginal cost help

    the marginal cost c (in dollars) of manufacturing x cell phones in thousands is given by
    C (x) = 5x^2-200x + 4000

    A. how many cel phones should be manufactured to minimize the marginal cost ?

    B. what is the minimum marginal cost?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,407
    Thanks
    1294
    Differentiate the function,

    Set the derivative equal to 0 and solve for x.

    Substitute this value of x into your function to get the minimum cost.


    If you're not allowed to use a Calculus solution, then complete the square to get the function into turning point form. The turning point is the minimum value.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member eumyang's Avatar
    Joined
    Jan 2010
    Posts
    278
    Thanks
    1
    Quote Originally Posted by Prove It View Post
    If you're not allowed to use a Calculus solution, then complete the square to get the function into turning point form. The turning point is the minimum value.
    Interesting -- I call this "vertex form."

    \begin{aligned}<br />
C(x) &= 5x^2 - 200x + 4000 \\<br />
&= 5(x^2 - 40x) + 4000 \\<br />
&= 5(x^2 - 40x + 400 - 400) + 4000 \\<br />
&= 5(x^2 - 40x + 400) - 2000 + 4000 \\<br />
&= 5(x - 20)^2 + 2000<br />
\end{aligned}<br />

    Since the x^2 term has a positive coefficient, the vertex, which is (20, 2000), is a minimum. Now you can answer the question.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Minimizing Cost
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 16th 2011, 10:22 AM
  2. Minimizing Cost
    Posted in the Calculus Forum
    Replies: 1
    Last Post: December 3rd 2009, 08:25 AM
  3. Marginal Cost/Demand and Cost
    Posted in the Calculus Forum
    Replies: 4
    Last Post: November 4th 2009, 06:45 PM
  4. Marginal revenue and the marginal cost
    Posted in the Business Math Forum
    Replies: 1
    Last Post: November 28th 2008, 05:22 PM
  5. minimizing cost
    Posted in the Business Math Forum
    Replies: 1
    Last Post: February 20th 2007, 07:57 PM

Search Tags


/mathhelpforum @mathhelpforum