Results 1 to 3 of 3

Math Help - total revenue from the sale

  1. #1
    Junior Member
    Joined
    Feb 2008
    Posts
    32
    Awards
    1

    total revenue from the sale

    20. Assume the total revenue from the sale of x items is given by
    R(x) = 39ln (8x+1), while the total cost to produce x items is C(x) = x/5. Findthe approximate number of items that should be manufactured so that profit, R(x) - C(x) , is maximum.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by ArmiAldi View Post
    20. Assume the total revenue from the sale of x items is given by
    R(x) = 39ln (8x+1), while the total cost to produce x items is C(x) = x/5. Findthe approximate number of items that should be manufactured so that profit, R(x) - C(x) , is maximum.
    The following is a slightly altered version of the replies given at this thread:

    Quote Originally Posted by mr fantastic View Post
    Differentiate the function P(x) = R(x) - C(x) = {\color{red}39}\ln (8x + 1) - \frac{x}{5} with respect to x. (You know how to differentiate this, right?)

    Put that derivative equal to zero to find the x-coordinate of the stationary point. Test the nature of this solution to prove that this stationary point is a maximum turning point.

    Then the value of x found is the answer to the question.
    Quote Originally Posted by mr fantastic View Post
    \frac{dP}{dx} = {\color{red}39} \left( \frac{8}{8x+1} \right) - \frac{1}{5} = {\color{red}\frac{312}{8x+1} - \frac{1}{5}}.

    \frac{dP}{dx} = 0 \Rightarrow 0 = \frac{{\color{red}312}}{8x+1} - \frac{1}{5} \Rightarrow \frac{{\color{red}312}}{8x+1} = \frac{1}{5} \Rightarrow {\color{red}1560} = 8x + 1 \Rightarrow ......

    The sign test shows that the value of x corresponds to a maximum turning point.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Joined
    Aug 2007
    From
    USA
    Posts
    3,111
    Thanks
    2
    You did not provide any inforamtion concerning what methods might be appropriate. Are you studying the Derivative and its applications? Can you find the first derivative of R(x) - C(x)? That will send you on your way to a solution.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Total cost, revenue, profit
    Posted in the Calculus Forum
    Replies: 2
    Last Post: October 28th 2010, 04:28 AM
  2. Replies: 1
    Last Post: November 24th 2009, 12:43 PM
  3. cost, revenue, marginal and total etc
    Posted in the Business Math Forum
    Replies: 2
    Last Post: May 13th 2009, 02:49 PM
  4. marginal cost/revenue to total cost / revenue
    Posted in the Advanced Math Topics Forum
    Replies: 1
    Last Post: May 9th 2009, 11:41 AM
  5. Total revenue from
    Posted in the Calculus Forum
    Replies: 2
    Last Post: February 29th 2008, 05:35 PM

Search Tags


/mathhelpforum @mathhelpforum