Results 1 to 10 of 10

Math Help - Revenue function and Marginal revenue function of P

  1. #1
    Newbie
    Joined
    Mar 2011
    Posts
    5

    Revenue function and Marginal revenue function of P

    p = 8 - 2LNx

    Find the revenue function and the marginal revenue function

    i got these:

    revenue function R(x)= 6-2log(x)
    marginal revenue (r') = -2/x

    Is that correct?

    and i have no idea how to start these problems based on the same numbersHeadbang)


    (b) (2 pts) Find the number (in thousands) of hot dogs that can be sold during one
    game such that the marginal revenue is zero.
    (c) (2 pts) Find the instantaneous rate of change of the marginal revenue.
    (xc) (2 pts) Use part (c) to justify that the answer in part (b) generates the maximum revenue. What is the maximum revenue?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    Mar 2011
    Posts
    5
    ok now i believe revenue function will be 8x-2xlog(x)
    and marginal revenue function should be 6-2log(x)
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member
    Joined
    Nov 2010
    From
    Hong Kong
    Posts
    255
    1. What is p?
    2. How did you arrive at your revenue function? ie what operation did you do on p function and why?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Mar 2011
    Posts
    5
    P is the profit function

    Revenue is X times P function
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Senior Member
    Joined
    Nov 2010
    From
    Hong Kong
    Posts
    255
    What is x?
    Why do you say revenue is X times the profit function? Is it given in the question?
    Is x the quantity?

    If you want a help on this question, at least post the full question.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Newbie
    Joined
    Mar 2011
    Posts
    5
    If p(x) is price-demand function, the revenue function is R(x) = xp(x).


    "p = 8 − 2 ln x for 5 ≤ x ≤ 50, where x is the
    number (in thousands) of hot dogs that can be sold during one game at a price of $p.
    (a) (4 pts) Find the revenue function and the marginal revenue function when x
    thousand hot dogs can be sold during one game"
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Senior Member
    Joined
    Nov 2010
    From
    Hong Kong
    Posts
    255
    Quote Originally Posted by Craftysince1990 View Post
    ok now i believe revenue function will be 8x-2xlog(x)
    and marginal revenue function should be 6-2log(x)
    I agree.
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Newbie
    Joined
    Mar 2011
    Posts
    5
    ok, thanks.

    Could you help me start out any of these Q's?

    (b) Find the number (in thousands) of hot dogs that can be sold during one
    game such that the marginal revenue is zero.
    (c) Find the instantaneous rate of change of the marginal revenue.
    (d) Use part (c) to justify that the answer in part (b) generates the maximum revenue. What is the maximum revenue?
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Senior Member
    Joined
    Nov 2010
    From
    Hong Kong
    Posts
    255
    for (b), just solve the equation 6-2log(x) for x. I got x=e^3.
    I am not sure what is 'instanteneous' rate of change, I may need to look it up first.
    Follow Math Help Forum on Facebook and Google+

  10. #10
    Senior Member
    Joined
    Nov 2010
    From
    Hong Kong
    Posts
    255
    Got it!

    (c) find second derivative of Revenue function= first derivative of the Marginal revenue function.
    That is -2/x.

    (d) Since x is a positive quanitity, -2/x is a negative number. That means, the Revenue function attains its maximum at the point where marginal revenue =0 (since the second derivative is negative). Then e^3 is the revenue maximumising quantity.

    to find maximum revenue, substitute e^3 in the Revenue function from (a).
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 20
    Last Post: November 27th 2012, 05:28 AM
  2. Tc function, marginal revenue etc.
    Posted in the Business Math Forum
    Replies: 1
    Last Post: July 23rd 2011, 10:02 PM
  3. Replies: 1
    Last Post: November 24th 2009, 12:43 PM
  4. Replies: 1
    Last Post: November 18th 2009, 07:16 PM
  5. marginal cost/revenue to total cost / revenue
    Posted in the Advanced Math Topics Forum
    Replies: 1
    Last Post: May 9th 2009, 11:41 AM

Search Tags


/mathhelpforum @mathhelpforum