Results 1 to 5 of 5

Math Help - At what rate is revenue rising or falling.

  1. #1
    Newbie
    Joined
    Nov 2009
    Posts
    2

    At what rate is revenue rising or falling.

    Problem:

    "For the past few months, OHaganBooks.com has seen its weekly sales increase. At the moment OHaganBooks.com is selling 1000 books per week and its sales are rising at a rate of 200 books per week. Also, it is now selling all its book for $20 each, but the price is dropping at a rate of $1 per week. I need to know at what rate OHaganBooks.com's revenue is rising or falling given these conditions. I would also like to see that company's revenue increase at a rate of $5,000 per week. At what rate would sales have to have been increasing to accomplish this?"


    So those are the two questions I have to answer. Pretty simple I'm guessing. I understand (R=pq) which is not hard to calculate for each week. I put the answers out in a table showing the difference in revenue from the previous week, and the total revenue for the week.

    However, I'm guessing there is some calculus technique I need to use here and I'm not quite sure what it is. If anyone could take a look at it and see what they think I would greatly appreciate it.
    Last edited by colinn; November 29th 2009 at 12:51 PM. Reason: Spelling errors.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Oct 2008
    Posts
    1,034
    Thanks
    49
    The rates to relate are of R, p and q, and since R=pq we can see that differentiating them all with respect to t will involve the product rule. I would think...



    ... where



    ... is the product rule - straight continuous lines differentiating downwards (integrating up) with respect to t.

    Spoiler:

    Spoiler:

    __________________________________________

    Don't integrate - balloontegrate!

    Balloon Calculus: standard integrals, derivatives and methods

    Balloon Calculus Drawing with LaTeX and Asymptote!
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Sep 2009
    Posts
    19
    Here is what I think,

    Let P(x) = the profit, they are selling there books 20$ a piece.
    Let f(x) = the number of books they are selling per week.

    f(x)=1000+200x where x is the week number.

    But they sell books 20$ but with price dropping of 1$ per week per book.

    P(x)=1000(20)-1000*x+200(20)*x-200*x

    I need to know at what rate OHaganBooks.com's revenue is rising or falling given these conditions:

    Take the derivative of P(x)

    P'(x)=-1000+4000-200=2800$

    Hence revenue are rising at a rate of 2800$ per week.

    At what rate would sales have to have been increasing to accomplish this?"

    You want the derivative of our function = 5 000$ per week.
    1000 books per week sold is fix...let u denote the rising sales.
    Then under the same condition:

    P(x)=1000*20-1000*x+u*20*x-u*x
    P'(x)=-1000+20*u-u=5 000

    Solve for u you get: 315.79 books, hence sales have to go up of
    316 books per week.

    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Nov 2009
    Posts
    2
    I appreciate the above answers, but I'm still not understanding the equations here I guess.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Sep 2009
    Posts
    19
    Ok,

    well this company is selling 1000 books a week. Moreover, the sales are raising by 200 books per week. That is, f(x)=number of book sold in one week.

    f(x)=1000+200x where x is the week number.

    They are selling the books 20$ each and the price of them is deacreasing by 1$ dollar a week. That is,

    f(x)=1000*(20$)-1000*x+200*x*(20)-200*x where x is the week number.

    In this problem, the price dropping is = to the week number...
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: November 24th 2009, 12:43 PM
  2. Replies: 1
    Last Post: November 18th 2009, 07:16 PM
  3. A balloon rising?
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 20th 2009, 03:12 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. Define domain and intervals of rising/falling
    Posted in the Calculus Forum
    Replies: 1
    Last Post: January 23rd 2009, 01:46 AM

Search Tags


/mathhelpforum @mathhelpforum