Results 1 to 10 of 10

Math Help - Revenue Word Problem

  1. #1
    Junior Member shepherdm1270's Avatar
    Joined
    Mar 2008
    Posts
    47

    Revenue Word Problem

    A local club is arranging a charter flight to Hawaii. The cost of the trip is $425 each for 75 passengers, with a refund of $5 per passenger for each passenger in excess of 75.

    a. find the number of passengers that will maximize the revenue received from the flight.

    b. find the maximum revenue
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by shepherdm1270 View Post
    A local club is arranging a charter flight to Hawaii. The cost of the trip is $425 each for 75 passengers, with a refund of $5 per passenger for each passenger in excess of 75.

    a. find the number of passengers that will maximize the revenue received from the flight.

    b. find the maximum revenue
    There is something missing from this question.

    All you have is the cost of the trip as a function of the number
    of passengers (worded so badly that I can't tell you the cost for any
    number of passengers over 75).

    It looks to me as though the marginal cost per extra passenger is always
    positive so there would be no maximum to the cost.

    RonL
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member shepherdm1270's Avatar
    Joined
    Mar 2008
    Posts
    47
    We did one in class, but my notes are kind of jumbled and I'm not sure how it was done. Here's what my notes looked like, see if this helps:

    Profit: $5/seat if the seats are between 60-80, and it's decremented 5 cents per seat over 80.


    Cost / # seats / profit
    5.00 60 300
    5.00 70 350
    5.00 80 400

    4.95 81 400.95
    4.90 82 401.80


    etc. etc.


    SO price per seat = 5-(x-80)(.05)
    R(x) = x(5-(x-80)(.05))
    R9x) = 9x-.05x^2


    ----------------------------------------------------------
    Last edited by shepherdm1270; March 29th 2008 at 07:15 PM.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member shepherdm1270's Avatar
    Joined
    Mar 2008
    Posts
    47
    oh yeah, then:

    R'(x) = 9-.10x
    9-.10x = 0
    9 = .10x
    90 = x
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member shepherdm1270's Avatar
    Joined
    Mar 2008
    Posts
    47
    ok i JUST worked on it some more, and i did the table and saw that 400 is the correct answer. then i worked on the formula and got this far:

    425-(x-75)(5) = price per seat

    R(x) = x (425 - (x - 75)(5))

    So i need to simplify it, find the derivative, and solve for x...

    the algebra is where i run into problems
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Junior Member shepherdm1270's Avatar
    Joined
    Mar 2008
    Posts
    47
    help anyone? would be much appreciated. I'm freaking out. *sigh*
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by shepherdm1270 View Post
    ok i JUST worked on it some more, and i did the table and saw that 400 is the correct answer. then i worked on the formula and got this far:

    425-(x-75)(5) = price per seat

    R(x) = x (425 - (x - 75)(5))

    So i need to simplify it, find the derivative, and solve for x...

    the algebra is where i run into problems Mr F says: Fact of life. The further you go in your mathematical studies, the more it will be expected that you can do basic algebra. If you are learning calculus (which you appear to be doing) then it's absolutely expected that you have basic algebraic competencey.
    Expand in side the brackets and simplify:

    R(x) = x(800 - x)

    => R(x) = 800x - x^2.

    The basic algebraic competency leading to this result is absolutely assumed in a course where calculus is being taught. You need to go back and thoroughly revise the basics.

    In another thread Captain B has already given a thorough discourse on how to find the turning point of a quadratic.
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Junior Member shepherdm1270's Avatar
    Joined
    Mar 2008
    Posts
    47
    this is the last math course I will ever be expected to take... I'm just trying to make it through. I'm 21 and haven't taken a math course since I was 17... needless to say, I'm a little rusty, and I'm not going to start over for one semesters worth of calculus... but thanks for the advice
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Junior Member shepherdm1270's Avatar
    Joined
    Mar 2008
    Posts
    47
    well see I got :

    x ( 425 - (x-75)(5))

    x ( 425 - (5x - 375)

    x ( 50 - 5x)

    ??
    Follow Math Help Forum on Facebook and Google+

  10. #10
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by mr fantastic View Post
    Expand in side the brackets and simplify:

    R(x) = x(800 - x)

    => R(x) = 800x - x^2.

    The basic algebraic competency leading to this result is absolutely assumed in a course where calculus is being taught. You need to go back and thoroughly revise the basics.

    In another thread Captain B has already given a thorough discourse on how to find the turning point of a quadratic.
    And I will take my own advice too!!

    R(x) = x (425 - (x - 75)(5)) = x (425 - 5x - (-375)) = x (425 - 5x + 375) = x (800 - 5x).

    NOT x (800 - x) as I first posted.

    So R(x) = 800x - 5x^2.

    R'(x) = 800 - 10x.

    0 = 800 - 10x => 800 = 10x => x = 80.
    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. Replies: 1
    Last Post: November 24th 2009, 12:43 PM
  3. Replies: 1
    Last Post: November 18th 2009, 07:16 PM
  4. Revenue Word Problem
    Posted in the Algebra Forum
    Replies: 1
    Last Post: November 15th 2009, 12:16 AM
  5. [SOLVED] revenue word problem...
    Posted in the Business Math Forum
    Replies: 1
    Last Post: March 4th 2008, 05:11 PM

Search Tags


/mathhelpforum @mathhelpforum