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  • Sep 30, 2010, 09:04 AM
    SaTho
    Calculus help
    A charter flight charges a fare of $300 per person plus $10 per person for each unsold seat on the plane. The plane holds 100 passengers. The total revenue received can be modelled by R(x)=-10x squared 700x 30,000, where x represents the number of unsold seats. The maximum revenue is $__ ,which occurs when __ seats are left unsold. How do I find the maximum revenue and the number of seats left unsold?
  • Sep 30, 2010, 09:38 AM
    Unknown008

    You can do it in two different ways. In both ways, you are finding the maximum point of the curve:

    y = -10x^2 + 700x + 30000

    1. Completing the square:











    From this, you know that the optimum occurs at coordinates (35, 42250)

    Hence, it occurs when the number of empty seats is 35 and the revenue is $42250

    2. Finding the derivative.





    At maximum, R'(x) = 0, so:







    Using this value of x in the formula,



    There you are :)
  • Sep 30, 2010, 09:50 AM
    ebaines

    Given an equation such as



    you find the function's minimum and/or maximum values by determining where the slope of the function is equal to zero. So for this problem:



    Solve for x. Then to see whether this point corresponds to a minimum or a maximum take the second derivative of the function and evaluate it at this value of x. If the second derivative is positive you have a local minimum; if it's negative you have a local maximum. Finally, sub that value of x back into your original equation to get the corresponding value of R.

    Please post back with what you get for answers.
  • Sep 30, 2010, 10:16 AM
    SaTho
    Comment on Unknown008's post
    Thank you so much!
  • Sep 30, 2010, 10:16 AM
    SaTho
    Comment on ebaines's post
    I got 35 and 42250

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