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Math Help - revenue problem

  1. #1
    Senior Member euclid2's Avatar
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    revenue problem

    An airline offers summer flights from toronto to london for groups of students. a minimum of 80 students must sign up for each flight, at a round-trip fare of $2400 per person. however, the airline will reduce the fare by $10 for each additional student who joins the flight. what number of passengers will give the airline the greatest revenue?
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  2. #2
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    Quote Originally Posted by euclid2 View Post
    An airline offers summer flights from toronto to london for groups of students. a minimum of 80 students must sign up for each flight, at a round-trip fare of $2400 per person. however, the airline will reduce the fare by $10 for each additional student who joins the flight. what number of passengers will give the airline the greatest revenue?
    let x = number of additional students

    R(x) = (2400-10x)(80+x)

    so, maximize R(x) ... remember the number of students is 80+x
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  3. #3
    Senior Member euclid2's Avatar
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    Quote Originally Posted by skeeter View Post
    let x = number of additional students

    R(x) = (2400-10x)(80+x)

    so, maximize R(x) ... remember the number of students is 80+x
    so R(x)= -10x^2 + 1600x + 192000

    R'(x)=-20x+1600 indicating a max

    setting R'(x)=0

    -20x+1600=0
    -20x=-1600
    x=80

    where do i go from here?
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  4. #4
    Senior Member euclid2's Avatar
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    how do i finish the problem from here?
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  5. #5
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    Quote Originally Posted by euclid2 View Post
    how do i finish the problem from here?
    answer the question ...

    what number of passengers will give the airline the greatest revenue?
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