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Math Help - Optimization Travel Agency

  1. #1
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    Optimization Travel Agency

    A travel agent currently has 80 people signed up for a tour. The price of a ticket is $5000 per person. The agency has chartered a plane seating 150 people at a cost of $250 000. Additional costs to the agency are incidental fees of $300 per person. For each $30 that the price is lowered, one new person will sign up. How much should the price per person be lowered to maximize the profit for the agency?

    What I have done;

    d(x) = 5000 - 30x
    p(x) = 80 + x
    R(x) = (5000-30x)(80+x)
    R'(x) = 2600 - 60x
    x = 130/3

    The price that should be lowered per person is 30(130/3) = 1300,
    but the answer is 1140

    so can anyone tell me what i am doing wrong? Thanks
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  2. #2
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    Quote Originally Posted by apocalyps3 View Post
    A travel agent currently has 80 people signed up for a tour. The price of a ticket is $5000 per person. The agency has chartered a plane seating 150 people at a cost of $250 000. Additional costs to the agency are incidental fees of $300 per person. For each $30 that the price is lowered, one new person will sign up. How much should the price per person be lowered to maximize the profit for the agency?

    What I have done;

    d(x) = 5000 - 30x
    p(x) = 80 + x
    R(x) = (5000-30x)(80+x)
    R'(x) = 2600 - 60x
    x = 130/3

    The price that should be lowered per person is 30(130/3) = 1300,
    but the answer is 1140

    so can anyone tell me what i am doing wrong? Thanks
    According to the highlighted condition your function R becomes:

    R(x) = (5000-30x)(80+x)-300x

    Keep in mind that the number of passengers must be a natural number!
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