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calculus

With x people on board, a South African airline makes a profit of (1104 − 3 x) rands per person for a specific flight.
A. How many people would the airline prefer to have on board?
Answer: x=
B. What is the maximum number of passengers that can board such that the airline still profits?
Answer: x=

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  1. If the profit is (1104-3x) per person, then the total
    profit = x(1104-3x) = 1104x - 3x^2

    d(profit)/dx = 1104 - 6x
    = 0 for max profit
    6x = 1104
    x = 184 , (max profit = 101568)

    To have any profit
    x(1104-3x) > 0
    critical values are x=0 or x=368

    so min number of passengers is 1 for a profit of 1101, max number of passengers is 367 for a profit of 1101

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