# calculus

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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?
B. What is the maximum number of passengers that can board such that the airline still profits?

• calculus -

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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