calculus
posted by Erika on .
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=

If the profit is (11043x) per person, then the total
profit = x(11043x) = 1104x  3x^2
d(profit)/dx = 1104  6x
= 0 for max profit
6x = 1104
x = 184 , (max profit = 101568)
To have any profit
x(11043x) > 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