Posted by **Erika** on Monday, November 1, 2010 at 8:13am.

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=

- calculus -
**Reiny**, Monday, November 1, 2010 at 8:32am
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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