The hourly operating cost of an airplane, which seats up to 405 passengers, is estimated to be $5,500. If an airline charges each passenger a fare of $100 per hour of flight, find the hourly profit P it earns operating the airplane as a function of the number of passengers x. (Be sure to specify the domain.)

Question

What is the least number of passengers it must carry in order to make a profit? HINT [The cost function is constant (Variable cost = 0).]

Profit: P(x)=100x-5500

I solved it:
P(x)=0
100x-5500=0
5500/100=55 Passengers.

I don't understand what is wrong
Thank You

Answer 1

hourly revenue = 100p for p passengers
hourly cost = 5500

revenue=cost when
100p = 5500
p = 55

looks fine to me. why do you think it's wrong? anything over 55 passengers makes a profit, at $100/hr per extra passenger.

Answer 2

Because the purpose is to make a profit. So the passengers should be 56.