an airline company offers a round-trip group flight from New York to London. If x people sign up for the flight, the cost of each ticket is to be 1000-2x dollars. Find the maximum revenue the airline company can receive from the sale of tickets from the flight?

Answer 1

r = x (1000-2x)

r = 1000 x -2 x^2

2 x^2 -1000 x = -r

x^2 - 500 x = -(1/2)r

x^2 -500 x + 250^2 = -(1/2)r + 250^2

(x-250)^2 = -(1/2)(r-2(250)^2 )

x = 250
r = 2*250^2 = 125,000