Question

A local club is arranging a charter flight to hawaii. the cost of the trip is ​$565 each for 84 ​passengers, with a refund of​ $5 per passenger for each passenger in excess of 84.
a. find the number of passengers that will maximize the revenue received from the flight.
b. find the maximum revenue.

Answer 1

If x= number of passengers in excess of 84,

Revenue, R = (565-5x)(84+x)= 47460+565x-420x-5x^2 =47460+145x-5x^2

(a) For maximum revenue, first derivative of revenue function is equal to 0.
That is,
dR/dx = 145-2*5x = 145-10x = 0 => 145=10x => x =14.5 = 15 passengers
Maximum number of passengers for maximum revenue = 84+15 =99 passengers 

(b) Maximum revenue = (565-5*15)(99) = (565-75)(99) =$48,510