Alocal club is arranging a charter flight to hawaii. the cost of the trip is $574 each for 81 passengers, with a refund of $5 per passenger for each passenger in excess of 81. find the number of passengers that will maximize the revenue recieved from the flight also find the maximum revenue.

Let x be the number of passengers.
The discounted cost is given by,

Cost = 574-5(x-81) = 574-5x + 405 = 979 -5x

Total revenue, R(x) = x(979 - 5x) = 979x - 5x^2

At maximum revenue, dR/dx = 0 => dR/dx = 979 - 10x = 0 =>10x = 979 => x =979/10 = 97.9 ≈ 98 passengers

Therefore,
Revenues, R(97) = 98[574 -5(98-81)] = 98[574-85] = $47,922