A local club is arranging a charter flight to Hawaii. The cost of the trip is $598 each for 84 passengers, with a refund of five dollars 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.
a. Let x be the number of passengers in excess of 84. Therefore, the total number of passengers is 84 + x. The revenue received from the flight can be calculated as follows:
Revenue = (84 + x)(598) - 5x
Revenue = 50232 + 598x - 5x
Revenue = 50232 + 593x
To find the number of passengers that will maximize revenue, we differentiate the revenue function with respect to x and set it equal to 0:
dRevenue/dx = 593
593 = 0
x = 0
Since x = 0, there will be exactly 84 passengers on the flight to maximize revenue.
b. Substitute x = 0 back into the revenue function:
Revenue = 50232 + 593(0)
Revenue = 50232
Therefore, the maximum revenue received from the flight will be $50,232.