Answer:
a) The number of passengers that will maximize the revenue received from the flight is 99.
b) The maximum revenue is $48,609.
Step-by-step explanation:
We have to analyse two cases to build a piecewise function.
If there are 80 or less passengers, we have that:
The cost of the trip is $586 for each passenger. So
If there are more than 80 passengers.
There is a refund of $5 per passenger for each passenger in excess of 80. So the cost for each passenger is
.
So we have the following piecewise function:
The maxium value of a quadratic function in the format of happens at:
The maximum value is:
So:
(a) Find the number of passengers that will maximize the revenue received from the flight.
We have to see if is higher than 80.
We have that, for ,
, so
The number of passengers that will maximize the revenue received from the flight is:
Rounding up, the number of passengers that will maximize the revenue received from the flight is 99.
(b) Find the maximum revenue.
This is .
The maximum revenue is $48,609.