A local club is arranging a charter flight to Hawaii. The cost of the trip is $\$ 551$ each for 85 passengers, with a refund of $\$ 5$ per passenger for each passenger in excess of 85 .
a. Find the number of passengers that will maximize the revenue received from the flight.
b. Find the maximum revenue.
a. The number of passengers that will maximize the revenue received from the flight is
(Round to the nearest integer as needed.)
b. The maximum revenue is $\$ \square$.

Step 1 ：The revenue from the flight is the product of the number of passengers and the cost per passenger. The cost per passenger is \(551 - 5*(n-85)\) where n is the number of passengers.

Step 2 ：We need to find the number of passengers that maximizes this product. This is a piecewise function that is linear for the number of passengers less than or equal to 85 and linear with a different slope for the number of passengers greater than 85.

Step 3 ：The maximum revenue occurs at the point where the two linear functions meet, which is at 85 passengers.

Step 4 ：So, the number of passengers that will maximize the revenue is \(\boxed{85}\).

Step 5 ：The maximum revenue is the product of the number of passengers and the cost per passenger at this number of passengers, which is \(85 * 551 = \$46835\).

Step 6 ：So, the maximum revenue is \(\boxed{46835}\) dollars.