Question

A local club is arranging a charter flight to Hawaii. The cost of the trip is

​$570570

each for

8282

​passengers, with a refund of​ $5 per passenger for each passenger in excess of

8282.

a. Find the number of passengers that will maximize the revenue received from the flight.

b. Find the maximum revenue.

Answer 1

a.

Let, number of passengers be (8282 + x).

Revenue (R) = $ (570570 - 5x)(8282+x).
= 4,725,460,740 - 5x² + 529160x .

dR/dx = 529160 - 10x.

d²R/dx² is negative.

So to maximize revenue, dR/dx = 0, which gives,

x = 52916.

Number of passengers for max revevnue = 8282 + 52916
= 61198.

b.

Max revenue = $ (570570 - 264580)(61198).

= $ 18,725,976,020.

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