A local 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.

Question

Daniella Vaughan

Mathematics

30 November, 10:49

A local 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.

+5

Answers (1)

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Brett Haas · Answer 1

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

A local 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 flightalso find the maximum revenue.

A local 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.