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31 May, 00:28

A local club is arranging a charter flight to hawaii. the cost of the trip is $565 each for 84 passengers, with a refund of $5 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.

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  1. 31 May, 00:40
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    If x = number of passengers in excess of 84,

    Revenue, R = (565-5x) (84+x) = 47460+565x-420x-5x^2 = 47460+145x-5x^2

    (a) For maximum revenue, first derivative of revenue function is equal to 0.

    That is,

    dR/dx = 145-2*5x = 145-10x = 0 = > 145=10x = > x = 14.5 = 15 passengers

    Maximum number of passengers for maximum revenue = 84+15 = 99 passengers

    (b) Maximum revenue = (565-5*15) (99) = (565-75) (99) = $48,510
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