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10 September, 21:27

A small cruising ship that can hold up to 66 people provides three-day excursions to groups of 42 or more. If the group contains 42 people, each person pays $58. The cost per person for all members of the party is reduced by $1 for each person in excess of 42. Find the size of the group that maximizes income for the owners of the ship.

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  1. 10 September, 21:32
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    50 people

    Step-by-step explanation:

    Let x represent the number of people on the cruise. The amount they each must pay is ...

    ... ($58 - (x - 42)) = $100 - x

    The revenue from the group is the product of the number of people and the amount each pays:

    ... r (x) = x· (100 - x)

    This describes a downward-opeing parabola with zeros at x=0 and x=100. The vertex (maximum) will be found halfway between those zeros, at x=50.

    A group size of 50 maximizes revenue from the cruise.
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