Question

A small cruising ship that can hold up to 52 people provides three-day excursions to groups of 34 or more. If the group contains 34 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 34 . Find the size of the group that maximizes income for the owners of the ship

Answer 1

X no. Of person

Price is 76 dollars person initially.

Subtract 1 dollar for each person more than 40 persons.

76-x, price for x added persons.

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Group cost, meaning revenue for the cruise ship company:

highlight%28%2876-x%29%2840%2Bx%29%29

Treat this as a revenue function, y for convenience.

highlight%28y=%2876-x%29%28x%2B40%29%29

This is factored. Find the maximum value. It will happen exactly in the middle between the two roots of %2876-x%29%28x%2B40%29=0.

Zeros are at 76 and -40. The independent value in the middle is %2876%2B%28-40%29%29%2F2=18.

MAXIMUM REVENUE: y=%2876-18%29%2818%2B40%29=3364 dollars.

NUMBER OF PEOPLE FOR THIS MAX IS highlight%28x=18%29