SOLUTION: A small cruising ship that can hold up to 64 people provides three-day excursions to groups of 40 or more. If the group contains 40 people, each person pays $76. The cost per per

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Question 1003563: A small cruising ship that can hold up to 64 people provides three-day excursions to groups of 40 or more. If the group contains 40 people, each person pays $76. The cost per person for all members of the party is reduced by $1 for each person in excess of 40. Find the size of the group that maximizes income for the owners of the ship.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
x, number of persons
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.