Question 1176830: A company charters a party boat that normally costs $40 per person. A group discount reduces
the fare by $0.25 for each ticket sold; the more tickets sold, the lower the per-person fare. The
maximum capacity of the boat is 90 people, including the crew of 5 people. What size of group
would maximize the boat owner’s revenue?
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! x is one person added
so that (40-0.25x)x=revenue=-0.25x^2+40x.
the maximum of this quadratic is x=-b/2a or -40/-0.5=80
When x=80
the per person fare is $20, and the revenue is $1600, and 85 people are on the boat.
can check with 85 customers, the maximum, where the per person fare is $18.75=$1593.75, not the maximum revenue.
and look at 79, where the per person cost is $20.25 and maximum revenue is $1599.75
Maximize revenue with a group size of 80.
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