The captain of a river boat cruise charges $36 per person, including lunch. The cruise averages 300 customers per day. The captain is considering increasing the price. A survey of customers indicates that for every $2 increase, there would be 10 fewer customers. What increase in price would maximize revenue?

You need to try to set it up yourself.





in general

(T = total)

where n is the number of $2 steps.



differentiate and set to zero to get maximum (or possibly a minimum)

Hopefully you know calculus. If not, post back and we'll try to solve it some other way.





The price to charge is, therefore, $48/person, and you'll have 240 people on the boat. You will also save money on lunch :D

You can check using 4 and 7 to assure yourself that n=6 is a maximum (it is).