Help with algebraic word problem

Question

you currently charge $12 and rent 36 canoes per day.  For every $.50 increase in price, you will lose 1 customer.  What price will maximize profits? How many customers will you lose?

Answer 1

Let P = price and C = customers.

The relationship between P and C is linear as follow:

 

slope = (36 -35)/(12-12.5)= -2 = (36-C)/(12-P)

Multiply and collect terms: C = 60 - 2P

 

Revenue = P*C = 60P - 2P²

Revenue is maximized when the derivative is 0 i.e. when 2P = 30 and P = 15 and C = 30

Revenue will be 450 and customers lost will be 6