You run a canoe-rental business on a small river in Ontario.

Question

You run a canoe-rental business on a small river in Ontario. You currently charge $12 per canoe and average 36 rentals a day. An industry journal says that, for every fifty-cent increase in rental price, the average business can expect to lose two rentals a day. Use this information to attempt to maximize your income. What should you charge?

Answer 1

Let R = rentals and P = price

The relationship between R and P is linear:

R = 108 - 6P

The income is PR = 108P - 6P²

The derivative of income with respect to price is 0 at P = 9, i.e. income will be maximized when P = 9