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Maximization of Profit for Canoe Rentals

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Imagine that you run a consulting business that helps small businesses with process improvement. Justin runs a small canoe-rental business somewhere in Florida and currently charge $10.50 per canoe rental. He has an average of 36 rentals per day. With the rising cost he wants to increase the charge for the rental however he wants to try to maintain the average of 36 rentals per day in order to make the price hike effective.

* Justin hires you to come in and help him figure out a strategy. He does not want to lose business because of the impending price hike.

* You did your homework and found an industry journal that 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 income and prepare a presentation that you will present to Justin.

* Break it down for Justin and show him your rational for what you think the new charge be for the canoe rental should be? This should also include a profit estimate for Justin's business.

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Solution Summary

We show how a businessman who rents out canoes can maximize his daily profits.

Solution Preview

Justin's daily profit is given by the formula

p = rc

where r is the number of daily canoe rentals and c is the cost of a rental in dollars. The number of rentals, r, is a function of the cost, so we have r = r(c). For a rental cost of $10.50, Justin gets 36 rentals per day, so we ...

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