SOLUTION: You run a canoe-rental business on a small river in Ohio. You currently charge $12 per canoe and average 36 rentals a day. An industry journal says that, for every fifty-cent incre

Question 979995: You run a canoe-rental business on a small river in Ohio. 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 by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
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?
:
Let's use x as the variable
.5x = no. of 50 cent increases
and
2x = no. of rentals lost
:
Revenue (r)
r(x)= (12+.5x)*(36-2x)
FOIL
r(x) = 432 - 24x + 18x - x^2
r(x) = -x^2 - 6x + 432
Max income occurs at the axis of symmetry, x =-b/(2a)
x =
x =
x = -3, a negative solution means you should lower the price
Charge 12 - 3(.50) = $10.50 for each canoe
Then -2x becomes + 6
10.50 * 36 + 6 = 42 canoes
max revenue then: 10.50 * 42 = $441

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