Question

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 1

@aum @ganeshie8

Answer 2

say :
n = number of rentals
p = chanrge per canoe

Answer 3

income can be expressed as :
\[\large \text{income} = n\times p\]

yes ?

Answer 4

yes

Answer 5

good, say change in price of canoe = x dollars
then, change in rental would be : 4x

right ?

Answer 6

yes

Answer 7

nope

Answer 8

oops

Answer 9

good, say change in price of canoe = x dollars
then, change in number of rentals would be : \(\large \color{Red}{-}\)4x

right ?

Answer 10

yes

Answer 11

it has to be negative because the number of rentals decrease if u increase the price

Answer 12

so can we express the income as below :
\[\large \text{income} = n\times p\]
\[\large \text{income} = (36-4x)\times (12+x)\]

?

Answer 13

okay I understand how we would then solve it, but don't get how we formed the equation

Answer 14

like how did we get -4x

Answer 15

`An industry journal says that, for every fifty-cent increase in rental price, the average business can expect to lose two rentals a day. `

Answer 16

that says, every 50cent increase in price lowers the number of rentals by 2

Answer 17

that means every 1 dollar increase in price lowers the number of rentals by 4

yes ?

Answer 18

okay

Answer 19

actually how do you solve it after ?