Question

The manager of a large apartment complex knows from experience that 100 units will be occupied if the rent is 350 dollars per month. A market survey suggests that, on the average, one additional unit will remain vacant for each 5 dollar increase in rent. Similarly, one additional unit will be occupied for each 5 dollar decrease in rent. What rent should the manager charge to maximize revenue?

Answer 1

let x = # of $5 price decreases.
Revenue = Price times Quantity
where
Price = 350 - 5x
and
Quantity = 100 + 1x

Answer 2

so what will equal?

Answer 3

your back..

Answer 4

yeah sorry had to run an errand

Answer 5

np... do you understand why I'm letting x be the number of price decreases?

Answer 6

becuase when the price is lower more people will rent?

Answer 7

basically. It's one of those "tricks" you pick up :)

Answer 8

So now onto the revenue function:

\(\large R(x) = (350 - 5x)(100+x)\)
FOIL to get
\(\large R(x) = 35000-150x - 5x^2\)

Answer 9

thats what i got, but im confused on what to do next

Answer 10

What rent should the manager charge to maximize revenue?

Key words are "maximize" and "revenue"

We have made the revenue function.
Now to "maximize". That means take the derivative, set it =0, solve for x.

Answer 11

-150+10x=0?

Answer 12

-150-10x=0?

Answer 13

Good.

Answer 14

and itll be 15

Answer 15

actually -15

Answer 16

ohh
and then you subtract that from 350?

Answer 17

Hmmmm. Since x was the number of price decreases ... so
x = 1 would mean subrtact $5 from the original rent,
x = 2 would mean subtract $10 from the original rent,
But x = -15 means we should actually increase the rent by 15*5 = $75 So 350 + 75 = 425

Answer 18

oohhh i understand

Answer 19

thank you so much

Answer 20

np

Answer 21

do you know how to find the value of marginal profit?

Answer 22

can you explain to me

The demand function and the cost function for units of a product are and . Find value of the marginal profit when 8100.
The value of the marginal profit when 8100 is