Question

The manager of a large apartment complex knows from experience that 120 units will be occupied if the rent is 400 dollars per month. A market survey suggests that, on the average, one additional unit will remain vacant for each 4 dollar increase in rent. Similarly, one additional unit will be occupied for each 4 dollar decrease in rent. What rent should the manager charge to maximize revenue?

Answer 1

I just need to know how to set it up.

Like the formula to use.

Answer 2

Revenue = price*sales

Answer 3

does that work for any problem like this?

Answer 4

say,
p = prince of each unit
s = total number of units sold/occupied

Answer 5

yes, revenue equation remains same. it will not change :)

Answer 6

R = p*s

Answer 7

For example, "A manufacture has been selling 1450 television sets a week at $390 each. A market survey indicates that for each $15 rebate offered to a buyer, the number of sets sold will increase by 150 per week.

a) Find the function representing the demand p(x), where x is the number of the television sets sold per week and p(x) is the corresponding price."

Answer 8

lets finish our original problem first ?

Answer 9

Ok but I think I got the majority of it

Answer 10

oh ok good :)
wat did u get for rent that maximizes the revenue ?

Answer 11

q(p) = 120 - (p-400) = 520 - p ?

Answer 12

whats q(p) ?

Answer 13

Sorry it's just a letter I like to use lol... Is the answer 440?

Answer 14

thats right :-

we're given :
ds/dp = -1/4

and we know :
R = p*s

differentiate with respect to p both sides

dR/dp = p*ds/dp + s
= -p/4 + s

set it equal to 0, u wud get p = 4s

solving u wud get,
p = 440, s = 110

Answer 15

so then I would do kinda the same thing for the other one I showed you?

Answer 16

the other one asks for DEMAND.
DEMAND is not same as REVENUE ok

Answer 17

so what formula would I use?

Answer 18

For example, "A manufacture has been selling 1450 television sets a week at $390 each. A market survey indicates that for each $15 rebate offered to a buyer, the number of sets sold will increase by 150 per week.

a) Find the function representing the demand p(x), where x is the number of the television sets sold per week and p(x) is the corresponding price."

Answer 19

for part a), you just need to create the price as a function of sales

Answer 20

say price of tvset = p
number of television sets sold = x

Answer 21

p = f(x)

Answer 22

\(p(x) = 390 + \frac{15}{150}(1450-x) \)

Answer 23

thats the equation of price, see if that makes sense

Answer 24

Yep thats what I have written down :)
P=-.1x+535

Answer 25

Looks good :)
thats all we're done for part a

Answer 26

Ok thank you. Final tomorrow! :O

Answer 27

good luck !

Answer 28

once u get the equation, its always a good idea to make sure u got it right
for ex :-
u said u got
P=-.1x+535

Answer 29

to check if its correct, simply put x = 1450
u should get the corresponding price 390

Answer 30

P=-.1x+535

put x = 1450

P = -.1*1450 + 535
= -145 + 535
= 390

so our equation for p(x) is \(\large \color{red}{\checkmark}\)

Answer 31

just a paranoid check ok :)

Answer 32

It's a multiple choice final so that will help

Thanks! :)