SOLUTION: A real estate handles an apartment complex with 1000 units when the rent per unit is $600 . month, 100 units are occupied. However it has been determined that for each $5.00 decre

Question 275693: A real estate handles an apartment complex with 1000 units
when the rent per unit is $600 . month, 100 units are occupied. However it has been determined that for each $5.00 decrease in monthly rent, 10 more units will be occupied.
A) write a function for the total montly revenue
B) sketch the graph of the revenue and determined the monthly rent that will generate the maximum revenue.
C) How many units will be occupied at this amount?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A real estate handles an apartment complex with 1000 units
when the rent per unit is $600 . month, 100 units are occupied. However it has been determined that for each $5.00 decrease in monthly rent, 10 more units will be occupied.
:
Let x = no. $5 decreases, and no. of 10 unit increases
:
A) write a function for the total monthly revenue
R(x) = (600 - 5x) * (100 + 10x)
FOIL
R(x) = 60000 + 6000x - 500x - 50x^2
R(x) = -50x^2 + 5500x + 60000
:
;
B) sketch the graph of the revenue and determined the monthly rent that will generate the maximum revenue.
Sketching the above equation will look like this (Revenue on the y axis)

;
x = 55 gives max revenue
Rent = 600-5(55) = $325 per month
:
:
C) How many units will be occupied at this amount?
100 + 10(55) = 650 units rented

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