SOLUTION: A real estate office handles 50 apartment units. When the rent is $540 per month, all units are occupied. However, for each $30 increase in rent, one unit becomes vacant. Each occu

Question 112130This question is from textbook
: A real estate office handles 50 apartment units. When the rent is $540 per month, all units are occupied. However, for each $30 increase in rent, one unit becomes vacant. Each occupied unit requires an average of $18 per month for service and repairs. What rent should be charged to obtain the maximum profit? This question is from textbook

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A real estate office handles 50 apartment units. When the rent is $540 per month, all units are occupied. However, for each $30 increase in rent, one unit becomes vacant. Each occupied unit requires an average of $18 per month for service and repairs. What rent should be charged to obtain the maximum profit?
:
Let x = no. of $30 increases
and
Also x = no. of vacant apartments
:
Y = Revenue
y = price per apt * no. of apts
:
y = (540+30x) * (50-x); FOIL this
:
y = 27000 - 540x + 1500x - 30x^2
:
y = -30x^2 + 960x + 27000; arranged as a quadratic equation (a parabola)
:
The axis of symmetry will be the value of x for max profit
x =
x =
x = 16; no. of increases of $30 and 16 apts vacant
:
Use x = 16 to find the rent for max profit:
540 + (30*16) = $1020 per month
:
Find the actual profit by subtracting the service fee from the rental of 34 apts:
(50-16)*(1020 - 18) =
34 * 1002 = $34,068
:
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