SOLUTION: A man can rent all of his apartments if he rents them for $500 each per month. However, for each $50 increase in rent he will rent two fewer apartments. To guarantee the best monet

Question 1148699: A man can rent all of his apartments if he rents them for $500 each per month. However, for each $50 increase in rent he will rent two fewer apartments. To guarantee the best monetary return, how much monthly rent should he charge and how many apartments will he rent out?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A man can rent all of his apartments if he rents them for $500 each per month.
However, for each $50 increase in rent he will rent two fewer apartments.
To guarantee the best monetary return, how much monthly rent should he charge and how many apartments will he rent out?
:
Let's assume he has 100 apartments, we need to know this.
let x = no. $50 increases in rent and each two apt decreases
then
Rev = total apts * apt rent amt
f(x) = (100 - 2x)(500 + 50x)
FOIL
f(x) = 50000 + 5000x - 1000x - 100x^2
a Quadratic equation
f(x) = -100x^2 + 4000x + 50000
simplify, divide by 100
-x^2 + 40x + 500 = 0
max rev occurs on the axis of symmetry x = -b/(2a)
x =
x = +20 ea $50 increases and 40 apt decreases
:
Max revenue occurs when he charges 500+20(50) = $1500!! Outrageous!
He will be renting 100 - 2(20) = 60 apartments
Revenue then 60 * 1500 = $90000 vs $50000 renting all 100 at 500 per month
:
"But how about the all the hardship you are causing these renters, is there a price on that?" What good is it, if you gain the whole world and lose your soul!!"

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