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?
:
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 = {{{(-40)/(2*-1)}}}
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!!"