the manager of a 100 unit apartment complex knows from experience that all units will be occupied if the rent is $800 per month. a market survey suggests that, on average, one additional unit remain vacant for each $10 increase in rent. what rent should the manager charge to maximize revenue?
2007-05-06 14:02:03 · 2 answers · asked by Patricia m 1 in Science & Mathematics ➔ Engineering
Total revenue = rent x occupied units
Let x = # of vacancies
Total revenue = (800 + 10x)(100 - x)
First term on right hand side = rent
2nd term on RHS = occupied units
Total revenue = -10x^2 + 200x +80,000
To find local minimums or maximums...take the first derivative of the total revenue function and set it equal to zero.
0 = -20x + 200
Solve for x:
x = 10
So 10 vacancies will maximize revenue.
So the rent the manager should charge is:
800 + 10(10) = $900/mo
2007-05-06 16:02:20 · answer #1 · answered by Doug 5 · 1⤊ 0⤋
$900. I forgot the math so I let Excel calculate total rent for ALL possible amounts and picked the highest.
2007-05-06 21:29:30 · answer #2 · answered by STEVEN F 7 · 0⤊ 1⤋