Hi, I am having trouble with this calculus problem shown below: can someone please show me the steps needed to solve this problem? I struggle with math so details will be rewarded!
An apartment complex can fill 100 units when the rent is $400 per month. It is estimated that for each $10 per month decrease in rent, 5 more units will become occupied. The complex has a monthly maintenance cost of $100 for each unit rented. What monthly rent should be charged to maximize the profit?
Oh and do I have the first equation set up correctly?: R=(400-10x)(100+5x)
Thanks for your help!
An apartment complex can fill 100 units when the rent is $400 per month. It is estimated that for each $10 per month decrease in rent, 5 more units will become occupied. The complex has a monthly maintenance cost of $100 for each unit rented. What monthly rent should be charged to maximize the profit?
Oh and do I have the first equation set up correctly?: R=(400-10x)(100+5x)
Thanks for your help!
-
Let n units = number occupied
P = Price
R = Revenue
C = Cost
A = Profit
n = 100-5(P-400)/10
n = 300-0.5P
R = nP
R = 300P-0.5P^2
C = 100n = 30,000-50P
A = R-C
A = 300P-0.5P^2-(30,000-50P)
A = 350P-0.5P^2-30,000
dA/dP = 350 - P = 0 for max profit
P = $350
P = Price
R = Revenue
C = Cost
A = Profit
n = 100-5(P-400)/10
n = 300-0.5P
R = nP
R = 300P-0.5P^2
C = 100n = 30,000-50P
A = R-C
A = 300P-0.5P^2-(30,000-50P)
A = 350P-0.5P^2-30,000
dA/dP = 350 - P = 0 for max profit
P = $350