SOLUTION: The owner of an apartment building with 50 units has found that if the rent for each unit is $360 per month, all the units will be filled. He wants to increase the rent but has ca

Algebra ->  Test -> SOLUTION: The owner of an apartment building with 50 units has found that if the rent for each unit is $360 per month, all the units will be filled. He wants to increase the rent but has ca      Log On


   

Question 255988: The owner of an apartment building with 50 units has found that if the rent for each unit is $360 per month, all the units will be filled. He wants to increase the rent but has calculated that one unit will become vacant for each $10 increase in monthly rent. What monthly rent would maximize the monthly income for the owner? What is his maximum monthly income.
I'm pretty sure the equation is y=-10x^2+140x+18000.
Then I did the (-b/2a) and got 7...what do I do after that?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
if you right, they you want to find f(-b/2a)

take the value of 7 and plug it into the equation to get:

y=-10x^2+140x+18000 becomes:

y=-10(7)^2+140(7)+18000 becomes:

y = -490 + 980 + 18000 = 18490 which should be the maximum rent he collects for the month.

graph of your equation looks like:

graph+%28600%2C600%2C-10%2C75%2C-5000%2C25000%2C-10%2Ax%5E2+%2B+140%2Ax+%2B+18000%29

y looks like it represents the total rent for the month.

x looks like it represents the number of units vacant for the month.

based on that the graph looks good.

7 vacant rooms means 43 filled at 360 + 70 = 430 per room = 18490.
6 vacant rooms means 44 filled at 360 + 60 = 420 per room = 18480.
8 vacant rooms means 42 filled at 360 + 80 = 440 per room = 18480.

you definitely get peak revenue with 7 vacant rooms.