Question 82188
Write the quadratic equation the models the city’s budget (Expected Revenue versus the Expected Cost).

At what population level would the city run its maximum budget surplus, and what is the value of the maximum budget surplus? 
What is the highest number of people the city can support without running a deficit?
----------
Revenue = 1000x
Expenses = 0.02x^2
---------
Budget = 1000x-0.02x^2
You have a quadrate with a=-0.02 ad b=1000
maximum budget occurs when x=-b/2a = -1000/(-0.04)= 25000 people.
--------------
No deficit means Revenue = Expenses
1000x = 0.02x^2
0.02x^2-1000x=0
0.02x(x-50000)=0
x= 0 or x=50000 people.
Revenue = Expenses when there are 50000 people.
================
Cheers,
Stan H.
--------------