SOLUTION: Imagine that you have just been elected the Mayor of Small City America. The City charter clearly stated that you are not allowed to run a budget deficit. Your first day in offic
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Question 82188: Imagine that you have just been elected the Mayor of Small City America. The City charter clearly stated that you are not allowed to run a budget deficit. Your first day in office, you asked the city controller to come over to your office for a “let me know what is happening” type of discussion. After drinking tea, you get down to business.
The controller informed you that the city founder believed in a simple fixed tax system. Currently, each city resident is tax at $1000 per year. The controller informed you that the city needs $1-million per year just to function even if there is no population to support. In addition to the fixed cost of running the city, the city needs to provide services to the residents. In order to help understand the cost of servicing the local population, the controller said that a local community college professor modeled the servicing cost, and said that the cost would be represented in the form of 0.2X2, where X is the number of city residents.
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?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
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?
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Revenue = 1000x
Expenses = 0.02x^2
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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.
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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.
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Cheers,
Stan H.
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