The business manager of a 90 unit apartment building is trying to determine the rent to be charged.  From past experience with similar buildings, when rent is set at $400, all the units are full.  For every $20 increase in rent, one additional unit remains vacant. What rent should be charged for maximum total revenue?  1. What is the maximum total revenue?   2. What is the formula for revenues  R  after   x  $20 price hikes in the apartment building?   3. Graph the function   4. Find the maximum revenue (or income) of the apartment building.   5. What is the rent that coincides with this maximum revenue?   6. What is the outcome of the rent hike of $20 results in 2 additional vacancies instead of 1 additional vacancy? Recalculate questions 3, 5, 6 for this new scenario.

Question

The business manager of a 90 unit apartment building is trying to determine the rent to be charged.  From past experience with similar buildings, when rent is set at $400, all the units are full.  For every $20 increase in rent, one additional unit remains vacant. What rent should be charged for maximum total revenue? 

1. What is the maximum total revenue?

 

2. What is the formula for revenues  R  after   x  $20 price hikes in the apartment building?

 

3. Graph the function

 

4. Find the maximum revenue (or income) of the apartment building.

 

5. What is the rent that coincides with this maximum revenue?

 

6. What is the outcome of the rent hike of $20 results in 2 additional vacancies instead of 1 additional vacancy? Recalculate questions 3, 5, 6 for this new scenario.

 

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