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
Asked Jan 23, 2020
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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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Expert Answer

Step 1

Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and specify the other subparts (up to 3) you’d like answered.

Initial rent = $400 , and total 90 units are there

For every $20 increase in rent, one additional unit remains vacant

Let him increase $20 x times 

So new rent = 400+20x and units occupied = (90-x)

Step 2

Total revenue = (400+2x)(90-x)

Calculus homework question answer, step 2, image 1
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Step 3

For maximum revenue R'(x)=0, s...

Calculus homework question answer, step 3, image 1
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