Question 170796: Shakira is the manager of a 200-unit apartment complex. She is exploring how the monthly rent affects the number of vancant apartments in the complex. She found that she will rent all the apartments if she sets the monthly rent at $400, and found that for each $50 increase in the monthly rent, one additional apartment will remain vacant.
She is part owner of the apartment complex, she would like to set the rent so that she can actually make some money.
1. How many apartments should remain vacant so that the monthly rental revenue will be as large as possible.
2. What monthly rent should she charge for each apartment in the apartment complex.
3. draw a graph between monthly rent and number of occupied apartments. Write the equation of the graph.
4. Draw a graph between monthly revenue and number of occupied apartments. Write the equation of the graph. Use formula to find the vertex of the equation.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Shakira is the manager of a 200-unit apartment complex. She is exploring how the monthly rent affects the number of vancant apartments in the complex. She found that she will rent all the apartments if she sets the monthly rent at $400, and found that for each $50 increase in the monthly rent, one additional apartment will remain vacant.
She is part owner of the apartment complex, she would like to set the rent so that she can actually make some money.
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Revenue = price per apartment * # of apartments rented
R = (400+50x)(200-x) = 80000 + 800x - 50x
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1. How many apartments should remain vacant so that the monthly rental revenue will be as large as possible.
max occurs when x = -b/2a = -800/(2*-50) = 8 (# of vacant apartments)
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2. What monthly rent should she charge for each apartment in the apartment complex.
R(8) = (400+50*8)(200-8) = $153,600
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3. draw a graph between monthly rent and number of occupied apartments. Write the equation of the graph.
(occupied , rent): (200,400), (199,450)
slope = (450-400)/(199-200) = -50
intercept: 400 = -50*200 + b
b = 10400
EQUATION:
rent = -50*occupied + b
r(x) = -50x + 10400
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4. Use formula to find the vertex of the equation.
Vertex: Which equation ?
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Cheers,
Stan H.
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