Answer:
$950 in order to maximize the revenue.
Explanation:
The computation of monthly rent in order to maximize revenue is shown below:-
R (x) = Rent price per unit × Number of units rented
= ($900 + $10 x) × (100 - x)
= $90,000 - 900 x + 1000 x - 10 x^2
R (x) = -10 x^2 + 100 x + $90,000
Here to maximize R (x), we will find derivative and equal it to zero
R1 (x) = -20 x + 100 = 0
20 x = 100
x = 5
Therefore the monthly rent is p(5) = $900 + 10(5)
= $900 + 50
= $950 in order to maximize the revenue.
If a market survey suggests that, on average, one additional unit will remain vacant for each $10 increase in rent. What rent should the manager charge to maximize revenue will be $1,000
x = $10 increases
Price=$900+10x
Quantity=100-x
First step is to find revenue by coming up with an equation
Revenue=Price × Revenue
R(x)=(900+10x) (100-x)
Second step is to maximize the revenue
R(x)=90,000 +200x-10x²
Third step is to find the derivative and set it to zero
R(x)=200-20x
0=200-20x
20x=200
Divide both side by 20x
x=200/20
x=10
Fourth step is to determine rent that the manager should charge to maximize revenue
Price=$900+10x
Price=$900+10(10)
Price=$900+$100
Price=$1,000
Inconclusion if a market survey suggests that, on average, one additional unit will remain vacant for each $10 increase in rent. What rent should the manager charge to maximize revenue will be $1,000
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