Question

You are the manager of an apartment complex with 50 units. When you set rent at $700/month, all apartments are rented. As you increase rent by $25/month, one fewer apartment is rented. Maintenance costs run $50/month for each occupied unit. What is the rent (in dollars) that maximizes the total amount of profit?

Answer #1

The manager of a large apartment complex knows from experience
that 90 units will be occupied if the rent is 300 dollars per
month. A market survey suggests that, on the average, one
additional unit will remain vacant for each 1 dollar increase in
rent. Similarly, one additional unit will be occupied for each 1
dollar decrease in rent. What rent should the manager charge to
maximize revenue?

The manager of a large apartment complex knows from experience
that 80 units will be occupied if the rent is 368 dollars per
month. A market survey suggests that, on the average, one
additional unit will remain vacant for each 8 dollar increase in
rent. Similarly, one additional unit will be occupied for each 8
dollar decrease in rent. What rent should the manager charge to
maximize revenue?

The manager of a large apartment complex knows from experience
that 100 units will be occupied if the rent is 340 dollars per
month. A market survey suggests that, on the average, one
additional unit will remain vacant for each 10 dollar increase in
rent. Similarly, one additional unit will be occupied for each 10
dollar decrease in rent. What rent should the manager charge to
maximize revenue?

The manager of a large apartment complex knows from experience
that 110 units will be occupied if the rent is 468 dollars per
month. A market survey suggests that, on the average, one
additional unit will remain vacant for each 9 dollar increase in
rent. Similarly, one additional unit will be occupied for each 9
dollar decrease in rent. What rent should the manager charge to
maximize revenue?

A real estate office handles a 80-unit apartment complex. When
the rent is $550 per month, all units are occupied. For each $45
increase in rent, however, an average of one unit becomes vacant.
Each occupied unit requires an average of $70 per month for service
and repairs. What rent should be charged to obtain a maximum
profit?

Marginal Revenue for an Apartment Complex
Lynbrook West, an apartment complex, has 100 two-bedroom units.
The monthly profit (in dollars) realized from renting x
apartments is represented by the following function.
P(x) = -9x2 +
1520x - 52000
(a)
What is the actual profit realized from renting the 41st unit,
assuming that 40 units have already been rented?
$
(b)
Compute the marginal profit when x = 40 and compare
your results with that obtained in part (a).
$

You own a 500-unit apartment complex and charge a monthly
rental rate of $1,200 per unit. When the apartments are 96%
occupied, monthly operating costs total $300,000, $240,000 of
which are variable costs. A nearby manufacturing plant has just
announced that it is closing in the upcoming year. As a result,
you anticipate occupancy will decrease to 85%. Using your
knowledge of cost behavior, what is your predicted monthly
operating income?
A.
$225,600
B.
$246,000
C.
$216,875
D.
$237,500
E....

You are considering a luxury apartment building project that
requires an investment of $12,500,000. The building has 35 units.
The firm expects that the maintenance cost for the apartment
building will be $250,000 in the first year, and to rise to
$300,000 in the second year, and to continue to increase by $50,000
in subsequent years. The cost to hire a manager for the building is
estimated to be $80,000 per year. After four years of operation,
the apartment building...

A box is constructed out of two different types of metal. The
metal for the top and bottom, which are both square, costs $2 per
square foot and the metal for the sides costs $6 per square foot.
Find the dimensions that minimize cost if the box has a volume of
15 cubic feet. Length of base x= ___Height of side
z=___
The manager of a large apartment complex knows from experience
that 80 units will be occupied if the...

Allen Benedict is thinking of buying an apartment complex that
is offered for sale by the firm of Getz and Fowler. The price,
$2.25 million, equals the property's market value. The following
statement of income and expense is presented for Benedict's
consideration:
The St. George Apartments Prior Year's Operating Results,
Presented by Gertz and Fowler, Brokers
30units, all 2-bedroom
apartments, $975/month
$351,000
water & dryer rentals
10,000
gross annual income
$361,000
Less operating
expenses:
Manager's salary
$10,000
Maintenance staff (1...

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