A woman has a building with 26 one-bedroom apartments, 40 two-bedroom apartments, and 60 three-bedroom apartments available to rent to students. She has set the rent at $550 per month for the one-bedroom units, $900 per month for the two-bedroom units, and $1,100 per month for the three-bedroom units. She must rent to one student per bedroom, and zoning laws limit her to at most 250 students in this building. There are enough students available to rent all the apartments. How many of each type of apartment should she rent to maximize her monthly revenue? Find the maximum possible monthly revenue. Round your profit to the nearest dollar.
A)Maximum revenue is $89,250 by renting 25 1 - BR, 35 2 - BR, and 40 3 - BR apartments.
B)Maximum revenue is $93,100 by renting 22 1 - BR, 35 2 - BR, and 45 3 - BR apartments.
C)Maximum revenue is $105,850 by renting 29 1 - BR, 40 2 - BR, and 49 3 - BR apartments.
D)Maximum revenue is $98,300 by renting 30 1 - BR, 42 2 - BR, and 40 3 - BR apartments.
E)Maximum revenue is $103,100 by renting 26 1 - BR, 40 2 - BR, and 48 3 - BR apartments.

Question

A woman has a building with 26 one-bedroom apartments, 40 two-bedroom apartments, and 60 three-bedroom apartments available to rent to students. She has set the rent at $550 per month for the one-bedroom units, $900 per month for the two-bedroom units, and $1,100 per month for the three-bedroom units. She must rent to one student per bedroom, and zoning laws limit her to at most 250 students in this building. There are enough students available to rent all the apartments. How many of each type of apartment should she rent to maximize her monthly revenue? Find the maximum possible monthly revenue. Round your profit to the nearest dollar. ​
A)Maximum revenue is $89,250 by renting 25 1 - BR, 35 2 - BR, and 40 3 - BR apartments.
B)Maximum revenue is $93,100 by renting 22 1 - BR, 35 2 - BR, and 45 3 - BR apartments.
C)Maximum revenue is $105,850 by renting 29 1 - BR, 40 2 - BR, and 49 3 - BR apartments.
D)Maximum revenue is $98,300 by renting 30 1 - BR, 42 2 - BR, and 40 3 - BR apartments.
E)Maximum revenue is $103,100 by renting 26 1 - BR, 40 2 - BR, and 48 3 - BR apartments.

Quizplus · Accepted Answer

To maximize revenue, the woman should aim to rent as many of the higher-priced, larger apartments as possible without exceeding the zoning limit of 250 students. One way to do this is to rent out all of the three-bedroom apartments, as there are more of those than there are two-bedroom apartments. Then, she should rent as many two-bedroom apartments as possible, and fill in the remaining space with one-bedroom apartments.

Using this strategy, the woman can rent out 48 three-bedroom apartments, leaving 12 slots for two-bedroom apartments. She can then rent out 40 of the two-bedroom apartments, leaving 26 slots for one-bedroom apartments. This gives a total of 48 x $1,100 + 40 x $900 + 26 x $550 = $103,100 in monthly revenue. Therefore, the best choice is E.

A Woman Has a Building with 26 One-Bedroom Apartments, 40