A 48-unit apartment building was sold to a new owner. The previous owner charged

Question

A 48-unit apartment building was sold to a new owner. The previous owner charged $700 per month rent and had a 100% occupancy rate. The new owner, aware that this rental amount was well below other rental prices in the area, immediately raised the rent to $750. Over the next 6 months an average of 47 units were occupied. The owner raised the rent to $800 and found that 2 of the units were unoccupied during the next 6 months. If the occupancy rate continues to decrease as the rent increases in the same manner as it did for the first two increases, what rent amount will maximize the owner’s rental income from this apartment building?

Explanation / Answer

given data is

initial rent is $700

incresing rate is $50 per 6 months

as first increment of $50 the  occupancy is decresed by 1

as second increment of $50 the  occupancy is decresed by 1 i.e 46

as third increment of $50 the  occupancy is decresed by 3 i.e 45

that means the occupancy is decresed to 1 is after 47 increments of rent

then maximum increment is 47*$50=$22350

the maximum rent is $22350+$700=23050

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