Question

The rasmus rental company own 1600 apartments, currently 800 of the apartments are being rented at $300 per month. A market survey shows the each $5 decreased in the month rent will result in 20 more apartments being rented. Determine a function that models the total monthly rental income, where x is the number of $5 decreases in monthly rent

Answer 1

`f(x)=`
`Min(800+(20* x),1600) * Max(300-(5* x),0)`

Explanation:

Initial the number of apartments rented are
`800`

Initial rent for each apartment is $
`300`

Given that the number of $5 decreases is
`x`

Number of apartments rented for
`x` number of decreases=
`Min(800+(20* x),1600)`

This is because the maximum number of apartments are 1600.

Rent for each apartment for
`x` number of decreases=
`Max(300-(5* x),0)`

This is because the rent cannot be negative.

So, the function for total rental income=
`Min(800+(20* x),1600) * Max(300-(5* x),0)`