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\times x),1600) \times Max(300-(5\times x),0)$

Step-by-step 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=$Min(800+(20\times x),1600)$

This is because the maximum number of apartments are 1600.

Rent for each apartment for $x$ number of decreases=$Max(300-(5\times x),0)$

This is because the rent cannot be negative.

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