Mr. Pablo owns an apartment building with 60 rooms. he can rent them all if he sets a monthly rent of $ 200 per room. With a higher rent, some rooms would be left empty. On average, for every $ 5 rent increase, a room would be left empty with no possibility of rent. Determine the functional relationship between total monthly income and the number of empty rooms. What monthly rent will maximize the total income? What is this maximum income?