A car rental agency rents $210$ cars per day at a rate of $$20$ per day. For each $$1$ increase in rate, $5$ fewer cars are rented. At what rate should the cars be rented to produce the maximum income? What is the maximum income?

The rental agency will earn a maximum income of $$,{?}_{\_\_\_\text{w}\text{h}\text{e}\text{n}}$itcharges$${?}_{\_\_\text{p}\text{e}\text{r}\text{d}\text{a}\text{y}\text{.}}$