The total revenue function for a product is $R(x)=55x-0\mathrm{.}02x^2,$ where $R$ is in dollars and $x$ is the number of items made and sold.

a$)$ Find the number of items that should be sold to maximize revenue.

$x=$

b$)$ What is the maximum revenue? $($Round to two decimal places if needed.$)$

$ $$

c$)$ What is the maximum revenue if production is limited to $1000$ items? $($Round to two decimal places if needed.$)$

$