An artist is planning to sell signed prints of her latest work. If $30$ prints are offered for sale, she can charge $$400$ each. However, if she makes more than $30$ prints, she must lower the price of all the prints by $$5$ for each print in excess of the $30.$ That is$,31$ prints reduce the price by $$5,32$ prints reduce the price by $$10,$ and so on$.$ How many prints should the artist make to maximize her revenue?

Let $x$ be the number of prints and $p$ the price per print. The demand equation is $p=$ and the revenue function is $R(x)=$