An artist is planning to sell signed prints of her latest work. If $40$ prints are offered for sale, she can charge $$550$ each. However, if she makes more than $40$ prints, she must lower the price of all the prints by $$5$ for each print in excess of the $40.$ That is$,41$ prints reduce the price by $$5,42$ prints reduce the price by $$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 $R(x)=$