TORONTO — Someone’s about to put Baby in a corner.Producer David Mirvish announced Sunday a March 29 closing date for the Toronto run of “Dirty Dancing, the Classic Story on Stage.” When it shutters, the tuner will have played 582 performances at the Royal Alexandra Theater. The show, based on the cult 1987 movie, opened in Toronto in November 2007 to mixed notices but played to capacity audiences for almost the entire first year of its run. After that sales dipped slightly, and while attendance has remained solid, discount pricing has been in effect at weekday performances in recent weeks. By the time “Dirty Dancing” closes, it will have played to 800,000 people, according to Mirvish Prods. The company claims the show has been responsible for C$500 million ($405 million) in economic spinoff to the city in ticket sales, concessions, hotels, restaurants and travel. Sources close to the production say it recouped its costs in December and has been running at a profit since. But the ailing economy, soft advance sales, heavy competition (four other major musicals are still running in Toronto) and the need to free up the theater for other upcoming Mirvish projects, such as “Priscilla Queen of the Desert,” prompted the producers’ decision to quit while they were ahead. “Dirty Dancing” has been a strong seller in London since it opened in the West End in October 2006. The show recently wrapped a Chicago run and is scheduled to play Boston and Los Angeles in the coming weeks before an anticipated Broadway bow in the fall.