David I. Mitchell, who did the scenic design for more than 30 Broadway shows, was nominated for seven Tony Awards and won two, for “Annie” and “Barnum,” died of cancer on Monday, Oct. 3, in Los Angeles. He was 79.His other Tony-nominated shows were “Trelawny of the Wells” in 1976, “Working” (1978), “Can-Can” (1981), “Foxfire” in 1983 and “The Boys of Winter” (1986). Other Broadway work included “La Cage aux Folles” and Neil Simon’s “Brighton Beach Memoirs” and “Biloxi Blues”; his last Rialto effort was the musical revue “Dream” in 1997. Mitchell was born in Honesdale, Pa., and attended Kutztown State Teachers College, where he was first introduced to theater. He spent two years in the Army, after which he studied theater design as a graduate student at Boston U. There his teacher was Horace Armistead, a designer for theater, opera and ballet and an early winner of the Tony Award for set design. In New York, Mitchell worked as an assistant to Ming Cho Lee for several years and, through him, began a longtime association with Joseph Papp, designing sets both for Shakespeare in the Park and the Public Theater. At the New York City Ballet, he designed works for Jerome Robbins and George Balanchine, as well as “Sleeping Beauty.” His opera designs included works at the New York City Opera (“Mephistophele”) and other U.S. opera houses as well as Deutsche Oper in Berlin (“Aida”). As a production designer for film, Mitchell’s credits include “Rich Kids,” Paul Simon pic “One Trick Pony” and “My Dinner With Andre.” He is survived by a daughter and son.