A 2011 University of Michigan study of more than a thousand middle school students found that those who regularly ate school lunches were 29 percent more likely to be obese than those who brought lunch from home. Of course, what a child eats for lunch is just one of many factors that determines whether he or she becomes overweight or obese. But many schools’ dependence upon revenue from vending machines and brand-name fast-food over the past decade may be a tipping point. Tony Geraci, executive director of child nutrition for Memphis City public schools, where 17 percent of high school students are obese, and Marion Nestle, professor of nutrition at New York University and author of “Safe Food: The Politics of Food Safety,” discuss the challenges of feeding children in schools.