The closure of restaurants, hotels and school cafeterias wiped out huge sources of demand for fresh food, leaving farmers with millions of pounds of excess. While increased sales at grocery stores have made up for some of that, not since the Great Depression has so much fresh food been destroyed. (In the 1930s, the problem was that people could not afford to buy all the crops farmers were producing, which led the federal government to establish an early food stamp program.)

The Agriculture Department grants are expected to be announced this week, but farmers say their losses far exceed what the grants can provide.

“These are not insolvable problems,” said Marion Nestle, a food studies professor at New York University. “These are problems that require a lot of people, sums of money and some thought. If the government were really interested in making sure that hungry people got fed and farmers were supported, they would figure out a way to do it.”