Lon Frahm may represent the future of farming. Inside a two-story office building overshadowed by 80-foot steel grain bins, he points to a map showing the patchwork of square and circular fields that make up his operation. It covers nearly 10% of the county’s cropland, and when he climbs into his Cessna Skylane to check crops from the air, he can fly 30 miles before reaching the end of his land. At 30,600 acres, his farm is among the country’s vastest, and it yields enough corn and wheat each year to fill 4,500 semitrailer trucks. Big operations like Mr. Frahm’s, which he has spent decades building, are prospering despite the deepest farm slump since the 1980s. Years of low prices for corn, wheat and other commodities brought on by a glut of grain world-wide are driving smaller American farmers out of business.