(Reuters) – Production at U.S. factories rose in September led by output gains in both durable and nondurable goods, indicating the manufacturing sector remains on reasonable footing despite the Federal Reserve’s efforts to hamper demand through higher interest rates. Manufacturing output rose 0.4% last month, keeping pace with an upwardly revised 0.4% gain in August, the Federal Reserve said on Tuesday. Economists polled by Reuters had forecast factory production would rise 0.2%. Output increased 4.7% from a year earlier. Overall industrial production rose 0.4%, after slipping 0.1% the prior …