By Dan Burns (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 – and lower inflation – through higher interest rates. But the Fed’s aggressive rate hike campaign has delivered another blow to the housing sector, with market sentiment among U.S. home builders sliding for the 10th month in a row in October as soaring mortgage rates and bottlenecks for building materials put new home purchases out of reach for m…