By Lucia Mutikani WASHINGTON (Reuters) – U.S. producer prices increased by the most in eight months in January amid a surge in the cost of hospital outpatient care and goods such as food and motor vehicles, another sign that high inflation could persist through much of this year. Broadening inflation pressures were underscored by other data on Tuesday showing a measure of prices received by factories in New York state surged to a record high in February, while manufacturers reported they continued to pay higher prices for inputs. The reports followed on the heels of news last week of a strong …