We investigate the production of ethanol through continuous fermentation using Saccharomyces cerevisiae in a single reactor and cascades of two or three reactors. We use path following methods to investigate how the ethanol yield varies with the residence time in each reactor configuration of the cascade. Yields currently obtained in industry using yeast are approximately 0.48. We find reactor designs where the product yield approaches the stoichiometric limit of 0.51. We also estimate the financial benefits that can be achieved in typical US ethanol plants through increasing the product yield from 0.48 to 0.51.