It is desired to separate the most volatile component (A) of a binary mixture by distillation. The feed contains 46% mol of A and is 50% vaporized. The liquid-vapor equilibrium data can be obtained with the average relative volatility, whose value is 2. The column operates with a total condenser which generates a saturated liquid. to obtain 85% mol of component A in the distillate and 83% mol of component B in the bottom. With the information provided determine: (a) The minimum reflux: (b) The optimum feed stage number: (c) The theoretical number of stages at a reflux of 2.3. d) The theoretical number of stages if the feed stage were 3. e) The theoretical number of stages if live steam were used instead of the partial reboiler and fed through the optimum stage.