A binary mixture containing 30 mol% hexane and 70mol% p-xylene is to be distilled. The mixture consists of an equimolar amount of vapour and liquid at a pressure of 1 atm and a flowrate of 200kmol/h. An overhead distillate is produced at a rate of 200 kmol/h containing 90mol% hexane. The bottom product contains 15mol% hexane. A liquid stream containing 65mol% hexane is also withdrawn at a rate of 250kmol/h. Hexane and p-xylene from a nearly ideal solution with a relative volatility of 7.0. If the reflux ratio is 4, calculate a)the flow rate of the feed and the bottom product b) the theoretical number of stages required to perform the separation c) the location of the feed and side stream plates.