A feed stock available at a rate of 1000 mole/hr and consisting of (all in mole\%): 20.0% Propane (P) 30.0% Isobutane (B) 20.0% Isopentane (IP) 30.0% Normal Pentane (NP) is to be separated into two fractions by distillation. The distillate is to contain all of the propane fed to the unit and 80% of the isopentane fed to the unit, and is to consist of 40.0 mole\% isobutene. The bottoms stream is to contain all of the normal pentane fed to the unit. Calculate the flow rates of each component in both the distillate and the bottoms