It is desired to separate propylene from trans$-2-$butene in a distillation column. The feed stream is available as saturated liquid at $15$ bar, and has the following compo$-$ sition propylene $45$ mol$/$s$,10$ mol$/$strans$-2-$butene, $15$ mol$/$scis$-2-$butene $,6$ mol$/$s$1-$butene, $5$ mol$/$sethylene$,4$ mol$/$spropane It is desired to recover $99\mathrm{.}5\%$ of the propylene in the distillate and $99\%$ of trans$-2-$ butene in the bottom stream. a$.$ Determine the tTEMPERATURE of the feed stream and the minimum number of plates that are required for the column. b$.$ Determine the mole fraction composition of the distillate and the bottoms. c$.$ If cooling water at $90\backslash$deg F is to be used in the condenser with AT min $=10\backslash$deg C$,$ what would be the lowest pressures at which the column should operate if the distillate is obtained as either saturated liquid or saturated vapor? Also, for these two cases, what would be the maximum temperatures in a total reboiler?