$(20$ pts$)$ A distillation column has a feed stream containing three components, $i,j,$ and $k,$ and three exit streams $($distillate$,$ side stream, and bottoms$).$ The distillate contains only i and $j$ components, while the bottoms product contains only $j$ and $k$ components. The side stream contains all three components. Draw and label column showing the flow rates $(F,$ D$,$ S$,$ and B$)$ and their respective mass fraction compositions $($i$.$e$.,x_{Dj}).$ Perform an overall mass balance and a component balance for component, $j.$ In algebraic form, solve for $x_{Dj}.$