A column equipped with a partial reboiler and total condenser, operating at steady state with a saturated$-$liquid feed, has a liquid sidestream in the rectifying section. Using the McCabe$-$Thiele assumptions: $($a$)$ derive the two operating lines in the rectifying section; $($b$)$ find the point of intersection of the operating lines; $($c$)$ find the intersection of the operating line between $F$ and LS with the diagonal; and $($d$)$ show the construction on a $y-x$ diagram.