A distillation column is separating benzene ( \(\alpha=2.25\) ), toluene ( \(\alpha=\) \(1.00)\), and cumene ( \(\alpha=0.21\) ). The column is operating at \(101.3 \mathrm{kPa}\). The column has a total condenser and a partial reboiler, and the optimum feed stage is used. Reflux is a saturated liquid, and \(\mathrm{L}_{0} / \mathrm{D}=\) 1.2. Feed rate is \(1000.0 \mathrm{kmol} / \mathrm{h}\). The saturated liquid feed is \(39.7 \mathrm{~mol} \%\) benzene, \(16.7 \mathrm{~mol} \%\) toluene, and \(43.6 \mathrm{~mol} \%\) cumene. Recover \(99.92 \%\) of the benzene in the distillate and \(99.99 \%\) of the cumene in the bottoms. For a first guess to this design problem, use the FUG approach to estimate the optimum feed stage and the total number of equilibrium stages. Note: The Underwood equations must be treated as a Case \(\mathrm{C}\) problem.