You serve as a chemical engineer at the BP refinery, with responsibility for overseeing operations involving the fractionating column. The column receives an equimolar mixture of Benzene and Toluene and consists of $5$ plates, including a condenser and reboiler, with a total condenser. This system maintains a constant volume and integrates a heating coil to warm the crude oil, alongside a shaft for agitating the oil within the tank. Designed to yield a distillate of $95\%$ purity with a $10\%$ waste in the bottoms, the column operates with a relative volatility of $3\mathrm{.}2$ and a reflux ratio of $3\mathrm{.}5.$ The feed remains in liquid state at its boiling point, and reflux is reintroduced to the column at $100$ degrees Celsius. The maximum feed rate is set at $10,000k\frac{g}{h},$ with the minimum feed rate established at $70\%$ of this maximum. Sieve plates are employed in the column.

Determine the condenser duty and reboiler heat$-$duty.

Determine the efficiency for this distillation column.

Assuming $100mm$ water pressure drop per plate. Estimate the bottoms pressure for this column.

Devise a troubleshooting strategy to find the root cause of the column malfunctioning.