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Three distillation schemes for separating an equimolar, constant relative volatility $ABC$ mixture into nearly pure components are shown. The usual simplifying assumptions such as constant molal overflow, negligible heat loss, ideal trays are valid. All the schemes are designed for minimum total reboiler duty. Given that the relative volatilities are in the ratio $\alpha _{A}:\alpha _{B}:\alpha _{C}\equiv 8:2:1$, the correct option that arranges the optimally-designed schemes in ascending order of total reboiler duty is

- $I, II, III$
- $III, I, II$
- $II,I, III$
- $III, II, I$