Using the Peng-Robinson equations for thermodynamic properties, calculate the product compositions, stage temperatures, interstage vapor and liquid flow rates and compositions, reboiler duty, and condenser duty for the following multiple-feed distillation column, which has 30 equilibrium stages exclusive of a partial condenser a partial reboiler and operates at 250 psia. Feeds (both bubble-point liquids at 250 psia):Distillate rate = 36.0 lbmolhr.Reflux rate = 150.0 lbmol/hr.Determine whether the feed locations areoptimal.

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Pound-moles per Hour Feed 2 to Stage 6 Feed 1 to Stage 15 from the Bottom from the Bottom Component 1.5 Ethane 0.5 Propane 24.0 10.0 16.5 22.0 n-Butane n-Pentane 7.5 14.5 n-Hexane 0.5 3.0