Linear programming is to be used to optimize the operation of the solvent splitter column shown in Fig E. The feed is naphtha, which has a value of $40/bbl in its alternate use as a gasoline blending stock. The light ends sell at $50/bbl, while he bottoms are passed through a second distillation column to yield two solvents. A medium solvent comprising 50 to 70% of the bottoms can be sold for $70/bbl., while the remaining heavy solvent (30 to 50% of the bottoms) can be sold for $40/bbl.
Another part of the plant requires 200 bbl/day of medium solvent; an additional 200 bbl/day can be sold to an external market. The maximum feed that can be processed in column 1 is 2000 bbl/day. The operational cost (i.e., utilities) associated with each distillation column is $2.00/bbl feed. The operating range for column 2 is given as the percentage split of medium and heavy solvent. Solve the linear programming problem to determine the maximum revenue and percentages of output streams in column2.