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Illustrating how, when there are alternative optima,
Simplex method chooses an extreme point solution, whereas
Interior Point/Barrier (without crossover) chooses
an interior solution that, loosely speaking, is an average
of all extreme point solutions.
When there are alternative optima, and there are secondary
multi-critera, some users may prefer the unique solution of
the barrier method to the essentially random arbitrary choice
of one of the extreme point optima.