Duality Theorem
Druggist’s max revenue = Purchasers min cost
One direction of duality easy , for any feasible x, y:
q(prot) y(s-prot) + q(carbo) y(s-carbo) <= x(st) c(st) + x(pb) c(pb)
Since each food can be replaced by its vitamin equivalent, with no increase in cost, all adequate diets must be at least as expensive as any price the druggist would charge.