Example
Minimize c(st) x(st) + c(pb) x(pb) subject to
prot(st) x(st) + prot(pb) x(pb) >= q(prot)
carbo(st) x(st) + carbo(pb) x(pb) >= q(carbo)
c(n) = per unit cost of food n, x(n) quantity of food n to purchase per day, prot(n) = units protein per unit of food n, carbo (n) = units carbo per unit n q(prot) = protein units per day needed, q(carbo) = carbo units per day
Dual -- druggist selling synthetic protein and carbohydrate pills
maximize q(prot) y(s-prot) + q(carbo) y(s-carbo) subject to
y(s-prot) prot(st) + y(s-carbo) carbo(st) <= c(st)
y(s-prot) prot(pb) + y(s-carbo) carbo(pb) <= c(pb)
y(s-prot), y(s-carbo) >= 0
Can then sell amount q(prot) of protein per day and q(carbo) of carbo per day.