For [x(st), x(pb)] and [y(s-prot), y(s-carbo)] feasible =>
[prot(st) x(st) + prot(pb) x(pb)] y(s-prot) >= q(prot) y(s-prot)
[carbo(st) x(st) + carbo(pb) x(pb)] y(s-carb) >= q(carbo) y(s-carb)
q(prot) y(s-prot) + q(carbo) y(s-carbo) <=
[prot(st) x(st) + prot(pb) x(pb)] y(s-prot) +
[carbo(st) x(st) + carbo(pb) x(pb)] y(s-carbo)
= x(st) [y(s-prot) prot(st) + y(s-carbo) carbo(st) ] +
x(pb) [y(s-prot) prot(pb) + y(s-carbo) carbo(pb)]
<= x(st) c(st) + x(pb) c(pb)
When they are equal, they both must be optimal.