I understand the strong duality theorem:
A linear program that has an optimal solution, also has a dual problem. That dual problem also has an optimal solution with an optimal cost equal to that of the original linear program
What I don't understand is, why is sharing the same optimal cost such a big deal? I would have thought that sharing the same minimizer/optimal point would be worth noting, because then the solution vector of one (the primal or the dual) can be used for the other. But, I do not understand why sharing the same optimal cost is worth noting....what am I missing out on big here?
thanks you.