I am working from the Bertsimas and Tsitsiklis textbook, exercise 6.2 in chapter 6 available here. This problem is using the resolution theorem to reformulate problems and get the Dantzig-Wolfe Decomposition. I am unable to resolve (no pun intended) this bit of theory. The resolution therorem is repeated here:
I know that the solution says it is not necessary to include the rays $w_1$ and $w_2$ because the original problem is bounded. I understand very clearly that the original problem is bounded - there are non-negativity constraints, and bounds on the variables.
But, how does just because the problem is bounded mean that we do not have to include all of the variables $w_1$ and $w_2$?