I have a standard form problem $P = \max\{r'x:Ax\leq b, x\geq0\}$ with dual $D=\min\{b'y:A'y\geq r,y\geq 0\}$.
I want to obtain bounds on optimal dual variables $\bar y$. In other words, if $\bar y$ is optimal, how to obtain upper bounds $\bar y_i\leq something$, for some component $i$?
Hopefully the bound does not depend on $b$, but on $r$ and $A$ only.
My intuition is that $y_i$ is the gain by an extra unit of $b_i$, hence the following problem should provide a bound: $P_i = \max\{r'x:Ax\leq e_i, x\geq0\}$, with $e_i$ the canonical vector.
Any pointers are much appreciated.