A Tight Lower Bound for the Weights of Maximum Weight Matching in Bipartite Graphs

Let $\text{Ga}$ be the collection of all weighted bipartite graphs each having $\sigma$ and $m$, as the size of a vertex partition and the total weight, respectively. We give a tight lower bound $\lceil \frac{m-\sigma}{\sigma} \rceil+1$fortheset${$\mathit{\text{Wt}}$($\mathit{\text{mwm}}$(G))~|~G \in \Ga}$ which denotes the collection of weights of maximum weight bipartite matchings of all graphs in $\text{Ga}$.