I have just begun learning about LP duality and how to take the dual of an LP, however this question I've come across has me stumped:
\begin{alignat}{4} \max \quad & \rlap{\sum_{j=1}^{m} \sum_{i=1}^{n}v_{ij}x_{ij}} \\ \text{s.t. } \quad & \sum_{j=1}^{m}x_{ij} &=1 & \quad\forall\, i\in \{1,...n\} \\ & \sum_{i=1}^{n}x_{ij} &\leq b & \quad\forall\, j\in \{1,...m\},\\ \text{where } \quad&x_{ij} \ge 0 \\ & \rlap{v_{ij} \text{ are constants}.} \end{alignat}