# How to visualize duality

In My course of linear programming we are given the definition of a primal/dual problem. However I cannot really get my heard around what it actually is? It helps us in later exercises. Are we simplyfying the problem? Are we making it better to work with? \begin{align} \max & \sum_{j=1}^nb_jy_j \\ \text{s.t.} &\sum_{j=1}^n a_{ij}x_i = b_i &1\leq i \leq m\\ &x_j \geq 0 &i\leq j \leq n \end{align} \begin{align} \min & \sum_{i=1}^mb_iy_i \\ \text{s.t.} &\sum_{i=1}^m a_{ij}y_i \geq c_j &i\leq j \leq n\\ &y_i \in \mathbb{R} &i\leq i\leq m \end{align}