A manufacturing company has a $3 \times 2$ matrix $P$ where entry $P_{ij}$ is the number of units of product $j$ made by factory $i$. If $P = \begin{pmatrix} 100 & 150 \\ 120 & 80 \\ 90 & 110 \end{pmatrix}$, what is the total production of product 2 across all factories?