$y$ Intercept of $x+y=5$ is $(0,5)$
$y$ -intercept of $x+3 y=9$ is $(0,3)$
The intersection point of $x+y=5$ and $x+3 y=9$ is $(3,2)$
Therefore, the corner points are $(0,5),(0,3),(3,2)$
At $(0,5), Z=35$
At $(0,3), Z=21$
At $(3,2), Z=47$
So, $Z_{\max }=47$ at $(3,2)$.
