The feasible region is shown in the picture above. The horizontal axis is the X axis.
If you now draw a family of lines parallel to [tex] 5x+4y=C[/tex] through the region, increasing $C$, that is, the X-intercept, we will have the maximum value of $C$ when the line passes through the endpoint $(-2,6)$ .
Hence, $C=5(-2)+4(6)=14$
