Solution:
It is seen from the given figure, that the corner points are as follows:
and 
On evaluating the value of 
for the feasible region RQPS.
![\[\begin{tabular}{|l|l|} \hline Corner points & Value of $\mathrm{Z}=\mathrm{x}+2 \mathrm{y}$ \\ \hline $\mathrm{R}(7 / 2,3 / 4)$ & $\mathrm{Z}=7 / 2+2(3 / 4)=5$ \\ \hline $\mathrm{Q}(3 / 2,15 / 4)$ & $\mathrm{Z}=3 / 2+2(15 / 4)=9$ \\ \hline $\mathrm{P}(3 / 13,24 / 13)$ & $\mathrm{Z}=3 / 13+2(24 / 13)=51 / 13$ \\ \hline $\mathrm{S}(18 / 7,2 / 7)$ & $\mathrm{Z}=18 / 7+2(2 / 7)=22 / 7$ \\ \hline \end{tabular}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-9cabe59c1b330b9e35e3eee8bee6267f_l3.png "Rendered by QuickLaTeX.com")
It is seen from the above table that the minimum value of 
is 
and maximum value of is 9.
Thus, the maximum value of is 9 at 
and the minimum value of is at 
.