Solution:
It is given that: 
Taking 
![\[\begin{tabular}{|l|l|l|} \hline$x$ & 1 & 0 \\ \hline$y$ & 0 & 1 \\ \hline \end{tabular}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-766ed106222930fafcfc0eaf56599d71_l3.png "Rendered by QuickLaTeX.com")
Now, plotting all the constrain equations it can be seen that the shaded area 
The area is feasible. Therefore, maximum value will occur at the corner points 
On evaluating the value of 
![\[\begin{tabular}{|l|l|} \hline Corner points & Value of Z \\ \hline $0(0,0)$ & $3(0)+4(0)=0$ \\ \hline $\mathrm{A}(1,0)$ & $3(1)+4(0)=3$ \\ \hline $\mathrm{B}(0,1)$ & $3(0)+4(1)=4$ \hline \end{tabular}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-e54cdf2df3792692e78e4d96a698bb9b_l3.png "Rendered by QuickLaTeX.com")
It can be seemn from the above table that the maximum value of 
So, the maximum value of 
