Solution:
It is given that: 
and the constraints 
Taking 
, we have
![\[\begin{tabular}{|l|l|l|} \hline$x$ & 1 & 0 \\ \hline$y$ & 0 & 1 \\ \hline \end{tabular}\]](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 
is the feasible region determined by the constraints.
The area is feasible. Therefore, maximum value will occur at the corner points 
On evaluating the value of 
, we obtain
![\[\begin{tabular}{|l|l|} \hline Corner points & Value of Z \\ \hline $0(0,0)$ & $3(0)+4(0)=0$ \\ \hline $\mathrm{A}(1,0)$ & $3(1)+4(0)=3$ \\ \hline $\mathrm{B}(0,1)$ & $3(0)+4(1)=4$ \hline \end{tabular}\]](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 
is 
So, the maximum value of is 4 at 
.