According to the question:
![\[\mathbf{Z}\text{ }=\text{ }\mathbf{11}x~+\text{ }\mathbf{7}y\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-5c7a02563203520b7505fe3ddb709e9f_l3.png "Rendered by QuickLaTeX.com")
and the constraints
![\[x~\text{£}\text{ }\mathbf{3},~y~\text{£}\text{ }\mathbf{2},~x~{}^\text{3}\text{ }\mathbf{0},~y~{}^\text{3}\text{ }\mathbf{0}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-32897c7ada69b747fc2df4430eae78b1_l3.png "Rendered by QuickLaTeX.com")
.
Plotting all the constrain equations we see that the shaded area OABC is the feasible region determined by the constraints.
The feasible region is bounded with four corner points
![\[O\left( 0,\text{ }0 \right),\text{ }A\left( 3,\text{ }0 \right),\text{ }B\left( 3,\text{ }2 \right)\text{ }and\text{ }C\left( 0,\text{ }2 \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-bd7cb3e2fe3a5fdf4564398f19ee1b3f_l3.png "Rendered by QuickLaTeX.com")
.
So, the maximum value can occur at any corner.
On evaluating the value of Z, we get
From the above table it’s seen that the maximum value of Z is
![\[47\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-478bcf681214c6572117bf0975c080c5_l3.png "Rendered by QuickLaTeX.com")
.
Therefore, the maximum value of the function Z is
at
![\[\left( 3,\text{ }2 \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-fb5671fef5edab2b7e17c050e6f216b2_l3.png "Rendered by QuickLaTeX.com")
.