Answer
26
Work Step by Step
Step I:
From the given constraints, draw all the lines and their region.
In the first constraints:
\[x\ge 0\], it is the region where x takes only positive values.
In the second constraints:
\[y\ge 0\], it is the region where y takes only positive values.
In the third constraints:
\[x+y\le 6\].
Draw first, \[x+y=6\].
It is the line with
\[\begin{align}
& x-\text{intercept}=6 \\
& y-\text{intercept}=6 \\
\end{align}\]
Now, put \[x=0,\text{ and }y=0\].
Which gives, \[0\le 6\], which is true, it means region contains the origin.
Step II:
The corner values are:
\[A\left( 6,0 \right),B\left( 2,0 \right),\text{ and }C\left( 2,4 \right)\]
Step III:
The value of the objective function at a point\[\left( 6,0 \right)\]is:
\[\begin{align}
& z=3\times 6+5\times 0 \\
& =18
\end{align}\]
The value of the objective function at a point\[\left( 2,0 \right)\]is:
\[\begin{align}
& z=3\times 2+5\times 0 \\
& =6
\end{align}\]
The value of the objective function at a point\[\left( 2,4 \right)\]is:
\[\begin{align}
& z=3\times 2+5\times 4 \\
& =26
\end{align}\]
Therefore, the maximum value of the objective function is 26.
