Answer
The graph is shown below:
Work Step by Step
Let us consider the given inequalities $\begin{align}
& y\ge 0 \\
& 3x+2y\ge 4 \\
& x-y\le 3 \\
\end{align}$
Substitute the equals symbol in place of the inequality and rewrite the equation as given below:
$\begin{align}
& y=0 \\
& 3x+2y=4 \\
& x-y=3 \\
\end{align}$
The first inequality is a horizontal line parallel to the x-axis. Now, take the origin $\left( 0,0 \right)$ as a test point for the equations and check the region in the graph to shade:
$\begin{align}
& y\ge 0\text{ },\text{ 3}x+2y\ge 4\text{ and }x-y\le 2 \\
& 0\ge 0\text{, }0\ge 4\text{ and }0\le 2 \\
\end{align}$
We see that the first inequality and the third inequality are correct for the test point $\left( 0,0 \right)$; therefore, the shaded region will contain the test point; the second inequality is incorrect, so it will not contain the test point (the origin). We combine these facts to graph the feasible region.
The final graph is shown below.
