Question

Solve the following system of inequalities graphically
$3x+2y\le 12,x\ge 1,y\ge 2$

Answer 1

The set of inequalities are given as,

$3x+2y\le 12$

$x\ge 1$

$y\ge 2$

Simplifying $3x+2y\le 12$ by substituting different values of $x$ and $y$.

When $x=0$, then, $y=6$

When $y=0$, then, $x=4$

So, the coordinates are $\left(0,6\right)$ and $\left(4,0\right)$.

Now, if $x=0$ and $y=0$, then,

$0\le 12$

Which is true, so the graph will be shaded towards the origin.

Now, $x=1$ will give a straight line and since $0\ge 1$ is not true, so the graph will be shaded away the origin.

In the same way, $y=2$ will give a straight line and since $0\ge 2$ is not true, so the graph will be shaded away from the origin.

The common area is the required feasible region.