Question

Solve the following inequalities by graphical method:
$2x+y\ge 6,3x+4y\le 12$

Answer 1

Solve for the points where the lines intersect the coordinate axes:

$2x+y\ge 6\Rightarrow \frac{x}{3}+\frac{y}{6}\ge 1\Rightarrow A=(3,0),B=(0,6)$

$3x+4y\le 12\Rightarrow \frac{x}{4}+\frac{y}{3}\le 1\Rightarrow C=(4,0),D=(0,3)$

The lines intersect at $E=(12/5,6/5)$.

Solving the inequalities we get $x\ge \frac{12}{5}$ and $y\le \frac{6}{5}$

The feasible region is the triangular region $\Delta AEC$ since $x\ge \frac{12}{5}$ and $y\le \frac{6}{5}$.