Solve the given inequalities $5 x+4 y \leq 20, x \geq 1, y \geq 2$ graphically in two – dimensional plane.
The graphical representation of $5 x+4 y \leq 20, x \geq 1, y \geq 2$ is given by common region in the figure below.
$5 x+4 y \leq 20$ .…… (1)
$x \geq 1 \ldots \ldots .(2)$
$y \geq 2 \ldots \ldots .(3)$
Inequality $(1)$ represents the region below line $5 x+4 y=20$ (including the line $5 x+4 y=20$ ).
Inequality (2) represents the region in front of line $x=1$ (including the line $x=1$ ).
Inequality (3) represents the region above line $y=2$ (including the line $y=2$ ).
Therefore,every point in the common shaded region including the points on the respective lines represents the solution for the given inequalities.
This can be represented as follows,