The shaded region in the figure is the solution set of the inequations.

1. Since, region(shaded) lies above x-axis

$\therefore y\ge 0$

2. Shaded region is on left of $x=6$

$\therefore x\le 6$

3. Shaded region is below $y=3$

$\therefore y\le 3$

4. Equation of line passing through (4,0) & (0,5) is

$y-0=\cfrac { 5 }{ -4 } \left( x-4 \right)$

$5x+4y-20=0$

$5x+4y=20$

If $5x+4y\ge 20$, Put (0,0) we get $0\ge 20$ FALSE.

$\therefore$ Region lies away from origin which is true

$\therefore \quad 5x+4y\ge 20$

5. Shaded region lies on right side of y-axis

$\therefore x\ge 0$

$\therefore 5x+4y\ge 20,x\le 6,y\le 3,x\ge 0,y\ge 0$