If feasible region is as shown in the figure, then the related inequalities are
If feasible region is as shown in the figure, then the related inequalities are
$3 x+4 y \geq 12, y-x \geq 0, y \leq 3, x, y \geq 0$
$3 x+4 y \leq 12, y-x \leq 0, y \geq 3, x, y \geq 0$
$3 x+4 y \leq 12, y-x \geq 0, y \leq 3, x, y \geq 0$
$3 x+4 y \geq 12, y-x \leq 0, y \geq 3, x, y \geq 0$
Solution
The shaded region lies:
on non-origin side of line $3 x+4 y=12$ i.e., $3 x+4 y \geq 12$,
on the side of the line $y-x=0$, where $y \geq x$ i.e., $y-x \geq 0$,
on origin side of line $y=3$
i.e., $y \leq 3$,
and in first quadrant
i.e., $x \geq 0, y \geq 0$.
