The shaded region in the following figure is the solution set of the inequations
The shaded region in the following figure is the solution set of the inequations
$x+2 y \geq 50,2 x+y \leq 100,2 x-y \leq 0$, $x, y \geq 0$
$x+2 y \leq 50,2 x+y \leq 100,2 x-y \leq 0$, $x, y \geq 0$
$x+2 y \geq 50,2 x+y \geq 100,2 x-y \leq 0$, $x, y \geq 0$
$x+2 y \leq 50,2 x+y \geq 100,2 x-y \leq 0$, $x, y \geq 0$
Solution
Take a test point $(10,40)$ which lies within the feasible region.
Since $10+2(40)=90 \geq 50$,
$2(10)+40=60 \leq 100$,
$2(10)-40=-20 \leq 0$
$\therefore \quad x+2 y \geq 50,2 x+y \leq 100,2 x-y \leq 0, x, y \geq 0$
