The region satisfying the inequalities $y - x \geq 2,\ x + y \leq 5,\ x \geq 0$ and $y \geq 0$ is

The minimum value of $z = 3x + 5y$, subject to constraints $x \leq 80$, $y \geq 60$, $x + y \leq 200$ & $x, y \geq 0$ occurs at the point...

The feasible region represented by the constraints $y - 2x \leq 4, x + y \geq 5, x \leq 4, y \geq 2, x, y \geq 0$ is ...........

The difference between the maximum and minimum values of the objective function $Z = 3x + 5y$, subject to the constraints $x + 3y \leq 60$, $x + y \geq 10$, $x - y \leq 0$, $x, y \geq 0$ is