Linear Programming

The feasible region represented by the constraints: $x + 2y \leq 120$; $x + y \geq 60$; $x - 2y \geq 0$; $x \geq 0$ and $y \geq 0$

Shade the feasible region for the inequations $x+y \geq 2,2 x+3 y \leq 6, x \geq 0, y \geq 0$ in a rough figure.

The feasible region for the inequations $x+y \leq 4$, $2 x+y \leq 5, x, y \geq 0$ is

The feasible region corresponding to the linear constraints of a Linear Programming problem is given below. Which of the following is NOT a constraint to the given LPP

Maximize $Z=7 x_{1}-3 x_{2}$ subject to, $x_{1}+2 x_{2} \leq 2,2 x_{1}+4 x_{2} \geq 8, x_{1} \geq 0, x_{2} \geq 0$.

Shade the feasible region for the inequations $6 x+4 y \leq 120,3 x+10 y \leq 180, x, y \geq 0$ in a rough figure.

The maximum value of $x+y$ subjected to $2 x+3 y \leq 12, x y \geq 0$

The feasible region for the inequations $x+2 y \geq 4,2 x+y \leq 6, x, y \geq 0$ is

The feasible region for the inequations $x+2 y \geq 4,2 x+y \leq 6, x, y \geq 0$ is

In the following figure, the shaded region represents the system of constraints:

The shaded area in the given figure is a solution set for some system of inequalities. The maximum value of the function $z=4 x+3 y$ subject to linear constraints given by the system is

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