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

Solve the following Linear Programming Problem graphically:
Maximise $Z = 3x + 2y$
subject to the constraints:
$x + 2y \leq 10$
$3x + y \leq 15$
$x, y \geq 0$

The maximum value of $Z = 60x + 10y$ whose corner points are $(10, 0)$,$(2, 4)$,$(1, 5)$,and $(0, 8)$ is . . . . . . .

In solving the $LP$ problem: "Minimize $z = 6x + 10y$ subject to $x \geq 6, y \geq 2, 2x + y \geq 10, x \geq 0, y \geq 0$." The redundant constraints are $....$

The corner points of the feasible region are $(0,0), (16,0), (8,12), (0,20)$. The maximum and minimum values of $Z = 22x + 18y$ are $m$ and $n$ respectively,then $m + n = \dots$

The corner points of the bounded feasible region are $(60,0), (120,0), (60,40), (40,20)$ and $(20,30)$. For the objective function $z=5x+10y$:
$(i)$ Maximum value of $z$.
$(ii)$ Minimum value of $z$.
$(iii)$ Maximum value of $z$ occurs at.
$(iv)$ Minimum value of $z$ occurs at.