The constraints $-x_{1} + x_{2} \leq 1$,$-x_{1} + 3x_{2} \leq 9$,and $x_{1}, x_{2} \geq 0$ define:

In a Linear Programming Problem ($L$.$P$.$P$.), the corner points of the feasible region defined by the constraints $3x - y \geq 6$, $x \leq 3$, $y \leq 2$, $y \geq 0$, and $x \geq 0$ are:

The solution set of the constraints $x + 2y \geq 11$,$3x + 4y \leq 30$,$2x + 5y \leq 30$,$x \geq 0$,$y \geq 0$ includes the point:

The corner points of the feasible region determined by the system of linear constraints are $(2, 72)$,$(15, 20)$,and $(40, 15)$. Let $Z = 6x + 3y$ be the objective function. The minimum value of $Z$ occurs at:

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

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