The corner points of the feasible region of the objective function $Z = 3x + 9y$ are $(0, 10)$,$(5, 5)$,$(15, 15)$,and $(0, 20)$. Then,the minimum value of $Z$ is:

For a Linear Programming Problem $(LPP)$,if the objective function is $Z = 4x + 3y$ and the corner points of the bounded feasible region are $(0,0), (25,5), (16,16),$ and $(5,24)$,then the maximum value of $Z$ occurs at 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:

In the following figure,the feasible region (shaded) for a $LPP$ is shown. Determine the maximum and minimum value of $Z=x+2y$.

The corner points of the feasible region determined by $A (20, 10)$,$B (18, 12)$,and $C (12, 12)$. The maximum value of the objective function $Z = 2x + 3y$ is . . . . . . .

Solve the following Linear Programming Problem graphically:
Minimise $Z = x + 2y$
subject to the constraints:
$2x + y \geq 3$
$x + 2y \geq 6$
$x, y \geq 0$