If for a linear programming problem the feasible region is bounded,then the objective function has . . . . . . .

The feasible solution for a $LPP$ is shown in the figure. Let $z=3x-4y$ be the objective function. The maximum value of $Z$ occurs at $......$

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:

Solve the Linear Programming Problem graphically:
Maximise $Z = 3x + 4y$
subject to the constraints: $x + y \leq 4, x \geq 0, y \geq 0.$

The vertices of the feasible region determined by some linear constraints are $(0,2), (1,1), (3,3), (1,5)$. Let $Z = px + qy$ where $p, q > 0$. The condition on $p$ and $q$ so that the maximum of $Z$ occurs at both the points $(3,3)$ and $(1,5)$ is . . . . . . .

Solve the Linear Programming Problem graphically:
Minimise $Z = 3x + 5y$
subject to the constraints:
$x + 3y \geq 3$
$x + y \geq 2$
$x, y \geq 0$