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 $m + n = \dots$

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

Corner points of the feasible region for an $LPP$ are $(0,2), (3,0), (6,0), (6,8)$ and $(0,5)$. Let $Z = 4x + 6y$ be the objective function. The minimum 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:

The corner points of the feasible region are $(0, 6)$,$(3, 3)$,$(9, 9)$,and $(0, 12)$. What is the maximum value of the objective function $z = 6x + 12y$?

The minimum value of $Z = 3x + 4y$ subject to the constraints $x + y \leq 4, x \geq 0, y \geq 0$ is . . . . . . .