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

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 . . . . . . .

Which of the following statements is correct?

If a Linear Programming Problem $(L.P.P.)$ has optimum solutions at two consecutive corner points of the feasible region,then the $L.P.P.$ has: