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:

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 $(0, 0), (0, 40), (20, 40), (60, 20), (60, 0)$. The maximum of the objective function $z = 40x + 30y$ is . . . . . . .

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

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 feasible region for a $LPP$ is shown in the figure. Find the minimum value of $Z=11x+7y$.