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 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 $z = 6x + 12y$?

If an $LPP$ admits an optimal solution at two consecutive vertices of a feasible region,then:

The maximum value of $Z=x+3y$ subject to the constraints $2x+y \leq 20$,$x+2y \leq 20$,$x \geq 0$,$y \geq 0$ is:

$z = 30x - 30y + 1800$ is an objective function. The corner points of the feasible region are $(15, 0), (15, 15), (10, 20), (0, 20),$ and $(0, 15)$. $z$ has the minimum value at $\ldots$ point.