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 . . . . . . .

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 objective function of an $LP$ problem is . . . . . . .

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

The difference between the maximum value and the minimum value of the objective function $z = 3x + y$ subject to the constraints $2x + 3y \leq 6$, $x + y \geq 1$, $x \geq 0$, $y \geq 0$ is....

For a Linear Programming $(LP)$ problem,the objective function is $z = 3x + 2y$. The coordinates of the corner points of the bounded feasible region are $A(3, 3)$,$B(20, 3)$,$C(20, 10)$,$D(18, 12)$,and $E(12, 12)$. The minimum value of $z$ is . . . . . . .