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 . . . . . . .

Minimize $Z = 13x - 15y$ subject to the constraints: $x + y \leq 7$,$2x - 3y + 6 \geq 0$,$x \geq 0$,$y \geq 0$.

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:

For a linear programming problem,the objective function is $Z = 3x + 2y$. If the corner points of the bounded feasible region are $(12, 0)$,$(4, 2)$,$(1, 5)$,and $(1, 10)$,then the maximum value of $Z$ is . . . . . . .

The linear programming problem $(LPP)$ to maximize $z = 2x + 5y$ subject to the constraints $x + 3y \leq 6$, $2x + 6y \leq 18$, $x \geq 0$, and $y \geq 0$ has: