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

The corner points of the feasible region are $A(0,0)$,$B(16,0)$,$C(8,16)$,and $D(0,24)$. The minimum value of the objective function $z = 300x + 190y$ is . . . . . . .

Corner points of the bounded feasible region for an $LP$ problem are $(0,4), (6,0), (12,0), (12,16)$ and $(0,10)$. Let $z = 8x + 12y$ be the objective function. Match the following:
$(i)$ Minimum value of $z$ occurs at $\ldots$
$(ii)$ Maximum value of $z$ occurs at $\ldots$
$(iii)$ Maximum of $z$ is $\ldots$
$(iv)$ Minimum of $z$ is $\ldots$

In a Linear Programming Problem ($L$.$P$.$P$.), the corner points of the feasible region determined by the constraints $3x - y \geq 6$, $x \leq 3$, $y \leq 2$, $y \geq 0$, and $x \geq 0$ are:

The objective function of a Linear Programming Problem $(LPP)$ is

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 $m + n = \dots$