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 . . . . . . .

For the linear programming constraints $x+2y \geq 10$,$3x+4y \leq 24$,$x \geq 0$,and $y \geq 0$,which of the following is not a corner point of the feasible region?

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 $\ldots$

Corner points of the feasible region for an $\operatorname{LPP}$ are $(0,2), (3,0), (6,0), (6,8)$ and $(0,5)$. Let $F = 4x + 6y$ be the objective function. Find the value of $\text{Maximum of } F - \text{Minimum of } F$.

Let $x$ and $y$ be optimal solutions of a Linear Programming $(LP)$ problem. Then,which of the following is true?

The corner points of the feasible region are $A(3,3), B(20,3), C(20,10), D(18,12)$ and $E(12, 12)$. The maximum value of $Z=2x+3y$ is $.......$