The constraints $-x_{1} + x_{2} \leq 1$,$-x_{1} + 3x_{2} \leq 9$,and $x_{1}, x_{2} \geq 0$ define:

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 $\text{Maximum of } F - \text{Minimum of } F$.

For a linear programming problem,the objective function is $Z = 8000x + 12000y$. If the corner points of the feasible region are $(0,0)$,$(20,0)$,$(12,6)$,and $(0,10)$,then the maximum value of $Z$ occurs at which corner point?

$A$ feasible solution to an $LP$ problem . . . . . . .

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

If for a linear programming problem the feasible region is bounded,then the objective function has . . . . . . .