If $x+y \leq 2, x \geq 0, y \geq 0$,the point at which the maximum value of $3x+2y$ is attained will be:

Solve the following Linear Programming Problem graphically:
Minimise $Z = x + 2y$
subject to the constraints:
$2x + y \geq 3$
$x + 2y \geq 6$
$x, y \geq 0$

The corner points of the bounded feasible region are $(0,1), (0,7), (2,7), (6,3), (6,0), (1,0)$. For the objective function $Z = 3x - y$:
$(i)$ At which point is $Z$ minimum?
$(ii)$ At which point is $Z$ maximum?
$(iii)$ The maximum value of $Z$ is $\ldots$
$(iv)$ The minimum value of $Z$ is $\ldots$

Corner points of the feasible region for an $LPP$ are $(0,2), (3,0), (6,0), (6,8)$ and $(0,5)$. Let $Z = 4x + 6y$ be the objective function. The minimum value of $Z$ occurs at

For the $LP$ problem,"Maximize $z = x + 4y$ subject to $3x + 6y \leq 6$,$4x + 8y \geq 16$ and $x \geq 0, y \geq 0$."

The feasible solution for a Linear Programming Problem $(LPP)$ is shown in the figure. Let $z = 3x - 4y$ be the objective function. The value of (Maximum value of $z$ + Minimum value of $z$) is equal to $....$