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?

The maximum value of $Z=x+3y$ subject to the constraints $2x+y \leq 20$,$x+2y \leq 20$,$x \geq 0$,$y \geq 0$ is:

The shaded region in the given figure is a graph of $.....$

The corner points of the bounded feasible region are $(60,0), (120,0), (60,40), (40,20)$ and $(20,30)$. For the objective function $z=5x+10y$:
$(i)$ Maximum value of $z$.
$(ii)$ Minimum value of $z$.
$(iii)$ Maximum value of $z$ occurs at.
$(iv)$ Minimum value of $z$ occurs at.

Maximize the function $Z = 11x + 7y$,subject to the constraints:
$x \leq 3, y \leq 2, x \geq 0, y \geq 0$

Show that the minimum of $Z$ occurs at more than two points.
Minimise and Maximise $Z = 5x + 10y$
subject to $x + 2y \leq 120, x + y \geq 60, x - 2y \geq 0, x, y \geq 0$.