The solution set of the constraints $x+2y \leq 2000$,$x+y \leq 1500$,$y \leq 600$ and $x \geq 0$ does not include the point

If the feasible region is as shown in the figure,then the related inequalities are:

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

The production of item $A$ is $x$ and the production of item $B$ is $y$. If the corner points of the bounded feasible region are $(1,0), (2,0), (0,2)$ and $(0,1)$,then the maximum profit $z = 2000x + 5000y$ is $\ldots \ldots$

The maximum value of $z = 4x + y$ subject to the constraints $x + y \leq 5$, $2x + y \leq 7$, $3x + 2y \leq 11$, $x \geq 0$, $y \geq 0$ is

The function to be maximized is given by $Z=2x+y$. The feasible region for this function $Z$ is the shaded region shown in the figure. The maximum value of $Z$ is . . . . . . and occurs at the point . . . . . . .