The shaded area in the given figure is a solution set for some system of inequalities. The maximum value of the function $z=4x+3y$ subject to linear constraints given by the system is

The shaded area in the given figure is a solution set for some system of inequations. The maximum value of the function $z=10x+25y$ subject to the linear constraints given by the system is

The shaded area in the figure below is the solution set for a certain linear programming problem. Then the linear constraints are given by:

The shaded area in the figure given below is a solution set of a system of inequations. The minimum value of the objective function $Z = 3x + 5y$,subject to the linear constraints given by this system of inequations,is:

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 $z = 9x + 13y$ subject to the constraints $2x + 3y \leq 18$,$2x + y \leq 10$,$x \geq 0$,$y \geq 0$ is: