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

In the following figure, the shaded region represents the system of constraints:

The graphical solution set for the system of inequations $x-2y \leq 2$,$5x+2y \geq 10$,$4x+5y \leq 20$,$x \geq 0$,$y \geq 0$ is given by

The difference between the maximum value and minimum value of the objective function $z = 3x + 5y$ of a linear programming problem subject to constraints $5x + 10y \leq 50$, $x + y \geq 1$, $y \leq 4$, $x \geq 0$, $y \geq 0$ is $3\lambda$. Then the value of $\lambda$ is

The maximum value of $Z=3x+5y$,subject to the constraints $x+4y \leq 24$,$y \leq 4$,$x \geq 0$,$y \geq 0$ is:

In the following figure, the shaded region represents the system of constraints: