The difference between the maximum value and the minimum value of the objective function $z = 3x + y$ subject to the constraints $2x + 3y \leq 6$, $x + y \geq 1$, $x \geq 0$, $y \geq 0$ is....

For the following shaded region,the linear constraints are:

If the difference between the maximum and minimum values of the objective function $z = 7x - 8y$ subject to the constraints $x + y \leqslant 20$,$y \geqslant 5$,$x, y \geqslant 0$ is $5k + 200$,then the value of $k$ is

The minimum value of $z = 3x + 5y$, subject to constraints $x \leq 80$, $y \geq 60$, $x + y \leq 200$ and $x, y \geq 0$ occurs at the point:

For the following shaded area,the linear constraints except $x, y \geq 0$ are

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