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

The maximum value of $z=7x+8y$ subject to the constraints $x+y \leq 20, y \geq 5, x \leq 10, x \geq 0, y \geq 0$ is

$A$ manufacturer of electronic circuits has a stock of $200$ resistors,$120$ transistors and $150$ capacitors and is required to produce two types of circuits $A$ and $B$. Type $A$ requires $20$ resistors,$10$ transistors and $10$ capacitors. Type $B$ requires $10$ resistors,$20$ transistors and $30$ capacitors. If the profit on type $A$ circuit is $Rs. 50$ and that on type $B$ circuit is $Rs. 60$,formulate this problem as a $LPP$ so that the manufacturer can maximize his profit.

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 point,at which the maximum value of $10x + 6y$ subject to the constraints $x + y \leq 12$,$2x + y \leq 20$,$x \geq 0$,$y \geq 0$ occurs,is

The feasible region for the constraints $x-y \geqslant 0$,$x-5y \leqslant -5$,$x \geqslant 0$,$y \geqslant 0$ is shown by the figure: