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

The solution set for minimizing the function $\mathrm{z}=x+y$ with constraints $x+y \geqslant 2, x+2 y \leqslant 8, y \leqslant 3, x, y \geqslant 0$ contains

The L.P.P. , minimize $z=30 x+20 y, x+y \leq 8$, $x+2 y \geq 4,6 x+4 y \geq 12, x \geqslant 0, y \geqslant 0$ has

A scholarship amount is given by $\mathrm{z}=550 x+300 y$ and is to be distributed among $x$ boys and $y$ girls. From the graph given below the maximum amount of scholarship is __________