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

The maximum value of $z=50x+15y$ subject to the constraints $x+y \leq 60$,$5x+y \leq 100$,$x \geq 0$,$y \geq 0$ is at the point:

The graphical solution set of the system of inequations $x+y \geq 1$,$7x+9y \leq 63$,$y \leq 5$,$x \leq 6$,$x \geq 0$,$y \geq 0$ is represented by:

$A$ cooperative society of farmers has $50$ hectares of land to grow two crops $X$ and $Y$. The profit from crops $X$ and $Y$ per hectare are estimated as Rs $10,500$ and Rs $9,000$ respectively. To control weeds,a liquid herbicide has to be used for crops $X$ and $Y$ at rates of $20$ litres and $10$ litres per hectare. Further,no more than $800$ litres of herbicide should be used in order to protect fish and wildlife using a pond which collects drainage from this land. How much land should be allocated to each crop so as to maximise the total profit of the society?

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

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