The graph with the correct feasible region of the $L.P.P.$ for the constraints $2x + y \leqslant 10$,$y \leqslant x$,$y \leqslant 2$,$x, y \geqslant 0$ is $\ldots$

The shaded area in the given figure is a solution set for some system of inequations. The maximum value of the function $z=10x+25y$ subject to the linear constraints given by the system is

For the following shaded region,the linear constraints are:

There are two factories located at place $P$ and place $Q$. From these locations,a certain commodity is to be delivered to each of the three depots situated at $A, B$ and $C$. The weekly requirements of the depots are $5, 5$ and $4$ units respectively,while the production capacities of the factories at $P$ and $Q$ are $8$ and $6$ units respectively. The cost of transportation per unit is given below:

From/To	$A$	$B$	$C$
$P$	$160$	$100$	$150$
$Q$	$100$	$120$	$100$

How many units should be transported from each factory to each depot in order that the transportation cost is minimum? What will be the minimum transportation cost?

$A$ man rides his motorcycle at the speed of $50 \, km/h$. He has to spend $Rs. \, 2$ per $km$ on petrol. If he rides it at a faster speed of $80 \, km/h$,the petrol cost increases to $Rs. \, 3$ per $km$. He has at most $Rs. \, 120$ to spend on petrol and one hour's time. He wishes to find the maximum distance that he can travel. Express this problem as a linear programming problem.

$A$ wholesale merchant wants to start a cereal business with $Rs \ 24000$. Wheat costs $Rs \ 400$ per quintal and rice costs $Rs \ 600$ per quintal. He has a storage capacity of $200$ quintals of cereal. He earns a profit of $Rs \ 25$ per quintal on wheat and $Rs \ 40$ per quintal on rice. If he stores $x$ quintals of rice and $y$ quintals of wheat,then for maximum profit,the objective function is: