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 graphical solution set of the system of in-equations $x+y \leq 70, x+2y \leq 100, 2x+y \leq 120, x \geq 0, y \geq 0$ is given by:

$A$ diet of a sick person must contain at least $4000$ units of vitamins,$50$ units of proteins,and $1400$ calories. Two foods $A$ and $B$ are available at a cost of ₹ $4$ and ₹ $3$ per unit respectively. If one unit of $A$ contains $200$ units of vitamins,$1$ unit of protein,and $40$ calories,while one unit of food $B$ contains $100$ units of vitamins,$2$ units of protein,and $40$ calories,formulate the problem so that the diet is the cheapest.

The shaded area in the given figure is a solution set for some system of inequalities. The maximum value of the function $z=4x+3y$ subject to linear constraints given by the system is

$A$ 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.

The shaded region in the following figure represents the solution set for a certain linear programming problem. The linear constraints for this region are given by: