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

In the following figure, the shaded region represents the system of constraints:

The solution set of the constraints $2x + 3y \leq 6$,$x + 4y \leq 4$,$x \geq 0$,and $y \geq 0$ includes the point $\ldots$ as a corner point.

$A$ production unit makes a special type of metal chip by combining copper and brass. The standard weight of the chip must be at least $5 \text{ gms}$. The basic ingredients,i.e.,copper and brass,cost $₹8$ and $₹5$ per $\text{gm}$ respectively. Durability considerations dictate that the metal chip must not contain more than $4 \text{ gms}$ of brass and should contain a minimum of $2 \text{ gms}$ of copper. Then,the minimum cost of the metal chip satisfying the above conditions is:

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 feasible region represented by the given constraints $2x + 3y \geqslant 12$,$-x + y \leqslant 3$,$x \leqslant 4$,$y \geqslant 3$ is denoted by