The graphical solution set of the system of inequations $2 x+3 y \leq 6, x+4 y \geq 4, x \geq 0, y \geq 0$ is given by

The region represented by the inequations $2 x+3 y \leqslant 18, x+y \geqslant 10, x \geqslant 0, y \geqslant 0$ is

A production unit makes special type of metal chips by combining copper and brass. The standard weight of the chip must be at least 5 gms. The basic ingredients i.e. copper and brass cost ₹8 and ₹ 5 per gm. The durability considerations dictate that the metal chip must no contain more than 4 gms of brass and should contain minimum 2 gms of copper. Then the minimum cost of the metal chip satisfying the above conditions is

For the following shaded region, the linear constraints are