For the following shaded area, the linear constraints except $$x,y \ge 0$$ are

The shaded area in the figure given below is a solution set of a system of inequations. The minimum value of objective function $$3 x+5 y$$, subject to the linear constraints given by this system of inequations is

The vertices of the feasible region for the constraints $$x+y \leq 4, x \leq 2, y \leq 1, x+y \geq 1, x, y \geq 0$$ are

The graphical solution set for the system of inequations $$x-2 y \leq 2,5 x+2 y \geq 10,4 x+5 y \leq 20, x \geq 0, y \geq 0$$ is given by