Solve the following problem related to a system of inequalities.
a. (i) Draw, on the same set of axes, the graphs of the inequalities
2x+y≤8, \; x+2y≤8, \; x≥0 \text{ and } y≥0.
b. (ii) Shade the region representing all ordered pairs (x,y) that satisfy the entire system.
c. (iii) List the coordinates of every corner (vertex) of this region.
d. (iv) State, with reason, whether the feasible region obtained in part (ii) is bounded, unbounded or empty.