Take the polyhedron P explained by linear inequalities:

x1 − x2   0
−x1 + x2   1
2x2   5
8x1 − x2   16
x1 + x2   4
x1, x2 2 R2

i) Determine the dimension of P.

ii) Find the inequalities which describe each extreme point of P.

iii) Find all the faces, vertices, facets, and edges of the P.

iv) Determine an interior point (if one exists).

v) Making use of the basic feasible solutions, determine the feasible point that maximizes 2x1 + 3x2 and minimizes same objective function.