5. Given ARmxn, b Rm, consider the pair of polyhedra P = {x = Rn Ax > b}, Q := {(y, z) = Rn: Ay - Az b, y 0, z 0} (a) Assume that is an extreme point of P. Show that (, z) is an extreme point of Q, where y = max{, 0} and := max{-, 0} are the positive and negative parts of . (b) Assume that (y, z) is an extreme point of Q such that y + z> 0 entrywise. Show that either i = 0 or i = 0 for each i, and that - is an extreme point of P. y