3. Suppose a polyhedron P = {x E R": Ax 2 b} # @ may contain a line. Prove that there exists xl, ..., x and d], ..., d* such that P = conv(x], ..., x } + cone{d], ..., d }. Hint: Show that (1) P = {xER: x =x+ - x , 3(x+,x ) EQ}, where Q = {(x+, x-) E R" X R": Axt - Ax- > b}; (2) Q has no line; (3) Representation Q by extreme points and extreme rays; (4) project out variables (x, x7) in the alternative set P