3. Suppose a polyhedron P = {x = R^: Ax b} # may contain a line. Prove that there exists x1,...,xN and d, ..., d such that P conv{x, ..., x} + cone{d, ..., dk}. Hint: Show that (1) - = - P = {x = Rn: x = x+ x, 3(x+, x) E Q}, where Q = {(x+, x) = R R: Ax+ Ax > b}; (2) Q has no line; (3) Representation Q by extreme points and extreme rays; (4) project out variables (x+,x) in the alternative set P.