Proof of bounded polyhedron = convex hull of extreme point(PhD)

Show that a non-empty bounded polyhedron is the convex hull of its extreme points. Hint: use Farkas Lemma

Proof in Linear Programming - extreme point

Can anyone help me to prove this? (Geometry in linear programming) (See attached file for full problem description with equations) --- (a) Let be a convex set. Prove that if is a vertex of S, then is an extreme point of S. (b) Give an example of a closed convex set and a point such that is an extreme point of S but is not a vertex of S. --- (See attached file for full problem description with equations)

Proof in Linear Programming - Extreme Point

Can anyone help me to prove this? I'm really stuck with geometry in Linear Programming... (See attached file for full problem description and equations) --- Assume P is a polyhedron and H is a supporting hyperplane to P. Prove that is an extreme point of if and only if is an extreme point of P.

seeking help for mathematical proof in LP: proof some def of Polyhedron

(See attached file for full problem description and equations) --- Assume P, Q are non-empty polyhedra. Let P + Q := {x + y: Prove that P + Q is a polyhedron. Prove that every extreme point of P + Q is the sum of an extreme point of P and an extreme point of Q. ---

solving transpotation problems

Find the optima solution for the following problem: TO FROM Chicago Atlanta supply St louis 40 63 250 Richmond 70 30 400 demand 300 350 650