Theory of Linear Programming: convex polytopes, equational form and basic feasible solutions

In preparation for the simplex algorithm we are taking a look at some algebraic and geometric concepts underlying linear programming.

00:00 linear programming vs linear algebra
02:05 convex polytopes
06:21 cubes and cross-polytopes
10:55 Writing LPs in the form Ax at most x
13:00 Equational form
18:14 basic feasible solutions: geometric intuition
22:38 What is a basic feasible solution (bfs)?
25:12 A basis has a unique basic feasible solution
26:49 examples of a solution being not basic
28:20 If there is an optimum, then there is an optimal bfs
30:48 basic feasible solutions correspond to vertices of the set of feasible solutions