OR Chapter 2. Simplex method (2,0) (2,2/3) (1,2)(0,2)

OR

3  Geometry in 2-D 0

OR

5 (4,3) x2x2 x1x1 (2,2/3)

OR

7 Solving LP graphically  (2,0) (2,2/3) (1,2)(0,2) x2x2 x1x1

OR Properties of optimal solutions

OR Multiple optimal solutions (2,0) (2,2/3) (1,2)(0,2) x2x2 x1x1

OR Obtaining extreme point algebraically (2,0) (2,2/3) (1,2)(0,2) x2x2 x1x1

OR

OR

Idea of algorithm? OR

OR Remark: There exists a polyhedron which is not full-dimensional. (extreme point is defined same as before.) x2x2 x1x1 x3x This polyhedron is 2-dimensional.

OR Algebraic Derivation of Extreme Points for LP

OR

OR x2x2 x1x1 x3x

OR =

OR

 Simplex method searches only basic feasible solutions, which is tantamount to searching the extreme points of the corresponding polyhedron until it finds an optimal solution. OR