MATH 340 Lecture Notes - Lecture 5: Linear Algebra, Linear Programming
Document Summary
Let"s go back and look at what we did in our rst example of the simplex method last time. We introduced slack variables and got a rst dictionary x5 = 5 2x1 x2 x3 3x4 x6 = 3 x1 3x2 x3 2x4. 6x1 +8x2 +5x3 +9x4 z = this dictionary is associated to the feasible solution x1 = x2 = x3 = x4 = 0, x5 = 5, x6 = 3, with value z = 0. In this dictionary the slack variables x5 and x6 are on the left-hand side of equations (we call them basic variables) and the original variables x1, x2, x3, x4 are on the right-hand sides (we call them non-basic variables). Each iteration of the simplex method performs a pivot: for the rst step we can choose x1 as the entering variable and x5 as the leaving variable for the dictionary. (remark: if the words basic and.
