MATH 340 Lecture Notes - Lecture 5: Linear Algebra, Linear Programming
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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.