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Simplex is algebraic equivalent to graphical method

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Unformatted text preview: hical extreme Polnts egulvalent to simplex solutions of linear equations . IsoGbjectlve Line motion equivalent to tteratlons of simplex algorithm Starting of IsoObjectlve Line equivalent to simplex initial feasible solution l 2 - 3X, -2X, = 0 subject to .vE +2x, + s, = 6 l 2x, cx, + s1 = 8 -XI + x, + s, = I x, +s4 =2 l .r,..r,.s,.s..s,.s, t o Graphical vs. Simplex Method Simplex Search Procedure Graphkal Method Based on 2dlmensional space Easy to vlsuallze Scale limited to 2 variable problems Simplex Method Based on matrix arithmetic (GaussJordan) More abstract Scale limited only by computational power l l l l l l EM-602 I QM-710 (NJ) Lecture 3 Page 3-3 -- Simplex Method Simplex Method (Preliminary Treatment - Paint Co) l l l l l (Pretiminary Treatment - Step Convert problem into standard form Restrict Variables (if unrestricted) Make Positive RHS for all constraints Add Slack (or subtract surptus) as needed to each constraint Make Objective Function’s RHS = starting value (0) Let the basic feasible solution consist of the slack variables = RHS All other variables are Non-Bask (~0) Fill in the initial simplex taMeaU (Tableau 0) with the starting solution (basic feasible solution) First Row: Objective Function Remaining Rows: Constraint Equations l l l l l Simplex Tableau Iteration 0 (Initial Tableau) z xz K, s1 s2 s3 s4 Saln Basic Z 1 I-3 -2 0 0 0 0 0 0 0 0 1 2 -1 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 Simplex Method (Preliminary Treatment - step 2) Find the Entering Variable (the Non-bask variabk which will become a basic variabte) The most negative (if maximizing) or most positive (if minimizing) entry in the r-Row A tie between two entries is settled arbitrarily The selected entry’s column iS highlighted and referred to as the “Entering...
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