lecture+3.3

Augmented form z 30 m pb 40 m pc 0 s1 0s 2 0s3 0

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Unformatted text preview: 0 Z + M PC - S 4 + A = 5 0 Z + 2 M PB + M PC - S5 + A = 25 0 Z + M PB + 2M PC - S6 + A = 25 1 0 0 0 0 0 0 Z M PB -30 -40 0 0 0 0 0 0 -100 0 M P 4 0 -1 0 0 0 0 0 1 C 30 S 1 1 0 -1 0 0 0 0 1 1 15 S 1 1 0 0 -1 0 0 0 1 2 = 10 S 0 1 0 0 0 -1 0 0 1 3 5 S 2 1 0 0 0 0 -1 0 1 4 25 S5 25 1 2 0 0 0 0 0 -1 1 S6 A Model: Fully Augmented Form and, non-negativity constraints 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 M PB 0 1 0 0 0 0 0 0 0 M PC 0 0 1 0 0 0 0 0 0 S1 0 0 0 1 0 0 0 0 0 S 2 0 0 0 0 1 0 0 0 0 S3 0 0 0 0 0 1 0 0 0 S 4 0 0 0 0 0 0 1 0 0 S5 0 0 0 0 0 0 0 1 0 S6 0 0 0 0 0 0 0 0 1 A 0 Model: Simplex Tableau Basis Z A S2 S3 S4 S5 S6 Z 1 0 0 0 0 0 0 MPB -30 4 1 1 0 2 1 MPC -40 0 1 1 1 1 2 S1 0 -1 0 0 0 0 0 S2 0 0 -1 0 0 0 0 S3 0 0 0 -1 0 0 0 S4 0 0 0 0 -1 0 0 S5 0 0 0 0 0 -1 0 S6 0 0 0 0 0 0 -1 A -100 1 1 1 1 1 1 Value 0 30 15 10 5 25 25 Ratio 1 0 0 0 0 0 0 Z M PB -30 -40 0 0 0 0 0 0 -100 0 M P 4 0 -1 0 0 0 0 0 1 C 30 S 1 1 0 -1 0 0 0 0 1 1 15 S 1 1 0 0 -1 0 0 0 1 2 = 10 S 0 1 0 0 0 -1 0 0 1 3 5 S4 2 1 0 0 0 0 -1 0 1 25 S5 1 2 0 0 0 0 0 -1 1 25 S6 A =0 Basis Z A S2 S3 S4 S5 S6 Z 1 0 0 MPB -30 4 1 1 0 2 1 =0 MPC -40 0 1 1 1 1 2 Model: Simplex Tableau S1 0 -1 0 0 0 0 0 S2 0 0 -1 0 0 0 0 S3 0 0 0 -1 0 0 0 S4 0 0 0 0 -1 0 0 Largest positive value 5 Basis S S6 0 0 0 0 0 0 -1 A -100 1 1 Value 0 30 15 10 5 25 25 Ratio 0 0 0 0 0 -1 0 Basis 0 0 0 0 A =1 30 1 1 1 Z - 30 M PB - 40 M PC - 0 S1 - 0 S2 - 0 S3 - 0 S4 - 0 S5 - 0 S 6 - 100 A = 0 A, S2 , S3 , S 4 , S5 , S6 0 Z - 30 0 - 40 0 - 0 0 - 0 - 0 20 - 0 25 - 0 5 - 0 5 - 100 30 = 0 15 A = 30 Z = 3000 Initial Feasible Solution A - S2 = 15 30 - S 2 = 15 S 2 = 15 A = 30 M PB = 0 A - S3 = 10 30 - S3 = 10 S3 = 20 A - S 4 = 5 30 - S 4 = 5 S4 = 25 S 2 = 15 S3 = 20 S 4 = 25 S5 = 5 S6 = 5 M PC = 0 S1 = 0 A - S5 = 25 30 - S5 = 25 S5 = 5 A - S6 = 25 30 - S6 = 25 S6 = 5 =- Basis Z A S2 S3 S4 S5 S6 Z 1 0 0 0 0 0 0 MPB -30 4 1 1 0 2 1 Z M PB MPC -40 0 1 1 1 1 2 0 Model: Simplex Tableau S1 -1 0 0 0 0 0 S2 0 0 -1 0 0 0 0 S3 0 0 0 -1 0 0 0 S4 0 0 0 0 -1 0 0 S5 0 0 0 0 0 -1 0 S6 0 0 0 0 0 0 -1 A -100 1 1 1 1 1 1 Value 0 30 15 10 5 25 25 Ratio Z - 30 M PB - 40 M PC - 0 S1 - 0 S 2 - 0 S3 - 0 S 4 - 0 S5 - 0 S 6 - 100 A = 0 The value of Z increases with increases in variables with a negative sign The value of Z decreases with increases in variables with a positive sign Min Z = 30 M PB + 40 M PC + 0 S1 + 0 S2 + 0 S3 + 0 S4 + 0 S5 + 0 S6 + 100 A If we want to decrease the value of Z, we must brin...
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This note was uploaded on 01/22/2013 for the course CE 111 taught by Professor Lizhi during the Winter '12 term at UC Irvine.

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