Linear Prog COP4355_Part_9

Linear Prog COP4355_Part_9 - Chapter 4 Linear Programming:...

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40 Chapter 4 Linear Programming: The Simplex Algorithm 4.8 (continued) Initial Tableau A B C S1 S2 S3 S4 S5 S6 A6 S7 A7 S8 A8 Cj 100 5 25 000000- M 0- M M Bi Θ S1 0 7 5 6 10000000000 130 18.57 S2 0 1 0 0 01000000000 2 0 2 0 S3 0 0 1 0 00100000000 5 0 + S4 0 0 0 1 00010000000 3 0 + S5 0 1 1 1 00001000000 3 0 3 0 A6 -1 M 1 0 0 00000- 110000 5 5 A7 -1 M 0 1 0 0000000- 1100 5,000 + A8 -1 M 0 0 1 000000000- 11 5 + Zj -M - M - M 00000 M - M M - M M - M -5,010 M Zj 100+ M 5+ M 25+ M M M M 0 Entering: A Leaving: Artificial 6 4.9 We can set up the problem for weekly production, daily production, or hourly production. We have chosen the hourly approach, and we will multiply by 40 to get the weekly results: if we chose the daily level, we would multiply the results by 5. MAX Z: 4T + 2R Subject to: T + 2R 4 T + R 2 (T, R 0)
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Solutions Manual and Workbook 41 4.9 (continued) Initial Tableau T R S1 S2 A2 Cj 4 2 0 0 - M Bi Θ S1 0 1 2 1 0 0 4 4 A2 - M 1 1 0 -1 1 2 2 Zj - M - M 0 M - M -2 M Zj 4+ M 2+ M 0- M 0 Entering: T Leaving: Artificial 2 Tableau 2 TRS 1S 2 A 2 Cj 4200- 1 M Bi Θ S1 0 0 1 1 1 -1 2 2 T 4 11 0- 1 1 2- 2 Zj 44 0- 4 4 8 Zj 0 -2 0 4 -4- M Entering: Slack 2 Leaving: Slack 1 Optimal Tableau T R S1 S2 A2 Cj M Bi S2 0 0 1 1 1 -1 2 T 412100 4 Zj 48400 16.00 Zj 6- 40- M
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42 Chapter 4
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This note was uploaded on 11/13/2011 for the course COP 4355 taught by Professor Koslov during the Spring '10 term at University of Florida.

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Linear Prog COP4355_Part_9 - Chapter 4 Linear Programming:...

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