Lecture26aa

# Lecture26aa - Lecture 3/28/08 Use of Simplex Tableaus 1....

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Lecture 3/28/08 Use of Simplex Tableaus 1. Minimization Problems 2. LP’s with Alternative Optimal Solutions 3. Unbounded LP’s

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Constraint Graph 400 300 200 100 x 2 100 200 300 400 x 1 0 Optimal Solution: x 1 =150, x 2 =100 2x 1 +x 2 =400 x 1 +2x 2 =350 Initial bfs 1st iteration bfs: x 1 =0, x 2 =175 Max z=2x 1 + 2.5x 2 s.t. x 1 + 2x 2 350 2 x 1 + x 2 400 x i 0 for i=1,2
Using Simplex Method to Solve Minimization Problems Method works if all constraints are type. Example: Problem #1 Page 151 in text: min z= 4x 1 - x 2 s.t. 2x 1 + x 2 8 x 2 5 x 1 - x 2 4 x ,x 0 Problem is optimal if coefficients of NBVs in row 0 are non-positive. The NBV with the highest positive coefficient in row 0 should be brought into basis.

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Standard Form) z - 4x 1 + x 2 =0 2x 1 + x 2 +s 1 =8 x 2 +s 2 =5 x 1 - x 2 + s 3 =4 x i , s j 0 for i=1,2; j=1,2,3 Initial Simplex Tableau: z x 1 x 2 s 1 s 2 s 3 RHS BV 1 -4 1 0 0 0 0 z=0 0 2 1 1 0 0
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## This note was uploaded on 04/17/2008 for the course CSA 273 taught by Professor Patton during the Spring '08 term at Miami University.

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Lecture26aa - Lecture 3/28/08 Use of Simplex Tableaus 1....

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