Lecture 5

# 3thesimplexalgorithmmaxlps theresultis canonical form

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Unformatted text preview: 0 8 4 1 x1 8 4 1 3 z 1 x1 4 1 4 z 1 x1 1 x2 -30 6 2 0.75 1 x2 15 6 2 0.75 1 x2 15 2 0.75 1 x2 15 -1 0.75 1 x3 -20 1 1.5 0.25 x3 -5 1 1.5 0.25 x3 -5 -1 1.5 0.25 x3 -5 -1 0.5 0.25 s1 s2 s3 s4 1 1 0.5 s1 s2 s3 30 1 s4 1 1 0.5 s1 s2 1 s3 30 -4 1 s4 1 0.5 s1 s2 1 1 s3 30 -4 -2 0.5 1 s4 1 rhs 48 20 4 5 rhs 240 48 20 4 5 rhs 240 16 20 4 5 rhs 240 16 4 4 5 ero row 3 divided by 1/2 60 times row 3 added to row 0 - 8 times row 3 added to row 1 - 4 times row 3 added to row 2 4.3 – The Simplex Algorithm (max LPs) The result is: Canonical Form 1 Row 0 z + 15x2 - Row 1 Row 2 - Basic Variable 5x3 x3 + s1 x2 + 0.5 x3 Row 3 x1 + 0.75x2 + 0.25x3 Row 4 x2 + 30s3 = 240 z = 240 - 4s3 = 16 s1 = 16 2 s3 =4 s2 = 4 + 0.5s3 =4 x1 = 4 =5 s4 = 5 + s2 - + s4 In canonical form 1, BV = {z, s1, s2, x1, s4} and NBV = {s3, x2, x3 }. yielding the bfs z = 240, s1 = 16, s2 = 4, x1 = 4, s4 = 5, s3 = x2 = x3...
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