Cls Notes 9-30 Rev Sim Proc

Cls Notes 9-30 Rev Sim Proc - I Emma/.329 ELEM flea-um...

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Unformatted text preview: I Emma/.329 ELEM flea-um KWQMX WM X0 "-7 ETK 29.56., SE {‘39. Mow-m 35502 85502 \ 2' . J 5 ‘ f} f“: .35" '- - . ' w-m. \_.‘ I. 5“ f Revised Simplex Example Note: didn’t print B printed {2, XB} coefficients as M matrix. max 2 = 2x1+ 4x2 + 6x3 + 5x4 + 6x5 3x1+ 2x2 + 3X3 + 4x4 + 7x5 <1“ 15 —x1+1x2 +4x3 + 2x4 — XS <= 12 xi >= 0 for all i Var 2, x1, x2, x3, x4, x5, SI, 32 M 1.000 0.000 0.000 Minv 1.000 0.000 0.000 1.000 0.000 1.000 0.000 0.000 0.000 1.000 0.000 0.000 0.000 1.000 xB index: { 1, 7, 8} CB: { 0, 0} Basic Vars: { z, 51, s2} sol: { 0.000, 15.000, 12.000} XN index: {2, 3, 4, S, 6} NonBasic Vars: { x1, x2, x3, x4, X5} 0.000 for var x 2 cj~zjz 2.000 for var x 3 cj—zj: 4.000 for var x 4 cj—zj: 6.000 for var x 5 cj~zj : 5.000 for var x 6 cj—Zj : 6.000 j*: 3 entering var X 4 i: 2 3.000 15.000 ratio: 5.000 i: 3 4.000 12.000 ratio: 3.000 min ratio: 3.000 leaving var 100 in SB: SB: { 1, 7, 4} Basic var: z = 0.000 Basic var: s} = 15.000 ’ Basic var: x3 : 12.000 SN: {2, 3, 8, 5,6} M 1.000 0.000 —6.000 FilezRevSimplexAlgi .mle 0.000 \1000 3.00 0.000 0.000 4.00 Miflv £000 0.000 0.000 W0.750 0.000 0.000 0.250 XB index: { 1, 7, 4} CB: { 0, 6} Basic Vars: { 22-, 31, X3} sol: { 18.000, 6.000, 3.000} XN index: { 2, 3, 8, 5, 6} NonBasic Vars: { X1, X2, 52, X4, X5} for var X 2 cj-zj: 3.500 forvarX3 cj-zj: 2.500 for var X 8 cj—Zj: 4.500 for var X 5 cj—zj: 2.000 for var X 6 cj—zj: 7.500 «is 3 )6 3.} f. j*: 5 entering varx6 i: 2 7.750 6.000 ratio: 0.774 min ratio: 0.774 leaving varloc in SB: 2 SB: { 1, 6, 4} Basic var: z = 18.000 Basic var: X5 = 6.000 Basic var: X3 = 3.000 SN: {2, 3, 8, 5,7} M 1-000 0.000[‘7.000 3.000 1...... 0.000 —1.000 4.000 Minv 1-000 396.833.2153.... .a 0.000 0.13:9 0.097 WT. ‘2“ 0.000 0.032 0.226 ‘ XB indeivfszwiiwfl ' CB: { 6, 6} Basic Vars: { 2, X5, x3} sol: { 23.806, 0.774, 3.194} XN index: {2, 3, 8, 5, 7} NonBaSic Vars: { X1, X2, 52, X4, sl} forvarXZ cj-zj: —0.129 for varX3 cj—z}: 1.290 for varx8 cj-zj: 0774 for varXS ej-zj: —0.419 forvarx? cj—zj: «0.968 j*: 2 entering vai'X3 i: 2 0.161 0.774 ratio: 4.800 i: 3 0.290 3.194 ratio: 11.000 min ratio: 4.800 leaving var 100 in SB: 2 SB: { 1, 3, 4} Basic var: z : 23.806 Basic var: X2 2 0.774 Basic var: X3 2 3.194 SN: {2, 6, 8,5, 7} M 1.000 (:4000 16,000, 0000\2000 3000—) W, 0.000 1.000 4.000 W‘ W Minv MW “w'mmw 1.000 2.000 0.000... ; 0.000 0.800 0600‘] .3, 00001—0200 0.400 w XB indeXmT’3jwsz' CB: { 4, 6} Basic Vars: { 2, X2, X3} 501: { 30.000, 4.800, 1.800} XN index: {2, 6, 8, 5, 7} NonBasic Vai‘s: { X1, X5, 32, x4, 31} for var X 2 ej-zj: —4.000 for var x 6 cj—Zj: —8.000 for varx 8 cj—zj: 0.000 for var x 5 cj—zj: —3.000 for var X 7 cj-zj: —2.000 No entering variable: opt soiution found SB: { 1, 3, 4} Basic var: z 3 30.000 Basic var: x2 : 4.800 Basic var: X3 = 1.800 MGR/LP (Revised 1/93) Date: 9/25/11 Time: 10:45:38 H:\MORLPS~1\hw1dll.lpe MODEL DESCRIPTION *‘Jr-k‘kJr*‘k*-k*‘)r****‘k*~k*****~k*~k***i************‘k*~k******* max x0 = 2x1 + 4x2 + 6x3 + 534 + 6x5 st 3x1 + 2x2 + 3x3 + 4x4 + 7x5 <= 15 —X1 + 1X2 + 4x3 + 2x4 — x5 <: 12 "non—neg" *‘k****‘firk‘k****‘k**********‘k*********‘k*‘k~k*‘k‘k******~k*‘k'k* Simplex Method Initial Tableau BASIS X0 X1 X2 X3 X4 X5 Slackl SlackZ SOL X0 1 00 —2 OO —4 00 —6 00 —5 00 —6 00 O 00 0 00 0 00 Slackl 0 00 3.00 2.00 3.00 4 00 7 00 l 00 0 00 15.00 Slack2 0 00 ~1 00 1.00 4 00 2 00 —1 00 0 00 1 00 12 00 Entering variable is X3 Leaving variable is SlackZ Normal pivot. Tableau: l BASIS X0 X1 X2 X3 X4 X5 Slackl Slackz SOL X0 1 00 —3 50 —2 50 0.00 —2 00 —7 50 0 00 l 50 18 00 Slackl 0.00 3.75 l 25 0 00 2.50 7 75 l 00 —0.75 6.00 X3 0.00 "0.25 0 25 1 00 0.50 —0 25 0 00 0.25 3.00 Entering variable is X5 Leaving variable is Slackl Normal pivot. Tableau: 2 BASIS X0 X1 X2 X3 X4 X5 Slackl SlaCk2 SOL. X0 1.00 0.13 —l.29 0.00 0.42 0.00 0.97 0.77 23.81 X5 0.00 0.48 0.16 0.00 0.32 1.00 0.13 —0.10 0.77 X3 0.00 —0.13 0.29 1.00 0.58 0.00 0.03 0.23 3.19 Entering variable is X2 Leaving variable is X5 Normal pivot. Tableau: 3 BASIS X0 X1 X2 X3 X4 X5 SlaCkl Slack2 SOL X0 1.00 4.00 0.00 0.00 3.00 8.00 2.00 0.00 30.00 X2 0.00 3.00 1.00 0.00 2.00 6.20 0.80 —0.60 4.80 X3 0.00 —1.00 0.00 1.00 0.00 —l.80 -0.20 0.40 1.80 ‘0“ Optimal Solution “AA X0 : 30.0000 Xl : 0.0000 X2 4.8000 X3 = 1.8000 X4 = 0.0000 X5 = 0.0000 ...
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Cls Notes 9-30 Rev Sim Proc - I Emma/.329 ELEM flea-um...

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