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{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "Pict:=%:" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 36 " A:= matrix(2,4,[10,3,1,0,2,3,0,1]);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG-%'matrixG6#7$7&\"#5\"\"$\"\"\" \"\"!7&\"\"#F+F-F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "b:=ve ctor(2,[52,18]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"bG-%'vectorG6# 7$\"#_\"#=" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "c:=vector(5,[ 0,5,6,0,0]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"cG-%'vectorG6#7'\" \"!\"\"&\"\"'F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "Abc:=s tackmatrix(-c,augment(b,A));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$Abc G-%'matrixG6#7%7'\"\"!!\"&!\"'F*F*7'\"#_\"#5\"\"$\"\"\"F*7'\"#=\"\"#F0 F*F1" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 33 "Iteration 1: Pivot on ent ry (2,2)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "Pivot(%,2,2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7%7'\"#E\"\"!#!\"*\"\"## \"\"\"F,F)7'#F(\"\"&F.#\"\"$\"#5#F.F4F)7'#\"#QF1F)#\"#7F1#!\"\"F1F." } }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 33 "Iteration 2: Pivot on entry (3,3 )" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "Pivot(%,3,3);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7%7'#\"$h\"\"\"%\"\"!F+#\" \"\"\"\")#\"#:F.7'#\"#\"\"'F+F-#F5\"#7#\"\"&F; " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 24 "An optimal table, with " } {TEXT 261 9 "x1 = 17/4" }{TEXT -1 3 ", " }{TEXT 262 9 "x2 = 19/6" } {TEXT -1 3 ", " }{TEXT 263 9 "z = 161/4" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "T:=%:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 48 "The 2nd \+ row of the table represents the equality" }}{PARA 0 "" 0 "" {TEXT -1 54 " " }{TEXT 264 38 " x1 = 17/4 - (1/8) x3 + (1/8) x4" }}{PARA 0 "" 0 "" {TEXT -1 21 "giving the Gomory cut" }}{PARA 0 "" 0 "" {TEXT -1 53 " \+ " }{TEXT 265 38 " 1 <= (1/4) + (7/8) x3 + (1/8) x4" }}{PARA 0 "" 0 "" {TEXT -1 72 "Th e corresponding line is written, in terms of the original variables \+ " }{TEXT 268 8 "x1, x2 ," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 69 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{MPLTEXT 1 0 79 "T1:=st ackmatrix(augment(T,vector(3,[0,0,0])),vector(6,[-3/4,0,0,-7/8,-1/8,1] ));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#T1G-%'matrixG6#7&7(#\"$h\"\" \"%\"\"!F-#\"\"\"\"\")#\"#:F0F-7(#\"#\"\"'F- F/#F7\"#7#\"\"&F=F-7(#!\"$F,F-F-#!\"(F0F6F/" }}}{EXCHG {PARA 0 "" 0 " " {TEXT -1 38 "Dual iteration 1: Pivot on entry (4,4)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "T1:=Pivot(%,4,4);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#T1G-%'matrixG6#7&7(#\"$\"G\"\"(\"\"!F-F-#\"#8F,# \"\"\"F,7(#\"#HF,F1F-F-#!\"\"F,F07(#\"#o\"#@F-F1F-#\"\"$F,#!\"#F:7(#\" \"'F,F-F-F1F0#!\")F," }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 6 "or " } {TEXT 269 9 "x1 = 29/7" }{TEXT -1 3 ", " }{TEXT 270 11 " x2 = 68/21" }{TEXT -1 4 " , " }{TEXT 271 10 " z = 281/7" }}}{EXCHG {PARA 0 "" 0 " " {TEXT -1 28 "The 3rd row of T1 gives" }}{PARA 0 "" 0 "" {TEXT -1 43 " " }{TEXT 272 40 " x2 = 68/21 - (3/7) x4 + (2/21) x5" }}{PARA 0 "" 0 "" {TEXT -1 14 " giving the cut" }}{PARA 0 "" 0 "" {TEXT -1 45 " \+ " }{TEXT 273 38 "1 <= 5/21 + 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