{VERSION 3 0 "IBM INTEL NT" "3.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 283 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 285 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 287 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 297 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 } {CSTYLE "" -1 298 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 299 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 301 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 302 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 } {CSTYLE "" -1 303 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 304 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 305 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 306 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 } {CSTYLE "" -1 307 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 308 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 309 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 310 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 } {CSTYLE "" -1 311 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 312 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 313 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 314 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 315 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 316 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 317 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 262 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 262 "" 0 "" {TEXT 314 56 "The Transportation Prob lem. Example of solving as an LP" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 17 "Define functions:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 79 "E_2 : = proc(n, i, alpha)\n mulrow(array(identity, 1..n,1..n), i, alpha); \nend:\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 73 "Pivot:=proc(A,i ,j) linalg[pivot](E_2(rowdim(A),i,1/A[i,j]) &* A,i,j) end;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&PivotGR6%%\"AG%\"iG%\"jG6\"F*F*-&%'linalg G6#%&pivotG6%-%#&*G6$-%$E_2G6%-%'rowdimG6#9$9%*&\"\"\"F=&F:6$F;9&!\"\" F:F;F@F*F*F*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 92 "Consider the tra nsportation problem, with shipping costs, supplies and demands as fol lows:" }}{PARA 0 "" 0 "" {TEXT -1 10 " " }{TEXT 299 105 " \+ Destination 1 Destination 2 Destination 3 \+ Destination 4 Supply" }}{PARA 0 "" 0 "" {TEXT -1 8 " \+ " }{TEXT 297 18 "Source 1 " }{TEXT -1 113 " 12 \+ 5 6 \+ 7 " }{TEXT 301 3 " 40" }}{PARA 0 "" 0 "" {TEXT -1 8 " " }{TEXT 305 9 "Source 2 " }{TEXT -1 123 " \+ 5 4 7 \+ 8 " }{TEXT 302 3 " 30" }} {PARA 0 "" 0 "" {TEXT -1 8 " " }{TEXT 306 11 "Source 3 " } {TEXT -1 121 " 6 7 \+ 8 5 " } {TEXT 303 3 " 30" }}{PARA 0 "" 0 "" {TEXT -1 7 " " }{TEXT 307 9 " Source 4" }{TEXT -1 121 " 12 11 \+ 12 11 \+ " }{TEXT 304 2 "40" }}{PARA 0 "" 0 "" {TEXT -1 8 " " } {TEXT 308 10 "Demand " }{TEXT -1 5 " " }{TEXT 298 94 " 50 30 40 \+ 20" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "A:=" } {TEXT -1 0 "" }{MPLTEXT 1 0 21 "array(1..8,1..16,[]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG-%&arrayG6%;\"\"\"\"\");F)\"#;7\"" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "for i from 1 to 8 do for j f rom 1 to 16 do A[i,j]:=0 od:od:evalm(A):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 77 "for i from 1 to 4 do for j from 1+4*(i-1) to 4*i do A [i,j]:=1 od:od:evalm(A):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "for i from 5 to 8 do for j from i-4 by 4 to 16 do A[i,j]:=1 od:od:eva lm(A):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "b:=vector(8,[40,3 0,30,40,50,30,40,20]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"bG-%'vec torG6#7*\"#S\"#IF*F)\"#]F*F)\"#?" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "Ab:=augment(A,b);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# >%#AbG-%'matrixG6#7*73\"\"\"F*F*F*\"\"!F+F+F+F+F+F+F+F+F+F+F+\"#S73F+F +F+F+F*F*F*F*F+F+F+F+F+F+F+F+\"#I73F+F+F+F+F+F+F+F+F*F*F*F*F+F+F+F+F.7 3F+F+F+F+F+F+F+F+F+F+F+F+F*F*F*F*F,73F*F+F+F+F*F+F+F+F*F+F+F+F*F+F+F+ \"#]73F+F*F+F+F+F*F+F+F+F*F+F+F+F*F+F+F.73F+F+F*F+F+F+F*F+F+F+F*F+F+F+ F*F+F,73F+F+F+F*F+F+F+F*F+F+F+F*F+F+F+F*\"#?" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "c:=vector(17,[12,5,6,7,5,4,7,8,6,7,8,5,12,11,12, 11,0]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"cG-%'vectorG6#73\"#7\" \"&\"\"'\"\"(F*\"\"%F,\"\")F+F,F.F*F)\"#6F)F/\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "Abc:=stackmatrix(-c,Ab);" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%$AbcG-%'matrixG6#7+73!#7!\"&!\"'!\"(F+!\"%F-!\")F,F -F/F+F*!#6F*F0\"\"!73\"\"\"F3F3F3F1F1F1F1F1F1F1F1F1F1F1F1\"#S73F1F1F1F 1F3F3F3F3F1F1F1F1F1F1F1F1\"#I73F1F1F1F1F1F1F1F1F3F3F3F3F1F1F1F1F673F1F 1F1F1F1F1F1F1F1F1F1F1F3F3F3F3F473F3F1F1F1F3F1F1F1F3F1F1F1F3F1F1F1\"#]7 3F1F3F1F1F1F3F1F1F1F3F1F1F1F3F1F1F673F1F1F3F1F1F1F3F1F1F1F3F1F1F1F3F1F 473F1F1F1F3F1F1F1F3F1F1F1F3F1F1F1F3\"#?" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "Pivot(%,2,1):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "Pivot(%,6,5):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "Pi vot(%,3,6):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "Pivot(%,7,10 ):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "Pivot(%,4,11):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "Pivot(%,8,15):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "Pivot(%,9,16);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7+73\"\"!\"\"'F)\"\"%F(F(!\"#!\"%\"\"#F(F(F -F(F(F(F(\"%+873\"\"\"F0F0F0F(F(F(F(F(F(F(F(F(F(F(F(\"#S73F(F0F0F0F(F0 F0F0!\"\"F(F(F(F3F(F(F(\"#?73F(F(F0F0F(F(F0F0F(F(F0F0F3F3F(F(F473F(F(F (F(F(F(F(F(F(F(F(F(F(F(F(F(F(73F(F3F3F3F0F(F(F(F0F(F(F(F0F(F(F(\"#573F (F(F3F3F(F(F3F3F0F0F(F(F0F0F(F(F873F(F(F(F3F(F(F(F3F(F(F(F3F0F0F0F(F47 3F(F(F(F0F(F(F(F0F(F(F(F0F(F(F(F0F4" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 12 "this is the " }{TEXT 283 4 "BFS " }{TEXT -1 6 " with " }{TEXT 285 15 "basic variables" }{TEXT -1 3 " " }{TEXT 309 76 "x11 = 40, x 21 = 10, x22 = 20, x32 = 10, x33 = 20, x43 = 20, x44 = 20 " } {TEXT -1 5 "and " }{TEXT 311 11 "cost = 1300" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 9 "Note the " }{TEXT 317 9 "zero row " }{TEXT -1 24 "(row \+ #5). We can either " }{TEXT 315 6 "delete" }{TEXT -1 3 " or" }{TEXT 316 7 " ignore" }{TEXT -1 4 " it." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "Pivot(%,3,2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'m atrixG6#7+73\"\"!F(F(!\"#F(!\"'!\")!#5\"\")F(F(\"\"#\"\"'F(F(F(\"%!=\" 73\"\"\"F(F(F(F(!\"\"F3F3F2F(F(F(F2F(F(F(\"#?73F(F2F2F2F(F2F2F2F3F(F(F (F3F(F(F(F473F(F(F2F2F(F(F2F2F(F(F2F2F3F3F(F(F473F(F(F(F(F(F(F(F(F(F(F (F(F(F(F(F(F(73F(F(F(F(F2F2F2F2F(F(F(F(F(F(F(F(\"#I73F(F(F3F3F(F(F3F3F 2F2F(F(F2F2F(F(\"#573F(F(F(F3F(F(F(F3F(F(F(F3F2F2F2F(F473F(F(F(F2F(F(F (F2F(F(F(F2F(F(F(F2F4" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "Pi vot(%,7,9);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7+73\"\"!F( \"\")\"\"'F(!\"'F(!\"#F(!\")F(\"\"#F,F-F(F(\"%+673\"\"\"F(F1F1F(!\"\"F (F(F(F2F(F(F(F2F(F(\"#573F(F1F(F(F(F1F(F(F(F1F(F(F(F1F(F(\"#I73F(F(F1F 1F(F(F1F1F(F(F1F1F2F2F(F(\"#?73F(F(F(F(F(F(F(F(F(F(F(F(F(F(F(F(F(73F(F (F(F(F1F1F1F1F(F(F(F(F(F(F(F(F573F(F(F2F2F(F(F2F2F1F1F(F(F1F1F(F(F373F (F(F(F2F(F(F(F2F(F(F(F2F1F1F1F(F773F(F(F(F1F(F(F(F1F(F(F(F1F(F(F(F1F7 " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "Pivot(%,2,3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7+73!\")\"\"!F)!\"#F)\"\"#F)F*F) F)F)F+F*F)F)F)\"%?573\"\"\"F)F.F.F)!\"\"F)F)F)F/F)F)F)F/F)F)\"#573F)F. F)F)F)F.F)F)F)F.F)F)F)F.F)F)\"#I73F/F)F)F)F)F.F.F.F)F.F.F.F/F)F)F)F073 F)F)F)F)F)F)F)F)F)F)F)F)F)F)F)F)F)73F)F)F)F)F.F.F.F.F)F)F)F)F)F)F)F)F2 73F.F)F)F)F)F/F/F/F.F)F)F)F.F)F)F)\"#?73F)F)F)F/F)F)F)F/F)F)F)F/F.F.F. F)F773F)F)F)F.F)F)F)F.F)F)F)F.F)F)F)F.F7" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "Pivot(%,4,6);" }}{PARA 11 "" 1 "" {TEXT -1 0 "" } {XPPMATH 20 "6#-%'matrixG6#7+73!\"'\"\"!F)!\"#F)F)F*!\"%F)F*F*F)F)F)F) F)\"%+573F)F)\"\"\"F.F)F)F.F.F)F)F.F.!\"\"F/F)F)\"#?73F.F.F)F)F)F)F/F/ F)F)F/F/F.F.F)F)F073F/F)F)F)F)F.F.F.F)F.F.F.F/F)F)F)\"#573F)F)F)F)F)F) F)F)F)F)F)F)F)F)F)F)F)73F.F)F)F)F.F)F)F)F)F/F/F/F.F)F)F)F073F)F)F)F)F) F)F)F)F.F.F.F.F)F)F)F)\"#I73F)F)F)F/F)F)F)F/F)F)F)F/F.F.F.F)F073F)F)F) F.F)F)F)F.F)F)F)F.F)F)F)F.F0" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 11 "t his is an " }{TEXT 310 16 "optimal solution" }{TEXT -1 6 " with " } {TEXT 287 15 "basic variables" }{TEXT -1 2 " " }{TEXT 312 71 "x12 = 2 0, x13 = 20, x21 = 20, x22 = 10, x31 = 30, x33 = 20, x34 = 20" } {TEXT -1 7 " and " }{TEXT 313 11 "cost = 1000" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "3 0 0" 79 }{VIEWOPTS 1 1 0 1 1 1803 }