{VERSION 4 0 "IBM INTEL NT" "4.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 11 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 3 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "ut:=100*x^.4*y^.6;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#utG,$*&)%\"xG$\"\"%!\"\"\"\"\")% \"yG$\"\"'F+F,\"$+\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "Bu: =4*x+6*y-100;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#BuG,(%\"xG\"\"%*& \"\"'\"\"\"%\"yGF*F*\"$+\"!\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 84 "Maximize Erndle's utility subject to the constraint that hash has \+ only $100 to lose." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "L:=ut +lambda*(100.0-4*x-6*y);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"LG,&*& )%\"xG$\"\"%!\"\"\"\"\")%\"yG$\"\"'F+F,\"$+\"*&%'lambdaGF,,($\"%+5F+F, *&F*F,F(F,F+*&F0F,F.F,F+F,F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "Lx:=diff(L,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#LxG,&*&*$)% \"yG$\"\"'!\"\"\"\"\"F-*$)%\"xG$F+F,F-F,$\"$+%F,*&\"\"%F-%'lambdaGF-F, " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "Ly:=diff(L,y);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#LyG,&*&*$)%\"xG$\"\"%!\"\"\"\"\"F-* $)%\"yG$F+F,F-F,$\"$+'F,*&\"\"'F-%'lambdaGF-F," }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 21 "Llam:=diff(L,lambda);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%LlamG,($\"%+5!\"\"\"\"\"*&\"\"%F)%\"xGF)F(*&\"\"'F)% \"yGF)F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "solve(\{Lx,Ly,L lam\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<%/%'lambdaG$\"#5\"\"!/%\"x GF&/%\"yGF&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "eval(Lx,\{la mbda = 10., x = 10., y = 10.\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$ \"\"!F$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "9 0 \+ 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }