{VERSION 5 0 "IBM INTEL NT" "5.0" } {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 "" 0 1 0 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 "Text Output" -1 2 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 0 0 0 0 0 1 3 0 3 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Warning" 2 7 1 {CSTYLE "" -1 -1 " " 0 1 0 0 255 1 0 0 0 0 0 0 1 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 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 60 "Solving the constrained version of Example 4.10 of the text." } }{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "p[1]:=339- (1/100)*s[1]-(3/1000)*s[2];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"pG 6#\"\"\",(\"$R$F'*&#F'\"$+\"F'&%\"sGF&F'!\"\"*&#\"\"$\"%+5F'&F.6#\"\"# F'F/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "p[2]:=399-(4/1000)* s[1]-(1/100)*s[2];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"pG6#\"\"#,( \"$*R\"\"\"*&#F*\"$]#F*&%\"sG6#F*F*!\"\"*&#F*\"$+\"F*&F/F&F*F1" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "R:=simplify(s[1]*p[1]+s[2]*p [2]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"RG,,&%\"sG6#\"\"\"\"$R$*& #F)\"$+\"F)*$)F&\"\"#F)F)!\"\"*&#\"\"(\"%+5F)*&F&F)&F'6#F0F)F)F1*&\"$* RF)F7F)F)*&#F)F-F)*$)F7F0F)F)F1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "C:=400000+195*s[1]+225*s[2];" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#>%\"CG,(\"'++S\"\"\"*&\"$&>F'&%\"sG6#F'F'F'*&\"$D#F'&F+6#\"\"#F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "Profit:=R-C;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'ProfitG,.&%\"sG6#\"\"\"\"$W\"*&#F)\"$+\"F)*$ )F&\"\"#F)F)!\"\"*&#\"\"(\"%+5F)*&F&F)&F'6#F0F)F)F1*&\"$u\"F)F7F)F)*&# F)F-F)*$)F7F0F)F)F1\"'++SF1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg):" }}{PARA 7 "" 1 "" {TEXT -1 80 "Warning, the protect ed names norm and trace have been redefined and unprotected\n" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "dP:=grad(Profit,vector([s[1] ,s[2]]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#dPG-%'vectorG6#7$,(\"$ W\"\"\"\"*&#F+\"#]F+&%\"sG6#F+F+!\"\"*&#\"\"(\"%+5F+&F06#\"\"#F+F2,(F/ #!\"(F6\"$u\"F+*&#F+F.F+F7F+F2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "CS:=s[1]+s[2]-10000;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#CSG ,(&%\"sG6#\"\"\"F)&F'6#\"\"#F)\"&++\"!\"\"" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 34 "dCS:=grad(CS,vector([s[1],s[2]]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$dCSG-%'vectorG6#7$\"\"\"F)" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 73 "solve(\{dP[1]=lambda*dCS[1],dP[2]=lambda*dCS [2],CS=0\},\{s[1],s[2],lambda\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#< %/&%\"sG6#\"\"##\"&++)\"#8/&F&6#\"\"\"#\"&++&F+/%'lambdaG\"#C" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 68 "He re is an equivalent way to write this, if you have more equations:" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "Eqns:=seq(dP[j]=lambda*dCS[j],j=1..2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%EqnsG6$/,(\"$W\"\"\"\"*&#F)\"#]F)&%\"sG6#F)F)!\"\"*& #\"\"(\"%+5F)&F.6#\"\"#F)F0%'lambdaG/,(F-#!\"(F4\"$u\"F)*&#F)F,F)F5F)F 0F8" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "Sol:=solve(\{Eqns,CS =0\},\{s[1],s[2],lambda\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$SolG <%/&%\"sG6#\"\"##\"&++)\"#8/&F(6#\"\"\"#\"&++&F-/%'lambdaG\"#C" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "a:=rhs(Sol[2]); b:=rhs(Sol[1 ]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"aG#\"&++&\"#8" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%\"bG#\"&++)\"#8" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "subs(\{s[1]=a,s[2]=b\},Profit);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6##\"(++#p\"#8" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+Bp2B`!\"%" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "18 0 0" 0 } {VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }