{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 "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 "Warning" -1 7 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 2 2 2 2 2 1 1 1 3 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 }{PSTYLE "Maple Plot" -1 13 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 62 "This is a Maple Worksheet version of Example 4.10 of the text. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{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#>&%\"pG6#\"\"\",(\"$R$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'&%\"s G6#F'F'F'*&\"$D#F'&F+6#\"\"#F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "Profit:=R-C;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'Pr ofitG,.&%\"sG6#\"\"\"\"$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):" }}} {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\"$u\"F+*&#F+F.F+F7F+F2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "Sol:=solve(\{dP[1]=0,dP[2]=0\},\{s[1],s[2]\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$SolG<$/&%\"sG6#\"\"\"#\"'+Sb\"$<\"/&F(6#\"\"## \"'+S#)F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "a:=rhs(Sol[1]) ; b:=rhs(Sol[2]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"aG#\"'+Sb\"$< \"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"bG#\"'+S#)\"$<\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "HP:=hessian(Profit,[s[1],s[2]]);" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#HPG-%'matrixG6#7$7$#!\"\"\"#]#!\"( \"%+57$F-F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "eigenvalues( HP);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$#!#8\"%+5#!#FF%" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 80 "Since the eigenvalues of HP are both negative (think of f''(x)<0), then there i s" }}{PARA 0 "" 0 "" {TEXT -1 34 "a global maximum at our point a,b." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "subs(\{s[1]=a,s[2]=b\},Profit);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6##\")+?f@\"#R" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf( %);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+c-TOb!\"%" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 99 "In the followin g two plots, note the values of Profit and the location of the maximum . 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