{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 1 }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 1 }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 1 }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 1 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }}
{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "restart: # CoinTossG
ame.mws" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "with(simplex):\n
" }}{PARA 7 "" 1 "" {TEXT -1 87 "Warning, the protected names maximize
 and minimize have been redefined and unprotected\n" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 28 "P:=matrix(2,2,[1,-1,-1,1]);\n" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%\"PG-%'matrixG6#7$7$\"\"\"!\"\"7$F+F*" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "m:=2; n:=2;\n" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#>%\"mG\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>
%\"nG\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "# Player 1's \+
problem" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "for j from 1 to \+
n do Player1[j]:=add(x[i]*P[i,j],i=1..m)>=v od;\n" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>&%(Player1G6#\"\"\"1%\"vG,&&%\"xGF&F'&F,6#\"\"#!\"\"" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%(Player1G6#\"\"#1%\"vG,&&%\"xG6#
\"\"\"!\"\"&F,F&F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "Unity
:=add(x[i],i=1..m)=1;\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&UnityG/,
&&%\"xG6#\"\"\"F*&F(6#\"\"#F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 80 "maximize(v,\{seq(Player1[j],j=1..n)\} union \{Unity\} union \{
seq(x[i]>=0,i=1..m)\});\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<%/%\"vG
\"\"!/&%\"xG6#\"\"##\"\"\"F+/&F)6#F-F," }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 20 "# Player 2's problem" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 64 "for i from 1 to m do Player2[i]:=add(y[j]*P[i,j],j=1.
.n)<=u od;\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%(Player2G6#\"\"\"1,
&&%\"yGF&F'&F+6#\"\"#!\"\"%\"uG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%
(Player2G6#\"\"#1,&&%\"yG6#\"\"\"!\"\"&F+F&F-%\"uG" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 27 "Unity:=add(y[j],j=1..n)=1;\n" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#>%&UnityG/,&&%\"yG6#\"\"\"F*&F(6#\"\"#F*F*" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 80 "minimize(u,\{seq(Player2[i],
i=1..m)\} union \{Unity\} union \{seq(y[j]>=0,j=1..n)\});\n" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#<%/%\"uG\"\"!/&%\"yG6#\"\"##\"\"\"F+/&F)6#F-
F," }}}{PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "restart: # MarketingGame.mws
" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "with(simplex):\n" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "m:=10: n:=6:" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 227 "P:=matrix(m,n,[\n[60,45,45,35,20,3
5],\n[65,60,45,50,35,50],\n[55,65,60,40,50,50],\n[55,55,65,30,40,40],
\n[75,70,70,60,45,35],\n[80,75,70,65,60,50],\n[80,80,75,55,65,40],\n[6
5,60,70,75,70,60],\n[80,65,60,80,75,65],\n[65,50,60,65,60,75]]):" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "# Player 1's problem" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "for j from 1 to n do Player1
[j]:=add(x[i]*P[i,j],i=1..m)>=v od:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 26 "Unity:=add(x[i],i=1..m)=1:" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 80 "maximize(v,\{seq(Player1[j],j=1..n)\} union \{Unit
y\} union \{seq(x[i]>=0,i=1..m)\});\n" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#<-/&%\"xG6#\"\"\"\"\"!/&F&6#\"\"#F)/&F&6#\"\"$F)/&F&6#\"\"%F)/&F&6#
\"\"&F)/&F&6#\"\"(F)/&F&6#\"\")F)/&F&6#\"#5#F(F1/&F&6#\"\"*FF/&F&6#\"
\"'FF/%\"vG#\"$!>F1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "# Pl
ayer 2's problem" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "for i f
rom 1 to m do Player2[i]:=add(y[j]*P[i,j],j=1..n)<=u od:" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "Unity:=add(y[j],j=1..n)=1:" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 80 "minimize(u,\{seq(Player2[i],
i=1..m)\} union \{Unity\} union \{seq(y[j]>=0,j=1..n)\});\n" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#<)/&%\"yG6#\"\"%\"\"!/&F&6#\"\"&F)/&F&6#\"\"
\"F)/&F&6#\"\"$#F1F5/&F&6#\"\"##F(\"#:/&F&6#\"\"'#F:F-/%\"uG#\"$!>F5" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "24 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 
1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }