{VERSION 5 0 "IBM INTEL NT" "5.0" }
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urier" 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 
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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "restart; #Maple simp
lex implementation " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "info
level[simplex]:=5;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%*infolevelG6#
%(simplexG\"\"&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "with(sim
plex);\n" }}{PARA 7 "" 1 "" {TEXT -1 87 "Warning, the protected names \+
maximize and minimize have been redefined and unprotected\n" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#71%&basisG%+convexhullG%&ctermG%,define_zero
G%(displayG%%dualG%)feasibleG%)maximizeG%)minimizeG%&pivotG%)pivoteqnG
%)pivotvarG%&ratioG%&setupG%,standardizeG" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 61 "cnst:=\{2*x1+3*x2+x3<=5, 4*x1+x2+2*x3<=11, 3*x1+4*x
2+2*x3<=8\}:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "z:=5*x1+4*x
2+3*x3:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "Sol:=maximize(z,
cnst union \{x1>=0, x2>=0, x3>=0\});\n" }}{PARA 6 "" 1 "" {TEXT -1 54 
"simplex[feasible]   verify that constraints are linear" }}{PARA 6 "" 
1 "" {TEXT -1 60 "simplex[feasible]   the variables are of type   UNRE
STRICTED" }}{PARA 6 "" 1 "" {TEXT -1 17 "simplex[feasible]" }}{PARA 6 
"" 1 "" {TEXT -1 18 "initial equations:" }}{PARA 6 "" 1 "" {TEXT -1 
72 "[_SL1 = 5-2*x1-3*x2-x3, _SL2 = 11-4*x1-x2-2*x3, _SL3 = 8-3*x1-4*x2
-2*x3]" }}{PARA 6 "" 1 "" {TEXT -1 54 "simplex[feasible]   initial equ
ations already feasible" }}{PARA 6 "" 1 "" {TEXT -1 18 "maximize:   eq
ns =" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7%/%%_SL1G,*\"\"&\"\"\"*&\"\"#
F(%#x1GF(!\"\"*&\"\"$F(%#x2GF(F,%#x3GF,/%%_SL2G,*\"#6F(*&\"\"%F(F+F(F,
F/F,*&F*F(F0F(F,/%%_SL3G,*\"\")F(*&F.F(F+F(F,*&F6F(F/F(F,*&F*F(F0F(F,
" }}{PARA 6 "" 1 "" {TEXT -1 19 "maximize:   trans =" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6#<\"" }}{PARA 6 "" 1 "" {TEXT -1 97 "simplex/max:   e
qns =    [_SL1 = 5-2*x1-3*x2-x3, _SL2 = 11-4*x1-x2-2*x3, _SL3 = 8-3*x1
-4*x2-2*x3]" }}{PARA 6 "" 1 "" {TEXT -1 68 "simplex/max:   ######   [_
AR, x1, x2, x3, _SL1, _SL2, _SL3]   ######" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6$%(eqns~=~G7%/%%_SL1G,*\"\"&\"\"\"*&\"\"#F)%#x1GF)!\"\"*
&\"\"$F)%#x2GF)F-%#x3GF-/%%_SL2G,*\"#6F)*&\"\"%F)F,F)F-F0F-*&F+F)F1F)F
-/%%_SL3G,*\"\")F)*&F/F)F,F)F-*&F7F)F0F)F-*&F+F)F1F)F-" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6$%'obj~=~G,(*&\"\"&\"\"\"%#x1GF'F'*&\"\"%F'%#x2GF'F
'*&\"\"$F'%#x3GF'F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$%2pivot~variabl
e~=~G%#x1G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$%2pivot~equation~=~G/%%_
SL1G,*\"\"&\"\"\"*&\"\"#F(%#x1GF(!\"\"*&\"\"$F(%#x2GF(F,%#x3GF," }}
{PARA 6 "" 1 "" {TEXT -1 27 "simplex[pivot]   working on" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#7%/%%_SL1G,*\"\"&\"\"\"*&\"\"#F(%#x1GF(!\"\"*&\"
\"$F(%#x2GF(F,%#x3GF,/%%_SL2G,*\"#6F(*&\"\"%F(F+F(F,F/F,*&F*F(F0F(F,/%
%_SL3G,*\"\")F(*&F.F(F+F(F,*&F6F(F/F(F,*&F*F(F0F(F," }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#%#x1G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%%_SL1G,*\"
\"&\"\"\"*&\"\"#F'%#x1GF'!\"\"*&\"\"$F'%#x2GF'F+%#x3GF+" }}{PARA 6 "" 
1 "" {TEXT -1 68 "simplex/max:   ######   [_AR, x1, x2, x3, _SL1, _SL2
, _SL3]   ######" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$%(eqns~=~G7%/%#x1G
,**&\"\"#!\"\"%%_SL1G\"\"\"F*#\"\"&F)F,*(\"\"$F,F)F*%#x2GF,F**&F)F*%#x
3GF,F*/%%_SL2G,(F,F,*&F)F,F+F,F,*&F.F,F1F,F,/%%_SL3G,*#F,F)F,*(F0F,F)F
*F+F,F,*&F)F*F1F,F,*&F)F*F3F,F*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$%'o
bj~=~G,**(\"\"&\"\"\"\"\"#!\"\"%%_SL1GF'F)#\"#DF(F'*(\"\"(F'F(F)%#x2GF
'F)*&F(F)%#x3GF'F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$%2pivot~variable
~=~G%#x3G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$%2pivot~equation~=~G/%%_S
L3G,*#\"\"\"\"\"#F(*(\"\"$F(F)!\"\"%%_SL1GF(F(*&F)F,%#x2GF(F(*&F)F,%#x
3GF(F," }}{PARA 6 "" 1 "" {TEXT -1 27 "simplex[pivot]   working on" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#7%/%#x1G,**&\"\"#!\"\"%%_SL1G\"\"\"F)#
\"\"&F(F+*(\"\"$F+F(F)%#x2GF+F)*&F(F)%#x3GF+F)/%%_SL2G,(F+F+*&F(F+F*F+
F+*&F-F+F0F+F+/%%_SL3G,*#F+F(F+*(F/F+F(F)F*F+F+*&F(F)F0F+F+*&F(F)F2F+F
)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%#x3G" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#/%%_SL3G,*#\"\"\"\"\"#F'*(\"\"$F'F(!\"\"%%_SL1GF'F'*&F(
F+%#x2GF'F'*&F(F+%#x3GF'F+" }}{PARA 6 "" 1 "" {TEXT -1 46 "simplex/max
:   ###### final description ######" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
$%(eqns~=~G7%/%#x1G,**&\"\"#\"\"\"%%_SL1GF*!\"\"F)F**&F)F*%#x2GF*F,%%_
SL3GF*/%%_SL2G,(F*F**&F)F*F+F*F**&\"\"&F*F.F*F*/%#x3G,**&F)F*F/F*F,F*F
**&\"\"$F*F+F*F*F.F*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$%'obj~=~G,*%%_
SL1G!\"\"\"#8\"\"\"*&\"\"$F(%#x2GF(F&%%_SL3GF&" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%$SolG<%/%#x2G\"\"!/%#x3G\"\"\"/%#x1G\"\"#" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "assign(Sol);\n" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 2 "z;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#8" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "restart;# Mixed constraint
s example" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "infolevel[simp
lex]:=5;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%*infolevelG6#%(simplexG
\"\"&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "with(simplex):" }}
{PARA 7 "" 1 "" {TEXT -1 87 "Warning, the protected names maximize and
 minimize have been redefined and unprotected\n" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 24 "z:=2*x[1]+4*x[2]+3*x[3];" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"zG,(*&\"\"#\"\"\"&%\"xG6#F(F(F(*&\"\"%F(&F*6#F'F(F(
*&\"\"$F(&F*6#F1F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "Con
st[1]:=x[1]+5*x[2]+x[3]<= 80;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%&C
onstG6#\"\"\"1,(&%\"xGF&F'*&\"\"&F'&F+6#\"\"#F'F'&F+6#\"\"$F'\"#!)" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "Const[2]:=4*x[1]+2*x[2]+2*x
[3]>=20;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%&ConstG6#\"\"#1\"#?,(*&
\"\"%\"\"\"&%\"xG6#F-F-F-*&F'F-&F/F&F-F-*&F'F-&F/6#\"\"$F-F-" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "Const[3]:=x[1]+x[2]+5*x[3]>=
10;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%&ConstG6#\"\"$1\"#5,(&%\"xG6
#\"\"\"F.&F,6#\"\"#F.*&\"\"&F.&F,F&F.F." }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 52 "Sol:=minimize(z,\{seq(Const[i],i=1..3)\},NONNEGATIVE)
;" }}{PARA 6 "" 1 "" {TEXT -1 54 "simplex[feasible]   verify that cons
traints are linear" }}{PARA 6 "" 1 "" {TEXT -1 59 "simplex[feasible]  \+
 the variables are of type   NONNEGATIVE" }}{PARA 6 "" 1 "" {TEXT -1 
17 "simplex[feasible]" }}{PARA 6 "" 1 "" {TEXT -1 18 "initial equation
s:" }}{PARA 6 "" 1 "" {TEXT -1 90 "[_SL1 = 80-x[1]-5*x[2]-x[3], _SL2 =
 -20+4*x[1]+2*x[2]+2*x[3], _SL3 = -10+x[1]+x[2]+5*x[3]]" }}{PARA 6 "" 
1 "" {TEXT -1 37 "simplex[feasible]   start of  Phase 1" }}{PARA 6 "" 
1 "" {TEXT -1 31 "simplex[feasible]   pivoting on" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#/%%_SL2G,,\"#?!\"\"*&\"\"%\"\"\"&%\"xG6#F*F*F**&\"\"#F*
&F,6#F/F*F**&F/F*&F,6#\"\"$F*F*%$_ARGF*" }}{PARA 6 "" 1 "" {TEXT -1 
27 "simplex[pivot]   working on" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7%/
%%_SL1G,,\"#!)\"\"\"&%\"xG6#F(!\"\"*&\"\"&F(&F*6#\"\"#F(F,&F*6#\"\"$F,
%$_ARGF(/%%_SL2G,,\"#?F,*&\"\"%F(F)F(F(*&F1F(F/F(F(*&F1F(F2F(F(F5F(/%%
_SL3G,,\"#5F,F)F(F/F(*&F.F(F2F(F(F5F(" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#%$_ARG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%%_SL2G,,\"#?!\"\"*&\"\"
%\"\"\"&%\"xG6#F*F*F**&\"\"#F*&F,6#F/F*F**&F/F*&F,6#\"\"$F*F*%$_ARGF*
" }}{PARA 6 "" 1 "" {TEXT -1 134 "simplex/max:   eqns =    [_SL1 = 100
-5*x[1]-7*x[2]-3*x[3]+_SL2, _AR = _SL2+20-4*x[1]-2*x[2]-2*x[3], _SL3 =
 10-3*x[1]-x[2]+3*x[3]+_SL2]" }}{PARA 6 "" 1 "" {TEXT -1 74 "simplex/m
ax:   ######   [_AR, x[1], x[2], x[3], _SL1, _SL2, _SL3]   ######" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6$%(eqns~=~G7%/%%_SL1G,,\"$+\"\"\"\"*&\"
\"&F)&%\"xG6#F)F)!\"\"*&\"\"(F)&F-6#\"\"#F)F/*&\"\"$F)&F-6#F6F)F/%%_SL
2GF)/%$_ARG,,F9F)\"#?F)*&\"\"%F)F,F)F/*&F4F)F2F)F/*&F4F)F7F)F//%%_SL3G
,,\"#5F)*&F6F)F,F)F/F2F/*&F6F)F7F)F)F9F)" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6$%'obj~=~G,,%%_SL2G!\"\"\"#?F&*&\"\"%\"\"\"&%\"xG6#F*F*F**&\"\"#F
*&F,6#F/F*F**&F/F*&F,6#\"\"$F*F*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$%2
pivot~variable~=~G&%\"xG6#\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$%2
pivot~equation~=~G/%%_SL3G,,\"#5\"\"\"*&\"\"$F(&%\"xG6#F(F(!\"\"&F,6#
\"\"#F.*&F*F(&F,6#F*F(F(%%_SL2GF(" }}{PARA 6 "" 1 "" {TEXT -1 27 "simp
lex[pivot]   working on" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7%/%%_SL1G,
,\"$+\"\"\"\"*&\"\"&F(&%\"xG6#F(F(!\"\"*&\"\"(F(&F,6#\"\"#F(F.*&\"\"$F
(&F,6#F5F(F.%%_SL2GF(/%$_ARG,,F8F(\"#?F(*&\"\"%F(F+F(F.*&F3F(F1F(F.*&F
3F(F6F(F./%%_SL3G,,\"#5F(*&F5F(F+F(F.F1F.*&F5F(F6F(F(F8F(" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#&%\"xG6#\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#/%%_SL3G,,\"#5\"\"\"*&\"\"$F'&%\"xG6#F'F'!\"\"&F+6#\"\"#F-*&F)F'&F+
6#F)F'F'%%_SL2GF'" }}{PARA 6 "" 1 "" {TEXT -1 74 "simplex/max:   #####
#   [_AR, x[1], x[2], x[3], _SL1, _SL2, _SL3]   ######" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6$%(eqns~=~G7%/%%_SL1G,,#\"$]#\"\"$\"\"\"*(\"\"&F+F*
!\"\"%%_SL3GF+F+*&#\"#;F*F+&%\"xG6#\"\"#F+F.*&\"\")F+&F46#F*F+F.*(F6F+
F*F.%%_SL2GF+F./%$_ARG,,*&F*F.F<F+F.#\"#?F*F+*(\"\"%F+F*F.F/F+F+*&#F6F
*F+F3F+F.*&\"\"'F+F9F+F./&F46#F+,,*&F*F.F/F+F.#\"#5F*F+*&#F+F*F+F3F+F.
F9F+*&F*F.F<F+F+" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$%'obj~=~G,,*&\"\"$
!\"\"%%_SL2G\"\"\"F)#\"#?F&F'*(\"\"%F)F&F'%%_SL3GF)F'*&#\"\"#F&F)&%\"x
G6#F1F)F)*&\"\"'F)&F36#F&F)F)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$%2piv
ot~variable~=~G&%\"xG6#\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$%2pivo
t~equation~=~G/%$_ARG,,*&\"\"$!\"\"%%_SL2G\"\"\"F)#\"#?F(F+*(\"\"%F+F(
F)%%_SL3GF+F+*&#\"\"#F(F+&%\"xG6#F3F+F)*&\"\"'F+&F56#F(F+F)" }}{PARA 
6 "" 1 "" {TEXT -1 27 "simplex[pivot]   working on" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#7%/%%_SL1G,,#\"$]#\"\"$\"\"\"*(\"\"&F*F)!\"\"%%_SL3GF
*F**&#\"#;F)F*&%\"xG6#\"\"#F*F-*&\"\")F*&F36#F)F*F-*(F5F*F)F-%%_SL2GF*
F-/%$_ARG,,*&F)F-F;F*F-#\"#?F)F**(\"\"%F*F)F-F.F*F**&#F5F)F*F2F*F-*&\"
\"'F*F8F*F-/&F36#F*,,*&F)F-F.F*F-#\"#5F)F**&#F*F)F*F2F*F-F8F**&F)F-F;F
*F*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#&%\"xG6#\"\"#" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6#/%$_ARG,,*&\"\"$!\"\"%%_SL2G\"\"\"F(#\"#?F'F**(\"\"%
F*F'F(%%_SL3GF*F**&#\"\"#F'F*&%\"xG6#F2F*F(*&\"\"'F*&F46#F'F*F(" }}
{PARA 6 "" 1 "" {TEXT -1 46 "simplex/max:   ###### final description #
#####" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$%(eqns~=~G7%/%%_SL1G,,\"#I\"
\"\"*&\"\"*F)%%_SL3GF)!\"\"*&\"\")F)%$_ARGF)F)*&\"\"#F)%%_SL2GF)F)*&\"
#SF)&%\"xG6#\"\"$F)F)/&F76#F2,,*(F9F)F2F-F0F)F-*&F2F-F3F)F-\"#5F)*&F2F
)F,F)F)*&F+F)F6F)F-/&F76#F),*F,F-*&F2F-F0F)F)*&F2F-F3F)F)*&\"\"%F)F6F)
F)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$%'obj~=~G,$%$_ARG!\"\"" }}{PARA 
6 "" 1 "" {TEXT -1 109 "simplex[feasible]   end of phase 1:   \{_AR = \+
0, x[3] = 0, _SL2 = 0, _SL3 = 0, x[2] = 10, _SL1 = 30, x[1] = 0\}" }}
{PARA 6 "" 1 "" {TEXT -1 26 "simplex[maximize]   eqns =" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#7%/%%_SL1G,,\"#I\"\"\"*&\"\"*F(%%_SL3GF(!\"\"*&
\"\")F(%$_ARGF(F(*&\"\"#F(%%_SL2GF(F(*&\"#SF(&%\"xG6#\"\"$F(F(/&F66#F1
,,*(F8F(F1F,F/F(F,*&F1F,F2F(F,\"#5F(*&F1F(F+F(F(*&F*F(F5F(F,/&F66#F(,*
F+F,*&F1F,F/F(F(*&F1F,F2F(F(*&\"\"%F(F5F(F(" }}{PARA 6 "" 1 "" {TEXT 
-1 27 "simplex[maximize]   trans =" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
<\"" }}{PARA 6 "" 1 "" {TEXT -1 122 "simplex/max:   eqns =    [_SL1 = \+
30-9*_SL3+2*_SL2+40*x[3], x[2] = 10-1/2*_SL2+2*_SL3-9*x[3], x[1] = -_S
L3+1/2*_SL2+4*x[3]]" }}{PARA 6 "" 1 "" {TEXT -1 74 "simplex/max:   ###
###   [_AR, x[1], x[2], x[3], _SL1, _SL2, _SL3]   ######" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6$%(eqns~=~G7%/%%_SL1G,*\"#I\"\"\"*&\"\"*F)%%_SL3G
F)!\"\"*&\"\"#F)%%_SL2GF)F)*&\"#SF)&%\"xG6#\"\"$F)F)/&F46#F/,*\"#5F)*&
F/F-F0F)F-*&F/F)F,F)F)*&F+F)F3F)F-/&F46#F),(F,F-*&F/F-F0F)F)*&\"\"%F)F
3F)F)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$%'obj~=~G,**&\"\"'\"\"\"%%_SL
3GF'!\"\"%%_SL2GF'*&\"#DF'&%\"xG6#\"\"$F'F'\"#SF)" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6$%2pivot~variable~=~G&%\"xG6#\"\"$" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6$%2pivot~equation~=~G/&%\"xG6#\"\"#,*\"#5\"\"\"*&F(!\"\"
%%_SL2GF+F-*&F(F+%%_SL3GF+F+*&\"\"*F+&F&6#\"\"$F+F-" }}{PARA 6 "" 1 "
" {TEXT -1 27 "simplex[pivot]   working on" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#7%/%%_SL1G,*\"#I\"\"\"*&\"\"*F(%%_SL3GF(!\"\"*&\"\"#F(%
%_SL2GF(F(*&\"#SF(&%\"xG6#\"\"$F(F(/&F36#F.,*\"#5F(*&F.F,F/F(F,*&F.F(F
+F(F(*&F*F(F2F(F,/&F36#F(,(F+F,*&F.F,F/F(F(*&\"\"%F(F2F(F(" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#&%\"xG6#\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#/&%\"xG6#\"\"#,*\"#5\"\"\"*&F'!\"\"%%_SL2GF*F,*&F'F*%%_SL3GF*F**
&\"\"*F*&F%6#\"\"$F*F," }}{PARA 6 "" 1 "" {TEXT -1 46 "simplex/max:   \+
###### final description ######" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$%(e
qns~=~G7%/%%_SL1G,*#\"$q'\"\"*\"\"\"*&F*!\"\"%%_SL3GF+F-*(\"\"#F+F*F-%
%_SL2GF+F-*&#\"#SF*F+&%\"xG6#F0F+F-/&F66#\"\"$,**&#F+F*F+F5F+F-#\"#5F*
F+*&\"#=F-F1F+F-*(F0F+F*F-F.F+F+/&F66#F+,**&F*F-F.F+F-*(\"\"&F+FBF-F1F
+F+*&#\"\"%F*F+F5F+F-#F4F*F+" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$%'obj~
=~G,**(\"\"%\"\"\"\"\"*!\"\"%%_SL3GF'F)*(\"\"(F'\"#=F)%%_SL2GF'F)*&#\"
#DF(F'&%\"xG6#\"\"#F'F)#\"$5\"F(F)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
>%$SolG<%/&%\"xG6#\"\"#\"\"!/&F(6#\"\"$#\"#5\"\"*/&F(6#\"\"\"#\"#SF2" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "assign(Sol);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "z;" }}{PARA 11 "" 1 "" {XPPMATH 20 "
6##\"$5\"\"\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "restart; \+
#Transportation problem" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "
infolevel[simplex]:=default;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%*in
folevelG6#%(simplexG%(defaultG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 13 "m:=3;#sources" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"mG\"\"$" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "n:=4;#sinks" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#>%\"nG\"\"%" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 59 "c:=matrix(m,n,[[1,2,3,4],[4,3,2,0],[0,2,2,1]]);#cost \+
matrix" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"cG-%'matrixG6#7%7&\"\"\"
\"\"#\"\"$\"\"%7&F-F,F+\"\"!7&F/F+F+F*" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 41 "z:=sum(sum(c[i,j]*x[i,j],j=1..n),i=1..m);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%\"zG,6&%\"xG6$\"\"\"F)F)*&\"\"#F)&F'6$F)F+
F)F)*&\"\"$F)&F'6$F)F/F)F)*&\"\"%F)&F'6$F)F3F)F)*&F3F)&F'6$F+F)F)F)*&F
/F)&F'6$F+F+F)F)*&F+F)&F'6$F+F/F)F)*&F+F)&F'6$F/F+F)F)*&F+F)&F'6$F/F/F
)F)&F'6$F/F3F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "s:=array(
[6,8,10]);#supplies" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"sG-%'vector
G6#7%\"\"'\"\")\"#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "sum(
s[i],i=1..m);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#C" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "d:=array([4,6,8,6]);#demands" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"dG-%'vectorG6#7&\"\"%\"\"'\"\")F*
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "sum(d[j],j=1..n);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#C" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 28 "#total supply = total demand" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 21 "for i from 1 to m do " }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 94 "Supply[i]:=sum(x[i,j],j=1..n)=s[i] end do; #all suppl
ies have to be taken out from each source" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>&%'SupplyG6#\"\"\"/,*&%\"xG6$F'F'F'&F+6$F'\"\"#F'&F+6$
F'\"\"$F'&F+6$F'\"\"%F'\"\"'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%'Su
pplyG6#\"\"#/,*&%\"xG6$F'\"\"\"F-&F+6$F'F'F-&F+6$F'\"\"$F-&F+6$F'\"\"%
F-\"\")" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%'SupplyG6#\"\"$/,*&%\"xG
6$F'\"\"\"F-&F+6$F'\"\"#F-&F+6$F'F'F-&F+6$F'\"\"%F-\"#5" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "i:='i';" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"iGF$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "
for j from 1 to n do" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "Demand[j]:=
sum(x[i,j],i=1..m)= d[j] end do; #all demands must be met" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#>&%'DemandG6#\"\"\"/,(&%\"xG6$F'F'F'&F+6$\"\"#F
'F'&F+6$\"\"$F'F'\"\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%'DemandG6
#\"\"#/,(&%\"xG6$\"\"\"F'F-&F+6$F'F'F-&F+6$\"\"$F'F-\"\"'" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#>&%'DemandG6#\"\"$/,(&%\"xG6$\"\"\"F'F-&F+6$\"
\"#F'F-&F+6$F'F'F-\"\")" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%'DemandG
6#\"\"%/,(&%\"xG6$\"\"\"F'F-&F+6$\"\"#F'F-&F+6$\"\"$F'F-\"\"'" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "j:='j';" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"jGF$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "
constraints:=\{seq(Supply[i],i=1..m)\} union \{seq(Demand[j],j=1..n)\}
:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "with(simplex):" }}
{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 42 "Sol:=minimize(z,constraints, NONNEGATIVE);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$SolG<./&%\"xG6$\"\"\"F*\"\"!/&F(6$F
*\"\"$F+/&F(6$F*\"\"%F+/&F(6$\"\"#F*F+/&F(6$F/F3F+/&F(6$F7F7F+/&F(6$F/
F*F3/&F(6$F7F3\"\"'/&F(6$F7F/F7/&F(6$F/F/FD/&F(6$F*F7FD/&F(6$F/F7F+" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "assign(Sol);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "z;" }}{PARA 11 "" 1 "" {XPPMATH 20 "
6#\"#G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "38 0 \+
0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }