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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 
-1 8 "Math 343" }}{PARA 0 "" 0 "" {TEXT -1 26 "Monday, September 13, 1
999" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }
}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "A:
=matrix(2,3,[1,2,3,4,5,6]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG-
%'MATRIXG6#7$7%\"\"\"\"\"#\"\"$7%\"\"%\"\"&\"\"'" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 20 "b:=vector([3,2,-5]);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"bG-%'VECTORG6#7%\"\"$\"\"#!\"&" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 13 "with(linalg):" }}{PARA 7 "" 1 "" {TEXT -1 
33 "Warning, new definition for basis" }}{PARA 7 "" 1 "" {TEXT -1 33 "
Warning, new definition for pivot" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 7 "?linalg" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "
gaussjord(A);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'MATRIXG6#7%7&\"\"
\"\"\"!$!?&Q:YQ:YQ:YQ:YQ:'!#IF)7&F)F($!?3Bp2Bp2Bp2Bp2BpF,F)7&F)F)F)F)
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "Digits:=10;" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%'DigitsG\"#5" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 13 "gaussjord(A);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'M
ATRIXG6#7%7&\"\"\"\"\"!$!+ah%Q:'!#5F)7&F)F($!+Cp2BpF,F)7&F)F)F)F)" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "with(simplex):" }}{PARA 7 "
" 1 "" {TEXT -1 33 "Warning, new definition for basis" }}{PARA 7 "" 1 
"" {TEXT -1 38 "Warning, new definition for convexhull" }}{PARA 7 "" 
1 "" {TEXT -1 33 "Warning, new definition for cterm" }}{PARA 7 "" 1 "
" {TEXT -1 35 "Warning, new definition for display" }}{PARA 7 "" 1 "" 
{TEXT -1 32 "Warning, new definition for dual" }}{PARA 7 "" 1 "" 
{TEXT -1 36 "Warning, new definition for feasible" }}{PARA 7 "" 1 "" 
{TEXT -1 36 "Warning, new definition for maximize" }}{PARA 7 "" 1 "" 
{TEXT -1 33 "Warning, new definition for pivot" }}{PARA 7 "" 1 "" 
{TEXT -1 36 "Warning, new definition for pivotvar" }}{PARA 7 "" 1 "" 
{TEXT -1 33 "Warning, new definition for ratio" }}{PARA 7 "" 1 "" 
{TEXT -1 33 "Warning, new definition for setup" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 181 "minimize(284*x1+103*x2+122*x3+176*x4+211*x5+1
36*x6,\n\{x1+x2+x3=1500,\n          x4+x5+x6=2000,\n x1      +x4      \+
=1300,\n    x2      +x5   =1700,\n       x3      +x6=500\},\nNONNEGATI
VE);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<(/%#x3G\"\"!/%#x1GF&/%#x4G\"%
+8/%#x6G\"$+&/%#x5G\"$+#/%#x2G\"%+:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 45 "f:=284*x1+103*x2+122*x3+176*x4+211*x5+136*x6;" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG,.%#x1G\"$%G%#x2G\"$.\"%#x3G\"$A
\"%#x4G\"$w\"%#x5G\"$6#%#x6G\"$O\"" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 18 "e1:=x1+x2+x3=1500;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
#>%#e1G/,(%#x1G\"\"\"%#x2GF(%#x3GF(\"%+:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 18 "e2:=x4+x5+x6=2000;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
#>%#e2G/,(%#x4G\"\"\"%#x5GF(%#x6GF(\"%+?" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 15 "e3:=x1+x4=1300;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%
#e3G/,&%#x1G\"\"\"%#x4GF(\"%+8" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 15 "e4:=x2+x5=1700;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#e4G/,&%#
x2G\"\"\"%#x5GF(\"%+<" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "e5
:=x3+x6=500;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#e5G/,&%#x3G\"\"\"%#
x6GF(\"$+&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "minimize(f,\{
e1,e2,e3,e4,e5\},NONNEGATIVE);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<(/%
#x3G\"\"!/%#x1GF&/%#x4G\"%+8/%#x6G\"$+&/%#x5G\"$+#/%#x2G\"%+:" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }
}{PARA 0 "" 0 "" {TEXT -1 42 "The following is for problem 9(b), page \+
95" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 61 "B:=matrix(2,6,[0,1,-2,-4,-2,-1,\n               1,0,0
,1,3,5]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"BG-%'MATRIXG6#7$7(\"
\"!\"\"\"!\"#!\"%F,!\"\"7(F+F*F*F+\"\"$\"\"&" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 13 "gaussjord(B);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
#-%'MATRIXG6#7$7(\"\"\"\"\"!F)F(\"\"$\"\"&7(F)F(!\"#!\"%F-!\"\"" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 56 "A:=matrix(2,5,[0,1,-2,-4,-2,\n               1,0,0,
1,3]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG-%'MATRIXG6#7$7'\"\"!
\"\"\"!\"#!\"%F,7'F+F*F*F+\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 18 "b:=vector([-1,5]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"bG-%
'VECTORG6#7$!\"\"\"\"&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "l
insolve(A,b);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'VECTORG6#7'&%#_tG6
#\"\"$,*\"#>\"\"\"&F(6#\"\"#F0F'!\"%&F(6#F-!#5F.,(F'!\"\"\"\"&F-F2!\"$
F2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "0 1 0" 8 
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