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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg):" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 82 "yh:=hessian(3*x1^2-5*x1-x1*x
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" {XPPMATH 20 "6#>%\"yG,4*$)%#x1G\"\"#\"\"\"$\"#I!\"\"*&\"\"&F*F(F*F-*
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" {MPLTEXT 1 0 16 "yx1:=diff(y,x1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
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{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "yx2:=diff(y,x2);" }}{PARA 
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{MPLTEXT 1 0 20 "yx2x2:=diff(yx2,x2);" }}{PARA 11 "" 1 "" {XPPMATH 20 
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{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&yx1x2G!\"\"" }}}{EXCHG {PARA 0 "> \+
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{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&yx2x3G\"\"#" }}}{EXCHG {PARA 0 "> \+
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> " 0 "" {MPLTEXT 1 0 15 "deth3:=det(yh);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%&deth3G\"$[%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 32 "solve(\{yx1,yx2,yx3\},\{x1,x2,x3\});" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#<%/%#x3G$!+'G9dy\"!#6/%#x1G$\"+H9dG*)!#5/%#x2G$\"+dG92T
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{PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "tr:=15.0*q1+18*q2;" }}{PARA 11 "" 
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}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "tc:=2*q1^2+2*q1*q2+3*q2^2;
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{MPLTEXT 1 0 12 "prof:=tr-tc;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%pr
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{XPPMATH 20 "6#>%&profhG-%'matrixG6#7$7$!\"%!\"#7$F+!\"'" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "h2:=det(profh);" }}{PARA 11 "" 1 "
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22 "profx1:=diff(prof,q1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'profx
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{PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "profx2:=diff(prof,q2);" }}{PARA 11 
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{XPPMATH 20 "6#7^r%.BlockDiagonalG%,GramSchmidtG%,JordanBlockG%)LUdeco
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ausselimG%*fibonacciG%+forwardsubG%*frobeniusG%*gausselimG%*gaussjordG
%(geneqnsG%*genmatrixG%%gradG%)hadamardG%(hermiteG%(hessianG%(hilbertG
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1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(lin
alg):" }}{PARA 7 "" 1 "" {TEXT -1 80 "Warning, the protected names nor
m and trace have been redefined and unprotected\n" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 18 "P1:=70-2*Q1-Q2-Q3;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%#P1G,*\"#q\"\"\"*&\"\"#F'%#Q1GF'!\"\"%#Q2GF+%#Q3GF+" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "p2:=120-Q1-4*Q2-2*Q3;" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#p2G,*\"$?\"\"\"\"%#Q1G!\"\"*&\"\"%F
'%#Q2GF'F)*&\"\"#F'%#Q3GF'F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 18 "p3:=90-Q1-Q2-3*Q3;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#p3G,*\"
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0 "" {MPLTEXT 1 0 41 "TC:=Q1^2+Q1*Q2+2*Q2^2+2*Q2*Q3+Q3^2+Q1*Q3;" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#TCG,.*$)%#Q1G\"\"#\"\"\"F**&F(F*%#Q
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{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "profit:=P1*Q1+P2*Q2+P3*Q3-TC
;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'profitG,4*&,*\"#q\"\"\"*&\"\"#
F)%#Q1GF)!\"\"%#Q2GF-%#Q3GF-F)F,F)F)*&%#P2GF)F.F)F)*&%#P3GF)F/F)F)*$)F
,F+F)F-*&F,F)F.F)F-*&F+F))F.F+F)F-*(F+F)F.F)F/F)F-*$)F/F+F)F-*&F,F)F/F
)F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "profh:=hessian(profi
t,[Q1,Q2,Q3]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&profhG-%'matrixG6
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