\(\(\( (*\ 
      Biblioteka\ za\ rad\ sa\ matricama\ *) \)\( (*VERZIJA\ 30.3 \( \(.2002\)\(.\)\)*) \)\(
\)\(<< 
      LinearAlgebra`MatrixManipulation`\)\)\)

\(\(Elimination[a_, b_, xs_, c_, lam_] := 

        Module[{an = a, xss = {}, pom = {}, indper = {}, i, n, m, p, q, h, L, 
            maxi, cn = c, l = lam}, 
		{m, n} = 
            Dimensions[a]; 
		\(brelim++\); \ 
          inp = 1; 
		 (*	Step\ 1\ *) 
		indper = 
            Sort[Range[n], 
              xs[\([#1]\)] > xs[\([#2]\)] &]; 
		xss = 
            xs[\([indper]\)]; 
			h = 1; 
		While[
            xss[\([h]\)] >= 1 && 
              h < n, \(h++\)]; 
\ \ \ \ \ \ \ \ \ \ \ \ h = 
            h - 1; \ 
		L = True; 
		If[h == n, \ L = False; \ 
            q = n;]; 			
		 (*\ Step\ 2\ *) 
		an = 
            Transpose[
              Append[\(Transpose[a]\)[\([indper]\)], 
                b]]; 
\ \ \ \ \ \ \ \ \ \ \ \ cn = 
            cn[\([indper]\)]; \ 	
		AppendTo[cn, \(-kor\)]; 		AppendTo[
            an, cn]; 
		p = 1; \ 
          q = 1; 
			While[\((L && \((q < m)\))\), 	
		\ \ 	 (*\ 
              Step\ 3\ *) 
\ \ 			pom = 
              Drop[\((Transpose[
                      Abs[an]])\)[\([p]\)], \(-1\)]; 
	
            pom = Drop[pom, 
                q - 1]; \ \ \ \ \ \ \ \ \ \ \ \ \ \ 
\ \ 			maxi = \(Position[pom, Max[pom]]\)[\([1, 1]\)] + q - 1; \ 		
\ \ \ \ 		If[
              an[\([maxi, p]\)] == 0, 
\ \ 		\ 		 (*\ 
                Step\ 4\ *) 						
		\ \ 	\ 	\(If[
                  p == h, 	
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ cn = 
                    an[\([m + 
                          1]\)]; 	\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ an = 
                    Drop[an, \(-1\)]; 
 (*\(Print["Vracam!!!!!!1111!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! ", 
                        List[an, indper, q - 1, cn, 
                          l]];\)*) 
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Return[
                    List[an, indper, q - 1, cn, 
                      l]], 
					\ \ \ \ \ \ \ \ \ \ \ \ \(\(p++\);\)
					\ \ \ ];\)
	\ \ \ 			, 
		\ 	\ \ \ \ \ \  (*\ 
                Step\ 5\ *) 
\ \ 	\ 	If[
                maxi != 
                  q, 
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ pom = 
                  an[\([maxi]\)]; \ \ an[\([maxi]\)] = 
                  an[\([q]\)]; 		an[\([q]\)] = 
                  pom; 
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ pom = 
                  l[\([maxi]\)]; \ \ l[\([maxi]\)] = 
                  l[\([q]\)]; 		l[\([q]\)] = 
                  pom;
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ]; \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ For[i = q + 1, \ 
                i ≤ 
                  m, \(i++\), 
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \(l[\([q]\)] = 
                    N[l[\([q]\)] + \ 
                        l[\([i]\)]*an[\([i, p]\)]/an[\([q, p]\)], 
                      20];\)
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ]; \ \ 
			\ \ \ \ \ \ Do[
                an[\([i]\)] = 
                  N[an[\([i]\)] - an[\([i, p]\)]*an[\([q]\)]/an[\([q, p]\)], 
                    20], 
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {i, q + 1, 
                  m}]; 
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 			
\ \ \ \ \ 	\ 		 (*\ 
                Step\ 6\ *) 			
				L = 
                Not[\((q == Min[h, m])\)\  || \ \((p == h)\)]; 
				If[
                L, \ \(p++\); \ \(q++\);];
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ];
]; 
cn = 
            an[\([m + 1]\)]; 	
an = 
            Drop[an, \(-1\)]; 
 (*\(Print["Vracam!!!!!!1111!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! ", 
                List[an, indper, q, cn, 
                  l]];\)*) 
		Return[
            List[an, indper, q, cn, l]];
];\)\)

(* 1. Pomocne fje:
     Koraci 1. i 2:
     Formira matricu novog sistema j-na dodavanjem vektora tipa:
    {0,..,0,j,0,..} dimenzije q - broj nej-na,pri cemu se  j=-1,0,1 nala-
     zi na i-tom mestu,gde je i - indeks  vrste matrice A  na koju se
     ovakav vektor dodaje. *)
form[x_,p_,q_]:=
  Module[{i,L={},y},
    For[i=1,i<=First[Dimensions[x]],i++,
	    If[i<=p,
    	   y=Join[x[[i]],ReplacePart[Table[0,{q}],1,i]],
	       If[i<=q,
              y=Join[x[[i]],ReplacePart[Table[0,{q}],-1,i]],
	          y=Join[x[[i]],Table[0,{q}]]
	    ]  ];
	    L=Append[L,y]
	 ];
     Return[L]
   ]              
 (* Korak 4:     Izracunava inicijalne vrednosti za x i s.   *)    
  inicp[a_,b_,c_]:=
     Module[{i,pom,ppom,maxpom=1,k,m},
     	k=Last[Dimensions[a]];    	m=First[Dimensions[a]];
     	For[i=1,i<=m,i++,  	
       	    pom=N[Sqrt[Sum[a[[i,j]]^2,{j,k}] ],20];       	    
       	    If[pom!=0,
      	       ppom=Max[N[Abs[b[[i]]/pom],20],1];
      	       If[ppom>maxpom, maxpom=ppom];
      	]   ];
      	If[maxpom==1, maxpom=100]; 
        Return[maxpom]
     ] 
(* Koraci 9. i 13:
     Neophodno je izracunati sisteme nej-na dimenzije Dimensions[x]
     po jednoj promenljivoj - alfa,uz uslove da je r-nje izmedju 0 i 1 za
     korak 9,odnosno da je >=0 za korak 13.
     F-je resi1 i resi2,za korake 9. i 13. respektivno,to cine svodjenjem
     na slucajeve:
         1.ako je dx[i]>0 za svako i tada je alfa=1,tj. alfa=oo,
  	     2.ako postoji i takvo da dx[i]<0 tada je 	alfa=Min[Abs[x[i]/dx[i]]].   *)
 resi1[x_,dx_]:=
    Module[{i,a=1,al={}},
            For[i=1,i<=First[Dimensions[x]],i++,
	            If[dx[[i]]<0,
                   al=Append[al,N[Abs[x[[i]]/dx[[i]]],20]]
	        ]   ];
            If[Min[al]<1,a=Min[al]];
            Return[N[a,20]]
     ]
resi2[x_,dx_]:=
  Module[{i,a=Abs[Max[]],al={}},
    For[i=1,i<=First[Dimensions[x]],i++,
	    If[dx[[i]]<0,
	       al=Append[al,Abs[x[[i]]/dx[[i]]]]
	]   ];
    a=Min[al];
    Return[N[a,20]]
  ]	
(*  2. Glavni program:     *)
PrimalDual[objective_,constraints_,eps_,iter_, Mm_,eps1_,eps2_,eps3_]:=
  (* eps1 je za kracenje x, eps2 za s, a eps3 za x.s<eps3 *)
 Module[{a={},b={}, ce=ce1=ce2={} ,x,x1,y,opcija, manje,vece,jednako,
            p,q,m,n,k,i,d,hhh,b1,l1,
            pi,s,s1,l,Xmat,Ymat,rxs,
            rb,rc,korak=1,
            Dlaff,DSaff,Dsaff,DXaff,Dxaff,
            AlfaPa,AlfaDa,
            SigCent,
            Dlcc,Dscc,Dxcc,
            dl,dx,ds,
            xzero={},k1,q1,is,j=0,lg,cut,xs,pp,eps4,
            pom={},permut=permut1={}, vR,vA={},vF={},vG={},vH={},vRight={},vRes={}
	     },	     
brelim=0; inp=0; kor=0;	 	
(*0.1.Korak:   *)
	(* Sledeca f-ja daje matricu koeficijenata A datog sistema:  *)
   manje=Cases[constraints,x_<=y_->x-y];
   vece=Cases[constraints,x_>=y_->x-y];
   jednako=Cases[constraints,x_==y_->x-y];
(*   Print["manje = ",manje," vece = ",vece," jednako = ",jednako]; *)
   p=Length[manje];   q=Length[vece];    m=Length[jednako];   
   For[i=1,i<=p,i++,
       b=Union[b,Map[Variables,manje,{1}][[i]]   ] 
   ];
   For[i=1,i<=q,i++,
       b=Union[b,Map[Variables,vece,{1}][[i]]   ] 
   ];
   For[i=1,i<=m,i++,
       b=Union[b,Map[Variables,jednako,{1}][[i]]  ] 
   ];                 
   For[i=1,i<=p,i++,
       a=Append[a,List[manje[[i]],b]]
   ];
   For[i=1,i<=q,i++,
       a=Append[a,List[vece[[i]],b]]
   ];
   For[i=1,i<=m,i++,
       a=Append[a,List[jednako[[i]],b]]
   ];
   a=Apply[Coefficient,a,{1}];
   ce=Coefficient[objective,b];            
   k=k1=First[Dimensions[ce]];                
   If[Mm==0, opcija=0, opcija=1];
   
   If[opcija==1,ce=-ce];
   b={};
   For[i=1,i<=p,i++,
       If[NumberQ[First[Cases[manje[[i]],x_]]],
          b=Append[b,-First[Cases[manje[[i]],x_]]],
          b=Append[b,0]
   ]   ];
   For[i=1,i<=q,i++,
       If[NumberQ[First[Cases[vece[[i]],x_]]],
          b=Append[b,-First[Cases[vece[[i]],x_]]],
          b=Append[b,0]
   ]   ];
   For[i=1,i<=m,i++,
       If[NumberQ[First[Cases[jednako[[i]],x_]]],
          b=Append[b,-First[Cases[jednako[[i]],x_]]],
          b=Append[b,0]
   ]    ];
   q=p+q;     m=q+m;  n=k+q;
 
(* 0.2.Korak:    *)	
   a=form[a,p,q];
   ce=Join[ce,Table[0,{q}]];   	
(* 1.Korak:   *)

ce1=ce;
   pi=inicp[a,b,ce];

    Print["pi=",pi];
   x=Table[pi,{n}];      s=x;
   l=Table[0,{m}];	
(* 2.Korak:    *)
  permut=Range[Dimensions[a][[2]]]; permut1=permut;
    rb=N[a.x-b];   rc=N[Transpose[a].l+s-ce];
    pok=0;      
    Xmat=DiagonalMatrix[x];   Smat=DiagonalMatrix[s];         
   rxs=N[Xmat.Smat.Table[1,{n}],20];
  is= DiagonalMatrix[N[1/s,20]];   d= DiagonalMatrix[N[x/s,20]];
(*Print["cond= ", MatrixConditionNumber[N[a.d.Transpose[a]]]]; *)
If[MatrixConditionNumber[N[a.d.Transpose[a]]]<=10^10,
eps4=10*MatrixConditionNumber[N[a.d.Transpose[a]]],
eps4=10^16];
(*Print["eps4=",eps4];*)


 (************** VELIKA PETLJA *****************)   
   While[x.s>eps && (korak<=iter),
    b1=b;l1=l;  x1=x; s1=s; permut1=permut;ce2=ce;
      n=k+q;	b1=b; l1=l;kor1=kor;
     (* Print["kriterijum= ",Abs[ce.x-b.l]/(1+Abs[ce.x])	];
      Print["cx=",ce.x];
      Print["bl=",b.l];*)
    (* 3.Korak:   *)
   Xmat=DiagonalMatrix[x];   Smat=DiagonalMatrix[s];         
   rxs=N[Xmat.Smat.Table[1,{n}],20];
  (* 4.Korak:   *)
is= DiagonalMatrix[N[1/s,20]];   d= DiagonalMatrix[N[x/s,20]];
(*Print["cond= ", MatrixConditionNumber[N[a.d.Transpose[a]]]];*)
(* Vera Elimination*)
If[pok==0,
If[( MatrixConditionNumber[N[a.d.Transpose[a]]]>eps4)&&(korak>1),	
 pok=1;
 (*	Print["ELIMINACIJA ZBOG AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA"];  	
  	Print["Pre eliminacije:++++++ ",b.l+kor];*)
	pom=Elimination[a,b,x/s,ce,l];
 
 	vR=pom[[3]];  ce=pom[[4]]; l=pom[[5]]; 
 (*	Print["VR============================= ",vR];*)
	 kor=Last[ce];
  (*Print[kor];*)
     ce=Drop[ce,-1];
		
 	a=N[Transpose[Drop[Transpose[pom[[1]]],-1]]];
	b=N[Flatten[Take[Transpose[pom[[1]]],-1]]];
		
	(*Print["a=",MatrixForm[a]];*)
	
	pom=pom[[2]];
	permut=permut[[pom]];
	x=x[[pom]];	s=s[[pom]];	rc=rc[[pom]];
(*	Print["rb=",rb];Print["rc=",rc];*)
	rb=N[a.x-b,20];
    rc=N[Transpose[a].l+s-ce,20];
 
		(*Print["Posle eleiminacije:++++++ ",b.l+kor];*)
    
	 Xmat=DiagonalMatrix[x];   Smat=DiagonalMatrix[s];         
   rxs=N[Xmat.Smat.Table[1,{n}],20];
   is= DiagonalMatrix[N[1/s,20]];   d= DiagonalMatrix[N[x/s,20]];
	
];,

If[ ((vR<Dimensions[a][[1]])&&(MatrixConditionNumber[vH-Transpose[vG].vF.vG]>eps4))
||( MatrixConditionNumber[N[vF]]>eps4),
	(*Print["ELIMINACIJA ZBOG vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv"];		
	Print["Pre eliminacije:++++++ ",b.l+kor];*)
	pom=Elimination[a,b,x/s,ce,l];
(* Print["Elimination:::::::::::::::::: ",pom];	*) 

  
	vR=pom[[3]];  ce=pom[[4]]; l=pom[[5]];
	(*Print["VR======================================== ",vR];*)
	 kor=Last[ce];
(*  Print[kor];*)
  ce=Drop[ce,-1];

 	a=N[Transpose[Drop[Transpose[pom[[1]]],-1]]];
 	b=N[Flatten[Take[Transpose[pom[[1]]],-1]]];

(*Print["a=",MatrixForm[a]];*)
	
	pom=pom[[2]];
	permut=permut[[pom]];
	x=x[[pom]];	s=s[[pom]];	rc=rc[[pom]];
	
	rb=N[a.x-b,20];
    rc=N[Transpose[a].l+s-ce,20];    
        (*	Print["Pre eliminacije:++++++ ",b.l+kor];*)
	 Xmat=DiagonalMatrix[x];   Smat=DiagonalMatrix[s];         
   rxs=N[Xmat.Smat.Table[1,{n}],20];	
   is= DiagonalMatrix[N[1/s,20]];   d= DiagonalMatrix[N[x/s,20]];
];
];(* Ovde biramo kriterijum za eliminaciju po A ili podmatricama *)

If[pok==0,
If[(vR<Dimensions[a][[1]])&&( MatrixConditionNumber[N[a.d.Transpose[a]]]>eps4)&&(korak>1),

	vA=a.d.Transpose[a];
	(* Print["moze: ",vR,":",Dimensions[a][[1]]];  *)
	(* matrica F *)
	vF=SubMatrix[vA,{1,1},{vR,vR}]; 
	(*Print["vF= ",MatrixForm[vF]]; *)
	(*Print["condVf= ", MatrixConditionNumber[N[vF]]];*)
		vF=N[Inverse[vF],20];
		
	(* matrica G *)
	vG=SubMatrix[vA,{1,vR+1},{vR,Dimensions[vA][[2]]-vR}];
	(*Print["vG=   ",vG//MatrixForm];*)
	(* matrica H *)
	vH=SubMatrix[vA,{vR+1,vR+1},{Dimensions[vA][[1]]-vR,Dimensions[vA][[2]]-vR}];
	vRight=N[-rb-a.(is.Xmat.rc-is.rxs),20];
	vRes=N[LinearSolve[vH-Transpose[vG].vF.vG, Drop[vRight,vR]-Transpose[vG].vF.Take[vRight,vR]],20]; 
	Dlaff=N[vF.Take[vRight,vR]-vF.vG.vRes,20];
	
	Dlaff=Join[Dlaff,vRes];
	
	hhh=vH-Transpose[vG].vF.vG;
	(*Print["condVg= ", MatrixConditionNumber[hhh]];*)
       
    	,
	Dlaff=N[LinearSolve[a.d.Transpose[a],
    				-rb-a.(is.Xmat.rc-is.rxs)],20
   	  ];
   	 (* Print["radim sa NEtransformisanim matricama"];*)
];,
(*pok=1*)
vA=a.d.Transpose[a];
	(* Print["moze: ",vR,":",Dimensions[a][[1]]];  *)
	(* matrica F *)
	vF=SubMatrix[vA,{1,1},{vR,vR}]; 
	(*Print["vF= ",MatrixForm[vF]]; *)
	(*Print["condVf= ", MatrixConditionNumber[N[vF]]];*)
		vF=N[Inverse[vF],20];
		
	(* matrica G *)
	vG=SubMatrix[vA,{1,vR+1},{vR,Dimensions[vA][[2]]-vR}];
	(*Print["vG=======  ",vG//MatrixForm];*)
	
	(* matrica H *)
		If[vR<Dimensions[a][[1]],
	   vH=SubMatrix[vA,{vR+1,vR+1},{Dimensions[vA][[1]]-vR,Dimensions[vA][[2]]-vR}];
	   vRight=N[-rb-a.(is.Xmat.rc-is.rxs),20];
	   vRes=N[LinearSolve[vH-Transpose[vG].vF.vG, Drop[vRight,vR]-Transpose[vG].vF.Take[vRight,vR]],10];	   
	   Dlaff=N[vF.Take[vRight,vR]-vF.vG.vRes,20];
	  
	   Dlaff=Join[Dlaff,vRes];
	   hhh=vH-Transpose[vG].vF.vG;
	   (*Print["condVg= ", MatrixConditionNumber[hhh]];
       Print["radim sa transformisanim matricama"];*),
       
       Dlaff=N[LinearSolve[a.d.Transpose[a],
    				-rb-a.(is.Xmat.rc-is.rxs)],20
   	  ];
       
      ];
];

   Dsaff=N[-rc-Transpose[a].Dlaff,20];
   Dxaff=N[-is.(rxs+Xmat.Dsaff),20];
          
(* 5.Korak:   *)
   mi=N[(x.s)/n,20];
          	         
(* 6.Korak:   *)
   AlfaPa=resi1[x,Dxaff];
   AlfaDa=resi1[s,Dsaff];

(* 7.Korak:   *)

   SigCent=N[((((x+AlfaPa*Dxaff).(s+AlfaDa*Dsaff))/n)/mi)^3,20];

(* 8.Korak:  *)
DXaff=DiagonalMatrix[Dxaff];     DSaff=DiagonalMatrix[Dsaff];         
rxs=N[-mi*SigCent,20]*Table[1,{n}]+N[DXaff.DSaff,20].Table[1,{n}];
(* vera *)
If[pok==0,
If[(vR<Dimensions[a][[1]])&&( MatrixConditionNumber[N[a.d.Transpose[a]]]>eps4)&&(korak>1),
	vRight=N[a.is.rxs,20];
	vRes=N[LinearSolve[vH-Transpose[vG].vF.vG, Drop[vRight,vR]-Transpose[vG].vF.Take[vRight,vR]],20]; 
	Dlcc=N[vF.Take[vRight,vR]-vF.vG.vRes,20];
	
	Dlcc=Join[Dlcc,vRes];
	
	 (*Print["radim sa transformisanim matricama"];*)
	,
	  (*Print["radim sa NEtransformisanim matricama"];*)
   	  Dlcc=N[LinearSolve[a.d.Transpose[a],
         			a.is.rxs],20
     	];
     	];
     	,(*pok=1*)
     	(* Print["radim sa transformisanim matricama"];*)
     	
     	
    If[vR<Dimensions[a][[1]], 	
     	vRight=N[a.is.rxs,20];
	vRes=N[LinearSolve[vH-Transpose[vG].vF.vG, Drop[vRight,vR]-Transpose[vG].vF.Take[vRight,vR]],20]; 
	Dlcc=N[vF.Take[vRight,vR]-vF.vG.vRes,20];
	
	Dlcc=Join[Dlcc,vRes];
	,
		  Dlcc=N[LinearSolve[a.d.Transpose[a],
         			a.is.rxs],20
     	];
     	];
	
];


    Dscc=N[-Transpose[a].Dlcc,20];
    Dxcc=N[-is.(rxs+Xmat.Dscc),20];

(* 9.Korak:    *)

    dx=Dxaff+Dxcc;  dl=Dlaff+Dlcc;   ds=Dsaff+Dscc;

(* 10. i 11.Korak:    *)

    AlfaPa=N[Min[0.99*resi2[x,dx],1],20];
    AlfaDa=N[Min[0.99*resi2[s,ds],1],20];

(* 12.Korak:      *)
  
    x=N[x+AlfaPa*dx,20]; l=N[l+AlfaDa*dl,20];  s=N[s+AlfaDa*ds,20];
 
 
    
(* Rezultat :     *)

Print["x.s= ",x.s," u koraku ",korak];	    



(* Azuriranje uslova za izlaz iz While petlje:   *)  
    rb=N[a.x-b,20];
    rc=N[Transpose[a].l+s-ce,20];
    korak++    
;
    If[x.s>x1.s1 && x1.s1<1,
    Print["Dosta je bilo!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!"];
          pom=Range[Length[permut1]];
          pom=Sort[pom,permut1[[#1]]<permut1[[#2]]&];
          x1= x1[[pom]];	  ce=ce2[[pom]];  
         (* Print["permut = ",permut," permut1= ",permut1];*)
    
          If[opcija==1,
              z=-(kor1+N[ce.x1,20]), z=kor1+N[ce.x1,20]	];
          Print["kor1= ",kor1];
         Print["zprimal= ",N[ce1.x1,20]];
    Print["zdual= ",N[b1.l1,20]];
  
          For[i=1, i<=Length[xzero],i++,
                x1=Insert[x1,0,xzero[[i]]];
          ];
          (*	Print[x1]; 	 Print["Permutacija: ",permut];
           Print["a = ",a];  Print["ce = ",ce];      Print["ce1 = ",ce1];*)
          Return[{N[z,20],Take[N[x1,20],k1]}];
    ];
  ];
(* End While *)

	(* Print["xzero = ",xzero];   
	   Print["korak  = ", korak" x.s = ",N[x.s,20]];  *)
      
  (*  x=x[[permut]]; ce=ce[[permut]]; *)
     pom=Range[Length[permut]];
    pom=Sort[pom,permut[[#1]]<permut[[#2]]&];
    x= x[[pom]];	  ce=ce[[pom]];  
    
  If[opcija==1,
       z=-(kor+N[ce.x,20]), z=kor+N[ce.x,20]	];
  Print["kor= ",kor];
  Print["zprimal= ",N[ce1.x,20]];
    Print["zdual= ",N[b.l,20]];
  For[i=1, i<=Length[xzero],i++,
       x=Insert[x,0,xzero[[i]]];
  ];
(*	Print[x]; 	(* Print["Permutacija: ",permut];*)
(* Print["a = ",a]; *)
Print["ce = ",ce];
Print["ce1 = ",ce1];*)
  Return[{N[z,20],Take[N[x,20],k1]}];
]

PrimalDual[
      3  x3 + 2  x4 + x5, {x1 + 2  x2 + x3 == 1000.02, 
        x1 + x2 + x4 == 1000.01, x1 - x2 + x5 == 999.99}, 10^-15, 40, 0, 
      0, 0, 0]

PrimalDual[.00000x1+.00000x2+3.00000x3+2.00000x4+1.00000x5+.00000x6+.00000x7+.00000x8+
2.00000x9+7.00000x10+4.00000x11+.00000x12+.00000x13+.00000x14+1.00000x15+
8.00000x16+11.00000x17+.00000x18,
(* NAME          HAGER *)
{1.00000x1+2.00000x2+1.00000x3+.00000x4+.00000x5-1.00000x6+.00000x7+.00000x8+
3.00000x9+81.00000x10+.00000x11+.00000x12+.00000x13+.00000x14+3.00000x15+
3.00000x16+21.00000x17+.00000x18==1000.02000,
1.00000x1+1.00000x2+.00000x3+1.00000x4+.00000x5-1.00000x6+.00000x7+.00000x8+
3.00000x9+.00000x10+2.00000x11+.00000x12+.00000x13+.00000x14+1.00000x15+
.00000x16-8.00000x17+.00000x18==1000.01000,
1.00000x1-1.00000x2+.00000x3+.00000x4+1.00000x5-1.00000x6+.00000x7+.00000x8+
3.00000x9+3.00000x10+.00000x11+.00000x12+.00000x13+.00000x14+3.00000x15+
4.00000x16+4.00000x17+.00000x18==999.99000,
1.00000x1+.00000x2+.00000x3+.00000x4+.00000x5-1.00000x6+.00000x7+.00000x8+
3.00000x9+.00000x10+9.00000x11+.00000x12+.00000x13+.00000x14+3.00000x15+
7.00000x16+1.00000x17+.00000x18>=.00000,
1.00000x1+.00000x2+.00000x3+.00000x4+.00000x5+.00000x6+.00000x7+.00000x8+
2.00000x9+5.00000x10+4.80000x11+.00000x12+.00000x13+.00000x14+1.00000x15+
3.00000x16+3.00000x17+.00000x18>=51100.00000,
6.00000x1+7.00000x2+2.00000x3+1.00000x4+3.00000x5-6.00000x6+.00000x7+.00000x8+
9.00000x9+.00000x10-4.00000x11+.00000x12+.00000x13+.00000x14+4.00000x15+
9.00000x16+2.00000x17+.00000x18>=6000.07000,
.00000x1+.00000x2+4.00000x3-7.00000x4+3.00000x5+.00000x6+1.00000x7+2.00000x8+
1.00000x9-4.00000x10+.00000x11-1.00000x12+.00000x13+.00000x14-9.00000x15+
4.00000x16+4.00000x17+.00000x18==1000.02000,
.00000x1+.00000x2-1.00000x3+0.00000x4+1.00000x5+.00000x6+2.00000x7+.00000x8+
1.00000x9+1.00000x10+1.00000x11-2.00000x12+.00000x13+.00000x14+9.00000x15+
8.00000x16+1.00000x17+.00000x18==2000.00000,
.00000x1+.00000x2-8.00000x3+9.00000x4-1.00000x5+.00000x6+.00000x7+2.00000x8+
.00000x9+1.00000x10-1.00000x11+.00000x12+.00000x13+.00000x14-7.00000x15+
6.00000x16+2.00000x17+.00000x18==.02000,
.00000x1+.00000x2+3.00000x3-5.00000x4+2.00000x5+.00000x6+1.00000x7+.00000x8+
5.00000x9+.00000x10+.00000x11-1.00000x12+.00000x13+.00000x14+2.00000x15+
8.00000x16+11.00000x17+.00000x18>=.00000,
.00000x1+.00000x2-5.00000x3+7.00000x4-2.00000x5+.00000x6+1.00000x7+.00000x8+
.00000x9+.00000x10-7.00000x11+.00000x12+.00000x13+.00000x14+3.00000x15+
8.00000x16+7.00000x17+.00000x18>=51100.00000,
.00000x1+.00000x2+9.00000x3-2.00000x4-7.00000x5+.00000x6+6.00000x7+7.00000x8+
5.00000x9+1.00000x10+4.00000x11-6.00000x12+.00000x13+.00000x14+1.00000x15+
1.90000x16+7.00000x17+.00000x18>=6000.07000,
.00000x1+.00000x2+6.00000x3-2.00000x4-4.00000x5+.00000x6+.00000x7+.00000x8-
9.00000x9+.00000x10+4.00000x11+.00000x12+1.00000x13+2.00000x14+1.00000x15-
8.00000x16+11.00000x17-1.00000x18==1000.02000,
.00000x1+.00000x2+8.00000x3-6.00000x4-2.00000x5+.00000x6+.00000x7+.00000x8+
.00000x9+.00000x10+.00000x11+.00000x12+1.00000x13+1.00000x14+3.00000x15+
1.00000x16+3.00000x17-1.00000x18==1000.01000,
.00000x1+.00000x2+2.00000x3-2.00000x4+0.00000x5+.00000x6+.00000x7+.00000x8+
3.00000x9+.00000x10+9.00000x11+.00000x12+3.00000x13+2.00000x14+1.00000x15+
1.00000x16+1.00000x17-3.00000x18==3000.02000,
.00000x1+.00000x2+1.00000x3+3.00000x4-4.00000x5+.00000x6+.00000x7+.00000x8+
2.00000x9+.00000x10+.00000x11+.00000x12+1.00000x13+.00000x14+6.00000x15+
.00000x16+43.00000x17-1.00000x18>=.00000,
.00000x1+.00000x2-4.00000x3+7.00000x4-3.00000x5+.00000x6+.00000x7+.00000x8+
6.00000x9+.00000x10+2.00000x11+.00000x12+1.00000x13+.00000x14+.00000x15+
2.00000x16+2.00000x17+.00000x18>=51100.00000,
.00000x1+.00000x2+6.00000x3-8.00000x4+2.00000x5+.00000x6+.00000x7+.00000x8+
4.00000x9+.00000x10+8.00000x11+.00000x12+6.00000x13+7.00000x14+9.00000x15+
1.00000x16+1.00000x17-6.00000x18>=6000.07000},10^-12,40,0,0,0,0]

PrimalDual[.00000x1+.00000x2-7.00000x3+4.00000x4+3.00000x5+.00000x6+.00000x7+8.00000x8+
1.00000x9-7.00000x10-3.00000x11+.00000x12+.00000x13+.00000x14-41.00000x15+
12.00000x16+11.00000x17+.00000x18,
(* NAME          HAGER1 *)
{1.00000x1+2.00000x2+1.00000x3+.00000x4+.00000x5-1.00000x6+.00000x7+.00000x8+
3.00000x9+81.00000x10+.00000x11+.00000x12+.00000x13+.00000x14+3.00000x15+
3.00000x16+21.00000x17+.00000x18==1000.02000,
1.00000x1+1.00000x2+.00000x3+1.00000x4+.00000x5-1.00000x6+.00000x7+.00000x8+
3.00000x9+.00000x10+2.00000x11+.00000x12+.00000x13+.00000x14+1.00000x15+
.00000x16-8.00000x17+.00000x18==1000.01000,
1.00000x1-1.00000x2+.00000x3+.00000x4+1.00000x5-1.00000x6+.00000x7+.00000x8+
3.00000x9+3.00000x10+.00000x11+.00000x12+.00000x13+.00000x14+3.00000x15+
4.00000x16+4.00000x17+.00000x18==999.99000,
1.00000x1+.00000x2+.00000x3+.00000x4+.00000x5-1.00000x6+.00000x7+.00000x8+
3.00000x9+.00000x10+9.00000x11+.00000x12+.00000x13+.00000x14+3.00000x15+
7.00000x16+1.00000x17+.00000x18>=.00000,
1.00000x1+.00000x2+.00000x3+.00000x4+.00000x5+.00000x6+.00000x7+.00000x8+
2.00000x9+5.00000x10+4.80000x11+.00000x12+.00000x13+.00000x14+1.00000x15+
3.00000x16+3.00000x17+.00000x18>=51100.00000,
6.00000x1+7.00000x2+2.00000x3+1.00000x4+3.00000x5-6.00000x6+.00000x7+.00000x8+
9.00000x9+.00000x10-4.00000x11+.00000x12+.00000x13+.00000x14+4.00000x15+
9.00000x16+2.00000x17+.00000x18>=6000.07000,
.00000x1+.00000x2+4.00000x3-7.00000x4+3.00000x5+.00000x6+1.00000x7+2.00000x8+
1.00000x9-4.00000x10+.00000x11-1.00000x12+.00000x13+.00000x14-9.00000x15+
4.00000x16+4.00000x17+.00000x18==1000.02000,
.00000x1+.00000x2-1.00000x3+0.00000x4+1.00000x5+.00000x6+2.00000x7+.00000x8+
1.00000x9+1.00000x10+1.00000x11-2.00000x12+.00000x13+.00000x14+9.00000x15+
8.00000x16+1.00000x17+.00000x18==2000.00000,
.00000x1+.00000x2-8.00000x3+9.00000x4-1.00000x5+.00000x6+.00000x7+2.00000x8+
.00000x9+1.00000x10-1.00000x11+.00000x12+.00000x13+.00000x14-7.00000x15+
6.00000x16+2.00000x17+.00000x18==.02000,
.00000x1+.00000x2+3.00000x3-5.00000x4+2.00000x5+.00000x6+1.00000x7+.00000x8+
5.00000x9+.00000x10+.00000x11-1.00000x12+.00000x13+.00000x14+2.00000x15+
8.00000x16+11.00000x17+.00000x18>=.00000,
.00000x1+.00000x2-5.00000x3+7.00000x4-2.00000x5+.00000x6+1.00000x7+.00000x8+
.00000x9+.00000x10-7.00000x11+.00000x12+.00000x13+.00000x14+3.00000x15+
8.00000x16+7.00000x17+.00000x18>=51100.00000,
.00000x1+.00000x2+9.00000x3-2.00000x4-7.00000x5+.00000x6+6.00000x7+7.00000x8+
5.00000x9+1.00000x10+4.00000x11-6.00000x12+.00000x13+.00000x14+1.00000x15+
1.90000x16+7.00000x17+.00000x18>=6000.07000,
.00000x1+.00000x2+6.00000x3-2.00000x4-4.00000x5+.00000x6+.00000x7+.00000x8-
9.00000x9+.00000x10+4.00000x11+.00000x12+1.00000x13+2.00000x14+1.00000x15-
8.00000x16+11.00000x17-1.00000x18==1000.02000,
.00000x1+.00000x2+8.00000x3-6.00000x4-2.00000x5+.00000x6+.00000x7+.00000x8+
.00000x9+.00000x10+.00000x11+.00000x12+1.00000x13+1.00000x14+3.00000x15+
1.00000x16+3.00000x17-1.00000x18==1000.01000,
.00000x1+.00000x2+2.00000x3-2.00000x4+0.00000x5+.00000x6+.00000x7+.00000x8+
3.00000x9+.00000x10+9.00000x11+.00000x12+3.00000x13+2.00000x14+1.00000x15+
1.00000x16+1.00000x17-3.00000x18==3000.02000,
.00000x1+.00000x2+1.00000x3+3.00000x4-4.00000x5+.00000x6+.00000x7+.00000x8+
2.00000x9+.00000x10+.00000x11+.00000x12+1.00000x13+.00000x14+6.00000x15+
.00000x16+43.00000x17-1.00000x18>=.00000,
.00000x1+.00000x2-4.00000x3+7.00000x4-3.00000x5+.00000x6+.00000x7+.00000x8+
6.00000x9+.00000x10+2.00000x11+.00000x12+1.00000x13+.00000x14+.00000x15+
2.00000x16+2.00000x17+.00000x18>=51100.00000,
.00000x1+.00000x2+6.00000x3-8.00000x4+2.00000x5+.00000x6+.00000x7+.00000x8+
4.00000x9+.00000x10+8.00000x11+.00000x12+6.00000x13+7.00000x14+9.00000x15+
1.00000x16+1.00000x17-6.00000x18>=6000.07000},10^-12,40,0,0,0,0]

PrimalDual[10.00000x1+20.00000x2-20.00000x3+40.00000x4+50.00000x5-10.00000x6+.00000x7+
0.00000x8+140.00000x9+880.00000x10+0.00000x11+.00000x12-10.00000x13-20.00000x14+
30.00000x15+190.00000x16+210.00000x17+10.00000x18,
(* NAME          HAGER2 *)
{1.00000x1+2.00000x2+1.00000x3+.00000x4+.00000x5-1.00000x6+.00000x7+.00000x8+
3.00000x9+81.00000x10+.00000x11+.00000x12+.00000x13+.00000x14+3.00000x15+
3.00000x16+21.00000x17+.00000x18==1000.02000,
1.00000x1+1.00000x2+.00000x3+1.00000x4+.00000x5-1.00000x6+.00000x7+.00000x8+
3.00000x9+.00000x10+2.00000x11+.00000x12+.00000x13+.00000x14+1.00000x15+
.00000x16-8.00000x17+.00000x18==1000.01000,
1.00000x1-1.00000x2+.00000x3+.00000x4+1.00000x5-1.00000x6+.00000x7+.00000x8+
3.00000x9+3.00000x10+.00000x11+.00000x12+.00000x13+.00000x14+3.00000x15+
4.00000x16+4.00000x17+.00000x18==999.99000,
1.00000x1+.00000x2+.00000x3+.00000x4+.00000x5-1.00000x6+.00000x7+.00000x8+
3.00000x9+.00000x10+9.00000x11+.00000x12+.00000x13+.00000x14+3.00000x15+
7.00000x16+1.00000x17+.00000x18>=.00000,
1.00000x1+.00000x2+.00000x3+.00000x4+.00000x5+.00000x6+.00000x7+.00000x8+
2.00000x9+5.00000x10+4.80000x11+.00000x12+.00000x13+.00000x14+1.00000x15+
3.00000x16+3.00000x17+.00000x18>=51100.00000,
6.00000x1+7.00000x2+2.00000x3+1.00000x4+3.00000x5-6.00000x6+.00000x7+.00000x8+
9.00000x9+.00000x10-4.00000x11+.00000x12+.00000x13+.00000x14+4.00000x15+
9.00000x16+2.00000x17+.00000x18>=6000.07000,
.00000x1+.00000x2+4.00000x3-7.00000x4+3.00000x5+.00000x6+1.00000x7+2.00000x8+
1.00000x9-4.00000x10+.00000x11-1.00000x12+.00000x13+.00000x14-9.00000x15+
4.00000x16+4.00000x17+.00000x18==1000.02000,
.00000x1+.00000x2-1.00000x3+0.00000x4+1.00000x5+.00000x6+2.00000x7+.00000x8+
1.00000x9+1.00000x10+1.00000x11-2.00000x12+.00000x13+.00000x14+9.00000x15+
8.00000x16+1.00000x17+.00000x18==2000.00000,
.00000x1+.00000x2-8.00000x3+9.00000x4-1.00000x5+.00000x6+.00000x7+2.00000x8+
.00000x9+1.00000x10-1.00000x11+.00000x12+.00000x13+.00000x14-7.00000x15+
6.00000x16+2.00000x17+.00000x18==.02000,
.00000x1+.00000x2+3.00000x3-5.00000x4+2.00000x5+.00000x6+1.00000x7+.00000x8+
5.00000x9+.00000x10+.00000x11-1.00000x12+.00000x13+.00000x14+2.00000x15+
8.00000x16+11.00000x17+.00000x18>=.00000,
.00000x1+.00000x2-5.00000x3+7.00000x4-2.00000x5+.00000x6+1.00000x7+.00000x8+
.00000x9+.00000x10-7.00000x11+.00000x12+.00000x13+.00000x14+3.00000x15+
8.00000x16+7.00000x17+.00000x18>=51100.00000,
.00000x1+.00000x2+9.00000x3-2.00000x4-7.00000x5+.00000x6+6.00000x7+7.00000x8+
5.00000x9+1.00000x10+4.00000x11-6.00000x12+.00000x13+.00000x14+1.00000x15+
1.90000x16+7.00000x17+.00000x18>=6000.07000,
.00000x1+.00000x2+6.00000x3-2.00000x4-4.00000x5+.00000x6+.00000x7+.00000x8-
9.00000x9+.00000x10+4.00000x11+.00000x12+1.00000x13+2.00000x14+1.00000x15-
8.00000x16+11.00000x17-1.00000x18==1000.02000,
.00000x1+.00000x2+8.00000x3-6.00000x4-2.00000x5+.00000x6+.00000x7+.00000x8+
.00000x9+.00000x10+.00000x11+.00000x12+1.00000x13+1.00000x14+3.00000x15+
1.00000x16+3.00000x17-1.00000x18==1000.01000,
.00000x1+.00000x2+2.00000x3-2.00000x4+0.00000x5+.00000x6+.00000x7+.00000x8+
3.00000x9+.00000x10+9.00000x11+.00000x12+3.00000x13+2.00000x14+1.00000x15+
1.00000x16+1.00000x17-3.00000x18==3000.02000,
.00000x1+.00000x2+1.00000x3+3.00000x4-4.00000x5+.00000x6+.00000x7+.00000x8+
2.00000x9+.00000x10+.00000x11+.00000x12+1.00000x13+.00000x14+6.00000x15+
.00000x16+43.00000x17-1.00000x18>=.00000,
.00000x1+.00000x2-4.00000x3+7.00000x4-3.00000x5+.00000x6+.00000x7+.00000x8+
6.00000x9+.00000x10+2.00000x11+.00000x12+1.00000x13+.00000x14+.00000x15+
2.00000x16+2.00000x17+.00000x18>=51100.00000,
.00000x1+.00000x2+6.00000x3-8.00000x4+2.00000x5+.00000x6+.00000x7+.00000x8+
.00000x9+.00000x10+8.00000x11+.00000x12+6.00000x13+7.00000x14+9.00000x15+
1.00000x16+1.00000x17-6.00000x18>=6000.07000},10^-12,40,0,0,0,0]

PrimalDual[-9800.00000x1+5976.00000x2+.00000x3+.00000x4+.00000x5+9992.00000x6+.00000x7+
.00000x8+.00000x9+3.00000x10+.00000x11+.00000x12+.00000x13+9989.00000x14+
992.00000x15-9978.00000x16+9687.00000x17+9993.00000x18-9800.00000x19+
9800.00000x20,(* NAME   07-20-02 *)
{-1.00000x1-4984.00000x2-2.00000x3-9733.00000x4-3993.00000x5+.00000x6-1.00000x7-
1.00000x8-8994.00000x9-9981.00000x10-9002.00000x11-3.00000x12-9971.00000x13+
1.00000x14-1.00000x15-9978.00000x16+9687.00000x17+9993.00000x18-1.00000x19+
1.00000x20==-8991.00000,-1.00000x1-4986.00000x2+.00000x3-9733.00000x4
-3993.00000x5-1.00000x6+.00000x7+.00000x8-8994.00000x9+9981.00000x10
-9002.00000x11-3.00000x12-9971.00000x13+
4892.00000x14-1.00000x15+9978.00000x16-9687.00000x17-9993.00000x18-1.00000x19+1.00000x20==-1.00000,
1.00000x1-1.00000x2-2.00000x3+.00000x4+.00000x5-1.00000x6-1.00000x7-1.00000x8+
.00000x9+9981.00000x10+.00000x11+.00000x12+.00000x13+4891.00000x14+.00000x15-
9978.00000x16+9687.00000x17+9993.00000x18+1.00000x19-1.00000x20==-8990.00000,
.00000x1-4984.00000x2-2.00000x3+.00000x4+.00000x5+.00000x6-1.00000x7-1.00000x8+
.00000x9-9981.00000x10+.00000x11+.00000x12+.00000x13+1.00000x14-1.00000x15+
.00000x16+.00000x17+.00000x18+.00000x19+.00000x20==-8990.00000,
.00000x1-4985.00000x2+2.00000x3+9733.00000x4+3993.00000x5+.00000x6+1.00000x7+
1.00000x8+8994.00000x9+.00000x10+9002.00000x11+3.00000x12+9971.00000x13+
1.00000x14-1.00000x15-9978.00000x16+9687.00000x17+9993.00000x18+.00000x19+
.00000x20==8991.00000,
-1.00000x1+4985.00000x2+.00000x3+9733.00000x4+3993.00000x5+1.00000x6+.00000x7+
.00000x8+8994.00000x9+.00000x10+9002.00000x11+3.00000x12+9971.00000x13-
4892.00000x14+1.00000x15+9978.00000x16-9687.00000x17-9993.00000x18-1.00000x19+
1.00000x20==1.00000,
-1.00000x1+4984.00000x2+.00000x3-9733.00000x4-3993.00000x5-1.00000x6+.00000x7+
.00000x8-8994.00000x9+9981.00000x10-9002.00000x11-3.00000x12-9971.00000x13+
4890.00000x14+1.00000x15+.00000x16+.00000x17+.00000x18-1.00000x19+1.00000x20==-
1.00000,
1.00000x1>=9728.00000,
1.00000x16>=8829.00000},10^-12,40,0,0,0,0]

PrimalDual[.00000x1+9652.00000x2+.00000x3+9953.00000x4+9774.00000x5+5.00000x6+.00000x7+
.00000x8+9089.00000x9+3.00000x10+.00000x11+8895.00000x12+9792.00000x13+
9883.00000x14+9873.00000x15+.00000x16+.00000x17+.00000x18+.00000x19+.00000x20,

(* NAME       10-20-06 *)

{-9081.00000x1-1051.00000x2-2.00000x3+1.00000x4+.00000x5-3.00000x6-1.00000x7-
3.00000x8+9981.00000x9+9782.00000x10-9329.00000x11+9918.00000x12+.00000x13+
81.00000x14+1.00000x15-1.00000x16-9881.00000x17-9785.00000x18-3.00000x19-
9997.00000x20==-9940.01000,
9081.00000x1+947.00000x2+2.00000x3-1.00000x4-997.00000x5+.00000x6+1.00000x7+
3.00000x8-9981.00000x9+9782.00000x10+9329.00000x11-9918.00000x12+.00000x13-
1003.00000x14+1.00000x15+1.00000x16+9881.00000x17+9785.00000x18+3.00000x19+
9997.00000x20==9940.01000,

-9081.00000x1-55.00000x2+2.00000x3+1.00000x4+.00000x5-3.00000x6+1.00000x7+
3.00000x8+9981.00000x9+9782.00000x10-9329.00000x11+9918.00000x12-1.00000x13+
88.00000x14-1.00000x15+1.00000x16-9881.00000x17-9785.00000x18-3.00000x19-
9997.00000x20==9939.99000,

.00000x1+1995.00000x2-2.00000x3-1.00000x4-997.00000x5-3.00000x6-1.00000x7-
3.00000x8-9981.00000x9+.00000x10+.00000x11-9918.00000x12-1.00000x13-
904.00000x14+.00000x15-1.00000x16+.00000x17+.00000x18+.00000x19+.00000x20==-
9940.00000,

.00000x1-993.00000x2-2.00000x3+.00000x4+997.00000x5-3.00000x6-1.00000x7-
3.00000x8-9981.00000x9+.00000x10+.00000x11+.00000x12+1.00000x13+1093.00000x14-
1.00000x15-1.00000x16+.00000x17+.00000x18+.00000x19+.00000x20==-9940.00000,
-9081.00000x1-941.00000x2-2.00000x3+.00000x4+.00000x5-3.00000x6-1.00000x7-
3.00000x8+.00000x9-9782.00000x10-9329.00000x11+.00000x12+1.00000x13+94.00000x14+
.00000x15-1.00000x16-9881.00000x17-9785.00000x18-3.00000x19-9997.00000x20==-
9940.01000,

-9081.00000x1-1992.00000x2-2.00000x3+1.00000x4-997.00000x5+.00000x6-1.00000x7-
3.00000x8-9981.00000x9+.00000x10-9329.00000x11-9918.00000x12+1.00000x13-
999.00000x14+.00000x15-1.00000x16-9881.00000x17-9785.00000x18-3.00000x19-
9997.00000x20==-9940.01000,

-9081.00000x1-996.00000x2+2.00000x3+.00000x4+.00000x5+3.00000x6+1.00000x7+
3.00000x8+.00000x9+.00000x10-9329.00000x11+.00000x12+1.00000x13-95.00000x14+
1.00000x15+1.00000x16-9881.00000x17-9785.00000x18-3.00000x19-
9997.00000x20==9939.99000,

.00000x1-1050.00000x2+2.00000x3+1.00000x4-997.00000x5+3.00000x6+1.00000x7+
3.00000x8+.00000x9+9782.00000x10+.00000x11+.00000x12+.00000x13-1092.00000x14-
1.00000x15+1.00000x16+.00000x17+.00000x18+.00000x19+.00000x20==9940.00000,

-9081.00000x1-1939.00000x2-2.00000x3+1.00000x4-997.00000x5+.00000x6-1.00000x7-
3.00000x8+9981.00000x9-9782.00000x10-9329.00000x11+9918.00000x12+1.00000x13-
996.00000x14-1.00000x15-1.00000x16-9881.00000x17-9785.00000x18-3.00000x19-
9997.00000x20==-9940.01000},10^-12,40,0,0,0,0]

PrimalDual[-9801.00000x1+9976.00000x2+.00000x3+9972.00000x4+3.00000x5+9992.00000x6+
.00000x7+.00000x8+.00000x9+8976.00000x10+.00000x11+9073.00000x12+.00000x13+
8789.00000x14+989.00000x15-9978.00000x16+9687.00000x17+9993.00000x18-
9801.00000x19+9801.00000x20,
(* NAME      10-20-11 *)
{-1.00000x1+4.00000x2-2.00000x3+1.00000x4+.00000x5-1.00000x6-1.00000x7-1.00000x8+
.00000x9+997.00000x10+.00000x11+9981.00000x12+.00000x13+997.00000x14+
9981.00000x15+9978.00000x16-9687.00000x17-9993.00000x18-1.00000x19+1.00000x20==-
8990.00000,
1.00000x1+993.00000x2+2.00000x3-1.00000x4-9918.00000x5+.00000x6+1.00000x7+
1.00000x8+.00000x9+997.00000x10+.00000x11-9981.00000x12+.00000x13+1001.00000x14+
9981.00000x15-9978.00000x16+9687.00000x17+9993.00000x18+1.00000x19-
1.00000x20==8990.00000,
-1.00000x1+4.00000x2+2.00000x3+1.00000x4+.00000x5-1.00000x6+1.00000x7+1.00000x8-
8994.00000x9+997.00000x10-9002.00000x11+9981.00000x12-9971.00000x13+
999.00000x14-9981.00000x15+9978.00000x16-9687.00000x17-9993.00000x18-1.00000x19+
1.00000x20==8989.00000,
1.00000x1+1993.00000x2-2.00000x3-1.00000x4-9918.00000x5-1.00000x6-1.00000x7-
1.00000x8-8994.00000x9+.00000x10-9002.00000x11-9981.00000x12-9971.00000x13+
4.00000x14+.00000x15+.00000x16+.00000x17+.00000x18+1.00000x19-1.00000x20==-
8991.00000,
1.00000x1+999.00000x2-2.00000x3+.00000x4+9918.00000x5-1.00000x6-1.00000x7-
1.00000x8+8994.00000x9+.00000x10+9002.00000x11+.00000x12+9971.00000x13+
1.00000x14-9981.00000x15+.00000x16+.00000x17+.00000x18+1.00000x19-1.00000x20==-
8989.00000,
.00000x1+1000.00000x2-2.00000x3+.00000x4+.00000x5-1.00000x6-1.00000x7-1.00000x8+
8994.00000x9-997.00000x10+9002.00000x11+.00000x12+9971.00000x13-998.00000x14+
.00000x15+9978.00000x16-9687.00000x17-9993.00000x18+.00000x19+.00000x20==-
8989.00000,
1.00000x1-994.00000x2-2.00000x3+1.00000x4-9918.00000x5+.00000x6-1.00000x7-
1.00000x8+8994.00000x9+.00000x10+9002.00000x11-9981.00000x12+9971.00000x13+
1.00000x14+.00000x15+9978.00000x16-9687.00000x17-9993.00000x18+1.00000x19-
1.00000x20==-8989.00000,
.00000x1-999.00000x2+2.00000x3+.00000x4+.00000x5+1.00000x6+1.00000x7+1.00000x8+
8994.00000x9+.00000x10+9002.00000x11+.00000x12+9971.00000x13-2.00000x14+
9981.00000x15+9978.00000x16-9687.00000x17-9993.00000x18+.00000x19+
.00000x20==8991.00000,
.00000x1-1994.00000x2+2.00000x3+1.00000x4-9918.00000x5+1.00000x6+1.00000x7+
1.00000x8+.00000x9+997.00000x10+.00000x11+.00000x12+.00000x13+999.00000x14-
9981.00000x15+.00000x16+.00000x17+.00000x18+.00000x19+.00000x20==8990.00000,
-1.00000x1-993.00000x2-2.00000x3+1.00000x4-9918.00000x5+.00000x6-1.00000x7-
1.00000x8+8994.00000x9-997.00000x10+9002.00000x11+9981.00000x12+9971.00000x13-
999.00000x14-9981.00000x15+9978.00000x16-9687.00000x17-9993.00000x18-1.00000x19+
1.00000x20==-8989.00000},10^-12,40,0,0,0,0]

PrimalDual[.00000x1+9976.00000x2+.00000x3+9972.00000x4+3.00000x5+9992.00000x6+.00000x7+
.00000x8+.00000x9+8976.00000x10+.00000x11+9073.00000x12+.00000x13+8789.00000x14+
989.00000x15+.00000x16+.00000x17+.00000x18+.00000x19+.00000x20,
(* NAME  10-20-12 *)
{-1.00000x1+4.00000x2-2.00000x3+1.00000x4+.00000x5-1.00000x6-1.00000x7-1.00000x8+
.00000x9+997.00000x10+.00000x11+9981.00000x12+.00000x13+997.00000x14+
9981.00000x15+9978.00000x16-9687.00000x17-9993.00000x18-1.00000x19+1.00000x20==-
8990.00000,
1.00000x1+993.00000x2+2.00000x3-1.00000x4-9918.00000x5+.00000x6+1.00000x7+
1.00000x8+.00000x9+997.00000x10+.00000x11-9981.00000x12+.00000x13+1001.00000x14+
9981.00000x15-9978.00000x16+9687.00000x17+9993.00000x18+1.00000x19-
1.00000x20==8990.00000,
-1.00000x1+4.00000x2+2.00000x3+1.00000x4+.00000x5-1.00000x6+1.00000x7+1.00000x8-
8994.00000x9+997.00000x10-9002.00000x11+9981.00000x12-9971.00000x13+
999.00000x14-9981.00000x15+9978.00000x16-9687.00000x17-9993.00000x18-1.00000x19+
1.00000x20==8989.00000,
1.00000x1+1993.00000x2-2.00000x3-1.00000x4-9918.00000x5-1.00000x6-1.00000x7-
1.00000x8-8994.00000x9+.00000x10-9002.00000x11-9981.00000x12-9971.00000x13+
4.00000x14+.00000x15+.00000x16+.00000x17+.00000x18+1.00000x19-1.00000x20==-
8991.00000,
1.00000x1+999.00000x2-2.00000x3+.00000x4+9918.00000x5-1.00000x6-1.00000x7-
1.00000x8+8994.00000x9+.00000x10+9002.00000x11+.00000x12+9971.00000x13+
1.00000x14-9981.00000x15+.00000x16+.00000x17+.00000x18+1.00000x19-1.00000x20==-
8989.00000,
.00000x1+1000.00000x2-2.00000x3+.00000x4+.00000x5-1.00000x6-1.00000x7-1.00000x8+
8994.00000x9-997.00000x10+9002.00000x11+.00000x12+9971.00000x13-998.00000x14+
.00000x15+9978.00000x16-9687.00000x17-9993.00000x18+.00000x19+.00000x20==-8989.00000,
1.00000x1-994.00000x2-2.00000x3+1.00000x4-9918.00000x5+.00000x6-1.00000x7-
1.00000x8+8994.00000x9+.00000x10+9002.00000x11-9981.00000x12+9971.00000x13+
1.00000x14+.00000x15+9978.00000x16-9687.00000x17-9993.00000x18+1.00000x19-
1.00000x20==-8989.00000,
.00000x1-999.00000x2+2.00000x3+.00000x4+.00000x5+1.00000x6+1.00000x7+1.00000x8+
8994.00000x9+.00000x10+9002.00000x11+.00000x12+9971.00000x13-2.00000x14+
9981.00000x15+9978.00000x16-9687.00000x17-9993.00000x18+.00000x19+
.00000x20==8991.00000,
.00000x1-1994.00000x2+2.00000x3+1.00000x4-9918.00000x5+1.00000x6+1.00000x7+
1.00000x8+.00000x9+997.00000x10+.00000x11+.00000x12+.00000x13+999.00000x14-
9981.00000x15+.00000x16+.00000x17+.00000x18+.00000x19+.00000x20==8990.00000,
-1.00000x1-993.00000x2-2.00000x3+1.00000x4-9918.00000x5+.00000x6-1.00000x7-
1.00000x8+8994.00000x9-997.00000x10+9002.00000x11+9981.00000x12+9971.00000x13-
999.00000x14-9981.00000x15+9978.00000x16-9687.00000x17-9993.00000x18-1.00000x19+
1.00000x20==-8989.00000,1.00000x1>=9786.00000,1.00000x16>=9439.00000},10^-12,40,0,0,0,0]

PrimalDual[.00000x1+9976.00000x2+.00000x3+9972.00000x4+3.00000x5+9992.00000x6+.00000x7+
.00000x8+.00000x9+8976.00000x10+.00000x11+9073.00000x12+.00000x13+8789.00000x14+
989.00000x15+.00000x16+.00000x17+.00000x18+.00000x19+.00000x20,
(* NAME 10-20-13 *)
{-1.00000x1+4.00000x2-2.00000x3+1.00000x4+.00000x5-1.00000x6-1.00000x7-1.00000x8+
.00000x9+997.00000x10+.00000x11+9981.00000x12+.00000x13+997.00000x14+
9981.00000x15+9978.00000x16-9687.00000x17-9993.00000x18-1.00000x19+1.00000x20==-
8990.00000,
1.00000x1+993.00000x2+2.00000x3-1.00000x4-9918.00000x5+.00000x6+1.00000x7+
1.00000x8+.00000x9+997.00000x10+.00000x11-9981.00000x12+.00000x13+1001.00000x14+
9981.00000x15-9978.00000x16+9687.00000x17+9993.00000x18+1.00000x19-
1.00000x20==8990.00000,
-1.00000x1+4.00000x2+2.00000x3+1.00000x4+.00000x5-1.00000x6+1.00000x7+1.00000x8-
8994.00000x9+997.00000x10-9002.00000x11+9981.00000x12-9971.00000x13+
999.00000x14-9981.00000x15+9978.00000x16-9687.00000x17-9993.00000x18-1.00000x19+
1.00000x20==8989.00000,
1.00000x1+1993.00000x2-2.00000x3-1.00000x4-9918.00000x5-1.00000x6-1.00000x7-
1.00000x8-8994.00000x9+.00000x10-9002.00000x11-9981.00000x12-9971.00000x13+
4.00000x14+.00000x15+.00000x16+.00000x17+.00000x18+1.00000x19-1.00000x20==-
8991.00000,
1.00000x1+999.00000x2-2.00000x3+.00000x4+9918.00000x5-1.00000x6-1.00000x7-
1.00000x8+8994.00000x9+.00000x10+9002.00000x11+.00000x12+9971.00000x13+
1.00000x14-9981.00000x15+.00000x16+.00000x17+.00000x18+1.00000x19-1.00000x20==-
8989.00000,
.00000x1+1000.00000x2-2.00000x3+.00000x4+.00000x5-1.00000x6-1.00000x7-1.00000x8+
8994.00000x9-997.00000x10+9002.00000x11+.00000x12+9971.00000x13-998.00000x14+
.00000x15+9978.00000x16-9687.00000x17-9993.00000x18+.00000x19+.00000x20==-
8989.00000,
1.00000x1-994.00000x2-2.00000x3+1.00000x4-9918.00000x5+.00000x6-1.00000x7-
1.00000x8+8994.00000x9+.00000x10+9002.00000x11-9981.00000x12+9971.00000x13+
1.00000x14+.00000x15+9978.00000x16-9687.00000x17-9993.00000x18+1.00000x19-
1.00000x20==-8989.00000,
.00000x1-999.00000x2+2.00000x3+.00000x4+.00000x5+1.00000x6+1.00000x7+1.00000x8+
8994.00000x9+.00000x10+9002.00000x11+.00000x12+9971.00000x13-2.00000x14+
9981.00000x15+9978.00000x16-9687.00000x17-9993.00000x18+.00000x19+
.00000x20==8991.00000,
.00000x1-1994.00000x2+2.00000x3+1.00000x4-9918.00000x5+1.00000x6+1.00000x7+
1.00000x8+.00000x9+997.00000x10+.00000x11+.00000x12+.00000x13+999.00000x14-
9981.00000x15+.00000x16+.00000x17+.00000x18+.00000x19+.00000x20==8990.00000,
-1.00000x1-993.00000x2-2.00000x3+1.00000x4-9918.00000x5+.00000x6-1.00000x7-
1.00000x8+8994.00000x9-997.00000x10+9002.00000x11+9981.00000x12+9971.00000x13-
999.00000x14-9981.00000x15+9978.00000x16-9687.00000x17-9993.00000x18-1.00000x19+
1.00000x20==-8989.00000,
1.00000x1>=9758.00000,
1.00000x16>=9297.00000},10^-12,40,0,0,0,0]

PrimalDual[9899.00000x1+8.00000x2+9801.00000x3+.00000x4+.00000x5+9774.00000x6+
.00000x7+9949.00000x8+9953.00000x9+.00000x10+.00000x11+.00000x12+
.00000x13+.00000x14+9792.00000x15+.00000x16+.00000x17+.00000x18+
.00000x19+.00000x20+x21+9652.00000x22+5.00000x23+9912.00000x24+
9883.00000x25+9889.00000x26+9073.00000x27+9787.00000x28+.00000x29+
.00000x30,
(*15-30-03*)
{9918.00000x1+9981.00000x2+x3+.00000x4-2.00000x5+997.00000x6+.00000x7+
x8+x9+.00000x10-x11+.00000x12+.00000x13+.00000x14+x15+.00000x16+
.00000x17-3.00000x18+.00000x19-2.00000x20+.00000x21+.00000x22+
.00000x23-9981.00000x24-997.00000x25+1993.00000x26-9981.00000x27-
3986.00000x28+.00000x29+.00000x30==-9971,

9918.00000x1+9981.00000x2+x3+9881.00000x4-2.00000x5+.00000x6+
8198.00000x7+x8-x9+2.00000x10-x11+9983.00000x12+9898.00000x13+
9329.00000x14+.00000x15+9997.00000x16+8981.00000x17-3.00000x18+
9081.00000x19-2.00000x20+9918.00000x21-x22-9918.00000x23+
9981.00000x24+997.00000x25-1001.00000x26+.00000x27+3.00000x28+
9785.00000x29+8977.00000x30==-9970,

9918.00000x1+.00000x2+x3+.00000x4+2.00000x5+997.00000x6+.00000x7-x8-
x9+.00000x10+x11+.00000x12+.00000x13+.00000x14-x15+.00000x16+.00000x17+
3.00000x18+.00000x19+2.00000x20+.00000x21+.00000x22-9918.00000x23+
9981.00000x24-997.00000x25+1997.00000x26+9981.00000x27+1998.00000x28+
.00000x29+.00000x30==9971,

9918.00000x1+9981.00000x2+x3+9881.00000x4+2.00000x5-997.00000x6+
8198.00000x7-x8+x9+2.00000x10+x11+9983.00000x12+9898.00000x13+
9329.00000x14-x15+9997.00000x16+8981.00000x17+3.00000x18+
9081.00000x19+2.00000x20-9918.00000x21+.00000x22+9918.00000x23-
9981.00000x24-997.00000x25-3.00000x26+9981.00000x27+2.00000x28+
9785.00000x29+8977.00000x30==9972,

-9918.00000x1+.00000x2+x3+9881.00000x4+2.00000x5+.00000x6+
8198.00000x7-x8+x9+2.00000x10+x11+9983.00000x12+9898.00000x13+
9329.00000x14+.00000x15+9997.00000x16+8981.00000x17+3.00000x18+
9081.00000x19+2.00000x20+9918.00000x21+x22-9918.00000x23+
9981.00000x24-997.00000x25+996.00000x26+.00000x27-1991.00000x28+
9785.00000x29+8977.00000x30==9972,

9918.00000x1+9981.00000x2-x3+.00000x4+2.00000x5+.00000x6+.00000x7+x8+
.00000x9+.00000x10+x11+.00000x12+.00000x13+.00000x14-x15+.00000x16+
.00000x17+3.00000x18+.00000x19+2.00000x20+.00000x21-x22+.00000x23+
.00000x24+.00000x25+x26-9981.00000x27+1987.00000x28+.00000x29+
.00000x30==9971,

.00000x1-9981.00000x2+.00000x3-9881.00000x4+2.00000x5+.00000x6-
8198.00000x7+.00000x8+x9-2.00000x10+x11-9983.00000x12-9898.00000x13-
9329.00000x14+.00000x15-9997.00000x16-8981.00000x17+3.00000x18-
9081.00000x19+2.00000x20-9918.00000x21+.00000x22+.00000x23+.00000x24-
997.00000x25+998.00000x26+9981.00000x27-998.00000x28-9785.00000x29-
8977.00000x30==9970,

.00000x1-9981.00000x2+.00000x3+.00000x4+2.00000x5-997.00000x6+
.00000x7-x8+x9+.00000x10+x11+.00000x12+.00000x13+.00000x14+x15+
.00000x16+.00000x17+3.00000x18+.00000x19+2.00000x20+.00000x21+
.00000x22-9918.00000x23+.00000x24-997.00000x25-x26+9981.00000x27-
992.00000x28+.00000x29+.00000x30==9971,

-9918.00000x1+9981.00000x2-x3+.00000x4-2.00000x5-997.00000x6+.00000x7+
x8+x9+.00000x10-x11+.00000x12+.00000x13+.00000x14+x15+.00000x16+
.00000x17-3.00000x18+.00000x19-2.00000x20-9918.00000x21-x22+
9918.00000x23+9981.00000x24+997.00000x25-2000.00000x26+9981.00000x27-
1000.00000x28+.00000x29+.00000x30==-9971,

9918.00000x1-9981.00000x2+.00000x3+9881.00000x4-2.00000x5-997.00000x6+
8198.00000x7+.00000x8+x9+2.00000x10-x11+9983.00000x12+9898.00000x13+
9329.00000x14-x15+9997.00000x16+8981.00000x17-3.00000x18+
9081.00000x19-2.00000x20+.00000x21-x22+.00000x23+9981.00000x24+
.00000x25-999.00000x26+.00000x27+994.00000x28+9785.00000x29+
8977.00000x30==-9970,

.00000x1-9981.00000x2+.00000x3+9881.00000x4+2.00000x5+.00000x6+
8198.00000x7+.00000x8-x9+2.00000x10+x11+9983.00000x12+9898.00000x13+
9329.00000x14+x15+9997.00000x16+8981.00000x17+3.00000x18+
9081.00000x19+2.00000x20+.00000x21+x22+.00000x23+.00000x24+.00000x25+
x26-9981.00000x27-993.00000x28+9785.00000x29+8977.00000x30==9972,

9918.00000x1-9981.00000x2+x3+9881.00000x4+2.00000x5+997.00000x6+
8198.00000x7+.00000x8-x9+2.00000x10+x11+9983.00000x12+9898.00000x13+
9329.00000x14+.00000x15+9997.00000x16+8981.00000x17+3.00000x18+
9081.00000x19+2.00000x20+9918.00000x21+.00000x22+9918.00000x23+
9981.00000x24+.00000x25+996.00000x26+.00000x27+4.00000x28+
9785.00000x29+8977.00000x30==9972,

9918.00000x1-9981.00000x2+.00000x3-9881.00000x4-2.00000x5-997.00000x6-
8198.00000x7-x8+.00000x9-2.00000x10-x11-9983.00000x12-9898.00000x13-
9329.00000x14+.00000x15-9997.00000x16-8981.00000x17-3.00000x18-
9081.00000x19-2.00000x20-9918.00000x21-x22-9918.00000x23+.00000x24+
997.00000x25-1994.00000x26+9981.00000x27+1997.00000x28-9785.00000x29-
8977.00000x30==-9972,

-9918.00000x1+.00000x2+x3-9881.00000x4+2.00000x5+.00000x6-
8198.00000x7+.00000x8+.00000x9-2.00000x10+x11-9983.00000x12-
9898.00000x13-9329.00000x14-x15-9997.00000x16-8981.00000x17+
3.00000x18-9081.00000x19+2.00000x20-9918.00000x21+x22+9918.00000x23+
.00000x24+997.00000x25-997.00000x26-9981.00000x27-999.00000x28-
9785.00000x29-8977.00000x30==9970,

9918.00000x1-9981.00000x2+x3+9881.00000x4-2.00000x5+.00000x6+
8198.00000x7+x8+.00000x9+2.00000x10-x11+9983.00000x12+9898.00000x13+
9329.00000x14+x15+9997.00000x16+8981.00000x17-3.00000x18+
9081.00000x19-2.00000x20-9918.00000x21+.00000x22+9918.00000x23+
9981.00000x24+.00000x25-4.00000x26+.00000x27-2987.00000x28+
9785.00000x29+8977.00000x30==-9970},10^-12,40,0,0,0,0]

PrimalDual[9912.00000x1+9953.00000x2+9883.00000x3+9777.00000x4+.00000x5+5.00000x6-
9901.00000x7+9774.00000x8+9792.00000x9+.00000x10+.00000x11-9893.00000x12-
9893.00000x13+.00000x14+.00000x15+9893.00000x16-9897.00000x17+.00000x18+
9893.00000x19+.00000x20+8.00000x21+9949.00000x22+73.00000x23+9652.00000x24+
1.00000x25+9899.00000x26+.00000x27+9801.00000x28+9697.00000x29+.00000x30,
(* NAME    15-30-04 *)
{9981.00000x1+1.00000x2+997.00000x3+.00000x4-2.00000x5+9918.00000x6+.00000x7+
997.00000x8+1.00000x9+8981.00000x10-1.00000x11+1.00000x12+1.00000x13+
8198.00000x14+9081.00000x15-1.00000x16+.00000x17-3.00000x18-1.00000x19-
2.00000x20+.00000x21+.00000x22+.00000x23-1.00000x24-9918.00000x25-1.00000x26+
9785.00000x27-997.00000x28+.00000x29+9881.00000x30==-9970.00000,

9981.00000x1+1.00000x2+997.00000x3+9777.00000x4-2.00000x5+.00000x6-9901.00000x7+
997.00000x8-1.00000x9+.00000x10-1.00000x11+.00000x12+.00000x13+.00000x14+
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1.00000x22-9981.00000x23+1.00000x24+9918.00000x25-1.00000x26+.00000x27-
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9981.00000x1+.00000x2+997.00000x3+.00000x4+2.00000x5+9918.00000x6+.00000x7-
997.00000x8-1.00000x9-8981.00000x10+1.00000x11-1.00000x12-1.00000x13-
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2.00000x20+.00000x21+.00000x22-9981.00000x23+1.00000x24-9918.00000x25-
1997.00000x26-9785.00000x27-4.00000x28+.00000x29-9881.00000x30==9970.00000,
9981.00000x1+1.00000x2+997.00000x3+9777.00000x4+2.00000x5-9918.00000x6-
9901.00000x7-997.00000x8+1.00000x9-8981.00000x10+1.00000x11-1.00000x12-
1.00000x13-8198.00000x14-9081.00000x15+1.00000x16-9897.00000x17+3.00000x18+
1.00000x19+2.00000x20-9981.00000x21+.00000x22+9981.00000x23-1.00000x24-
9918.00000x25-1997.00000x26-9785.00000x27-995.00000x28+9697.00000x29-
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997.00000x8+.00000x9-8981.00000x10+1.00000x11+1.00000x12+1.00000x13-
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2.00000x20+.00000x21-1.00000x22+.00000x23+.00000x24+.00000x25+1996.00000x26-
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5.00000x28-9697.00000x29+.00000x30==9971.00000,
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997.00000x8+1.00000x9+8981.00000x10+1.00000x11-1.00000x12-1.00000x13+
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996.00000x26+9785.00000x27+6.00000x28+.00000x29+9881.00000x30==9972.00000,
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997.00000x8+1.00000x9+8981.00000x10-1.00000x11-1.00000x12-1.00000x13+
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1996.00000x26+9785.00000x27-1992.00000x28+.00000x29+9881.00000x30==-9970.00000,
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2.00000x20+.00000x21-1.00000x22+.00000x23+1.00000x24+.00000x25+.00000x26-
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994.00000x28+9697.00000x29+9881.00000x30==9972.00000,
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9981.00000x21+.00000x22+9981.00000x23+1.00000x24+.00000x25-1001.00000x26+
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9785.00000x27-1000.00000x28-9697.00000x29-9881.00000x30==9970.00000,
9981.00000x1-1.00000x2+997.00000x3+9777.00000x4-2.00000x5+.00000x6-9901.00000x7+
997.00000x8+.00000x9+8981.00000x10-1.00000x11+.00000x12+.00000x13+8198.00000x14+
9081.00000x15+.00000x16-9897.00000x17-3.00000x18+.00000x19-2.00000x20-
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9785.00000x27-1.00000x28+9697.00000x29+9881.00000x30==-9970.00000,
1.00000x7>=9823.00000},10^-12,40,0,0,0,0]

PrimalDual[9912.00000x1+9953.00000x2+9883.00000x3+.00000x4+.00000x5+5.00000x6+.00000x7+

9774.00000x8+9792.00000x9+.00000x10+.00000x11+.00000x12+.00000x13+.00000x14+

.00000x15+.00000x16+.00000x17+.00000x18+.00000x19+.00000x20+8.00000x21+

9949.00000x22+73.00000x23+9652.00000x24+1.00000x25+9899.00000x26+.00000x27+

9801.00000x28+.00000x29+.00000x30,
(* NAME  15-30-06 *)
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1.00000x22-9981.00000x23+1.00000x24+9918.00000x25-1.00000x26+.00000x27-

6.00000x28+9697.00000x29+.00000x30==-9971.00000,

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997.00000x8-1.00000x9-8981.00000x10+1.00000x11-1.00000x12-1.00000x13-

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9901.00000x7-997.00000x8+1.00000x9-8981.00000x10+1.00000x11-1.00000x12-

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1.00000x19+2.00000x20-9981.00000x21+.00000x22+9981.00000x23-1.00000x24-

9918.00000x25-1997.00000x26-9785.00000x27-995.00000x28+9697.00000x29-

9881.00000x30==9970.00000,

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997.00000x8+1.00000x9+.00000x10+1.00000x11+.00000x12+.00000x13+.00000x14+

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9981.00000x21+1.00000x22+9981.00000x23+.00000x24+9918.00000x25-999.00000x26-

9785.00000x27-1000.00000x28-9697.00000x29-9881.00000x30==9970.00000,

9981.00000x1-1.00000x2+997.00000x3+9777.00000x4-2.00000x5+.00000x6-9901.00000x7+

997.00000x8+.00000x9+8981.00000x10-1.00000x11+.00000x12+.00000x13+8198.00000x14+

9081.00000x15+.00000x16-9897.00000x17-3.00000x18+.00000x19-2.00000x20-

9981.00000x21+.00000x22+9981.00000x23+1.00000x24+.00000x25+.00000x26+

9785.00000x27-1.00000x28+9697.00000x29+9881.00000x30==-9970.00000,

1.00000x7>=9823.00000},10^-12,40,0,0,0,0]

PrimalDual[9912.00000x1+9953.00000x2+9883.00000x3+9777.00000x4+.00000x5+5.00000x6-

9901.00000x7+9774.00000x8+9792.00000x9+.00000x10+.00000x11-9894.00000x12-

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9894.00000x19+.00000x20+8.00000x21+9949.00000x22+73.00000x23+9652.00000x24+

1.00000x25+9899.00000x26+.00000x27+9801.00000x28+9697.00000x29+.00000x30,



(* NAME    15-30-07 *)



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9881.00000x30==9970.00000,

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994.00000x28+9697.00000x29+9881.00000x30==9972.00000,

9981.00000x1-1.00000x2+997.00000x3+9777.00000x4+2.00000x5+9918.00000x6-

9901.00000x7+.00000x8-1.00000x9+.00000x10+1.00000x11+.00000x12+.00000x13+

.00000x14+.00000x15+.00000x16-9897.00000x17+3.00000x18+.00000x19+2.00000x20+

9981.00000x21+.00000x22+9981.00000x23+1.00000x24+.00000x25-1001.00000x26+

.00000x27+994.00000x28+9697.00000x29+.00000x30==9971.00000,

9981.00000x1-1.00000x2+.00000x3-9777.00000x4-2.00000x5-9918.00000x6+

9901.00000x7-997.00000x8+.00000x9+.00000x10-1.00000x11-1.00000x12-1.00000x13+

.00000x14+.00000x15+1.00000x16+9897.00000x17-3.00000x18+1.00000x19-2.00000x20-

9981.00000x21-1.00000x22-9981.00000x23+.00000x24+9918.00000x25-996.00000x26+

.00000x27+1999.00000x28-9697.00000x29+.00000x30==-9971.00000,

-9981.00000x1+.00000x2+997.00000x3-9777.00000x4+2.00000x5+.00000x6+9901.00000x7+

.00000x8+.00000x9-8981.00000x10+1.00000x11+1.00000x12+1.00000x13-8198.00000x14-

9081.00000x15-1.00000x16+9897.00000x17+3.00000x18-1.00000x19+2.00000x20-

9981.00000x21+1.00000x22+9981.00000x23+.00000x24+9918.00000x25-999.00000x26-

9785.00000x27-1000.00000x28-9697.00000x29-9881.00000x30==9970.00000,

9981.00000x1-1.00000x2+997.00000x3+9777.00000x4-2.00000x5+.00000x6-9901.00000x7+

997.00000x8+.00000x9+8981.00000x10-1.00000x11+.00000x12+.00000x13+8198.00000x14+

9081.00000x15+.00000x16-9897.00000x17-3.00000x18+.00000x19-2.00000x20-

9981.00000x21+.00000x22+9981.00000x23+1.00000x24+.00000x25+.00000x26+

9785.00000x27-1.00000x28+9697.00000x29+9881.00000x30==-9970.00000,

1.00000x7>=9812.00000,

1.00000x12>=9793.00000},10^-12,40,0,0,0,0]

PrimalDual[.00000x1+.00000x2+.00000x3+.00000x4+.00000x5+9779.00000x6+783.00000x7+

9783.00000x8+.00000x9+9783.00000x10-9923.00000x11-9897.00000x12+9895.00000x13-

9783.00000x14+781.00000x15+.00000x16+9783.00000x17+.00000x18+9811.00000x19+

9982.00000x20-9893.00000x21+.00000x22+.00000x23+.00000x24+.00000x25+

9974.00000x26+83.00000x27-9783.00000x28+.00000x29+9899.00000x30+.00000x31+

.00000x32+893.00000x33+9783.00000x34+.00000x35+9690.00000x36+.00000x37+

.00000x38+.00000x39+.00000x40+106.00000x41+.00000x42+.00000x43+.00000x44+

.00000x45+.00000x46+.00000x47+.00000x48+.00000x49+.00000x50-9783.00000x51+

9897.00000x52+.00000x53+.00000x54-9783.00000x55+9001.00000x56+.00000x57+

.00000x58+9897.00000x59+.00000x60,



(* NAME  15-60-09 *)



{7882.00000x1+9113.00000x2+9384.00000x3+8447.00000x4+9035.00000x5+.00000x6+

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1.00000x51-9993.00000x52-1.00000x53+9873.00000x54+1.00000x55+1.00000x56+

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1.00000x56+.00000x57+.00000x58+9002.00000x59+.00000x60==-9998.00000,

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9296.00000x39+1.00000x40+9909.00000x41+4.00000x42-1.00000x43-9.00000x44-

1.00000x45-7901.00000x46-81.00000x47-454.00000x48-9111.00000x49-9903.00000x50-

1.00000x51+9993.00000x52+1.00000x53-9873.00000x54-1.00000x55+1.00000x56-

300.00000x57-8881.00000x58-9002.00000x59-8992.00000x60==9997.00000,

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1.00000x7+1.00000x8-2.00000x9+1.00000x10-9923.00000x11-9897.00000x12+1.00000x13-

1.00000x14+9600.00000x15-8229.00000x16-1001.00000x17-9234.00000x18+

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8505.00000x25+9974.00000x26-1.00000x27-1.00000x28-8999.00000x29+1.00000x30+

2.00000x31-33.00000x32+9991.00000x33+1.00000x34-9439.00000x35-2.00000x36-

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1.00000x43-9.00000x44-1.00000x45-7901.00000x46-81.00000x47-454.00000x48-

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1.00000x55+1.00000x56-300.00000x57-8881.00000x58-9002.00000x59-

8992.00000x60==9997.00000,

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.00000x9+.00000x10-9923.00000x11-9897.00000x12+.00000x13+.00000x14-

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.00000x49+.00000x50+.00000x51+9993.00000x52+1.00000x53+.00000x54+.00000x55+

1.00000x56+.00000x57+.00000x58-9002.00000x59+.00000x60==9998.00000,

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1.00000x14+9600.00000x15-8229.00000x16+3.00000x17-9234.00000x18+.00000x19-

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.00000x26+.00000x27+1.00000x28-8999.00000x29+.00000x30+2.00000x31-33.00000x32+

.00000x33-1.00000x34-9439.00000x35+2.00000x36-8347.00000x37-9549.00000x38-

9296.00000x39+1.00000x40+.00000x41+4.00000x42-1.00000x43-9.00000x44-1.00000x45-

7901.00000x46-81.00000x47-454.00000x48-9111.00000x49-9903.00000x50+1.00000x51+

.00000x52+1.00000x53-9873.00000x54+1.00000x55-1.00000x56-300.00000x57-

8881.00000x58+9002.00000x59-8992.00000x60==9997.00000,

.00000x1+.00000x2+.00000x3+.00000x4+.00000x5-9779.00000x6-1.00000x7+1.00000x8+

.00000x9+1.00000x10+9923.00000x11+9897.00000x12-1.00000x13-1.00000x14+.00000x15+

.00000x16-1.00000x17+.00000x18-9811.00000x19+.00000x20+9893.00000x21+.00000x22+

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1.00000x30+2.00000x31+.00000x32+.00000x33+1.00000x34+.00000x35+2.00000x36+

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1.00000x51+.00000x52+1.00000x53+.00000x54-1.00000x55+.00000x56+.00000x57+

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1.00000x51+.00000x52+1.00000x53+9873.00000x54-1.00000x55+.00000x56+300.00000x57+

8881.00000x58-9002.00000x59+8992.00000x60==9999.00000,

7882.00000x1+9113.00000x2+9384.00000x3+8447.00000x4+9035.00000x5+.00000x6-

1.00000x7+1.00000x8+2.00000x9+1.00000x10+.00000x11+.00000x12+1.00000x13-

1.00000x14-9600.00000x15+8229.00000x16-1968.00000x17+9234.00000x18+.00000x19-

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9991.00000x33+1.00000x34+9439.00000x35+1.00000x36+8347.00000x37+9549.00000x38+

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300.00000x57+8881.00000x58+9002.00000x59+8992.00000x60==-9997.00000,

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.00000x7+.00000x8-2.00000x9+.00000x10-9923.00000x11-9897.00000x12-1.00000x13+

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9341.00000x20-9893.00000x21-9001.00000x22-9901.00000x23-20.00000x24-

8505.00000x25+9974.00000x26+.00000x27+.00000x28-8999.00000x29+1.00000x30-

2.00000x31-33.00000x32+.00000x33+.00000x34-9439.00000x35-1.00000x36-

8347.00000x37-9549.00000x38-9296.00000x39-1.00000x40-9909.00000x41-4.00000x42-

1.00000x43-9.00000x44-1.00000x45-7901.00000x46-81.00000x47-454.00000x48-

9111.00000x49-9903.00000x50+.00000x51+9993.00000x52-1.00000x53-9873.00000x54+

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9999.00000,

7882.00000x1+9113.00000x2+9384.00000x3+8447.00000x4+9035.00000x5+9779.00000x6+

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1.00000x55+.00000x56+300.00000x57+8881.00000x58+.00000x59+

8992.00000x60==9999.00000,

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.00000x9+.00000x10-9923.00000x11-9897.00000x12-1.00000x13+.00000x14+

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9893.00000x21+.00000x22+.00000x23+.00000x24+.00000x25+9974.00000x26+.00000x27+

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1.00000x56+.00000x57+.00000x58+.00000x59+.00000x60==9998.00000,

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9893.00000x21+.00000x22+.00000x23+.00000x24+.00000x25-9974.00000x26+1.00000x27-

1.00000x28+.00000x29+.00000x30-2.00000x31+.00000x32-9991.00000x33+1.00000x34+

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4.00000x42+.00000x43+.00000x44+.00000x45+.00000x46+.00000x47+.00000x48+

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2.00000x31-33.00000x32+9991.00000x33-1.00000x34-9439.00000x35+995.00000x36-

8347.00000x37-9549.00000x38-9296.00000x39+1.00000x40+.00000x41+4.00000x42-

1.00000x43-9.00000x44-1.00000x45-7901.00000x46-81.00000x47-454.00000x48-

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1.00000x55+1.00000x56-300.00000x57-8881.00000x58+.00000x59-

8992.00000x60==9997.00000,

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33.00000x32+9991.00000x33+.00000x34+9439.00000x35+1993.00000x36+8347.00000x37+

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1.00000x56+300.00000x57+8881.00000x58+9002.00000x59+8992.00000x60==-9997.00000,

1.00000x12>=9394.00000},10^-12,40,0,0,0,0]

PrimalDual[9188.00000x1+9949.00000x2-9866.00000x3+.00000x4+9981.00000x5+9889.00000x6+
9866.00000x7+9866.00000x8+.00000x9-9881.00000x10+.00000x11+8871.00000x12+
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.00000x31+9952.00000x32+9774.00000x33+.00000x34+.00000x35+9953.00000x36+
8.00000x37+.00000x38+.00000x39+9073.00000x40,
(* NAME   20-40-05 *)


{.00000x1-1.00000x2+1.00000x3-2.00000x4+.00000x5+9289.00000x6-1.00000x7-
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10^-12,40,0,0,0,0]

\(PrimalDual[
      30  x1 + \ 60  x2 + \ 50  x3, {\ 3  x1 + \ 4  x2 + \ 2  x3 <= \ 60, \ 
        x1 + \ 2  x2 + \ 2  x3 <= \ 30, 
2  x1 + \ x2 + \ 2  x3 <= \ 40}, 
      10^\(-12\), 40, 1, 0, 0, 0]\)