> assign(%);

> f3z:=Z[1,1]*z11+Z[1,2]*z12+Z[1,3]*z13+Z[1,4]*z14+Z[1,5]*z15+Z[1,6]*z16+Z[2,1]*z21+Z[2,2]*z22+Z[2,3]*z23+Z[2,4]*z24+Z[2,5]*z25+Z[2,6]*z26+Z[3,1]*z31+Z[3,2]*z32+Z[3,3]*z33+Z[3,4]*z34+Z[3,5]*z35+Z[3,6]*z36+Z[4,1]*z41+Z[4,2]*z42+Z[4,3]*z43+Z[4,4]*z44+Z[4,5]*z45+Z[4,6]*z46+Z[5,1]*z51+Z[5,2]*z52+Z[5,3]*z53+Z[5,4]*z54+Z[5,5]*z55+Z[5,6]*z56+Z[6,1]*z61+Z[6,2]*z62+Z[6,3]*z63+Z[6,4]*z64+Z[6,5]*z65+Z[6,6]*z66;

f3z := 1285/3

> [z11,z12,z13,z14,z15,z16];[z21,z22,z23,z24,z25,z26];[z31,z32,z33,z34,z35,z36];[z41,z42,z43,z44,z45,z46];[z51,z52,z53,z54,z55,z56];[z61,z62,z63,z64,z65,z66];f3z;

[0, 0, 0, 0, 0, 50]

[0, 0, 6, 12, 0, 0]

[0, 0, 0, 12, 0, 0]

[0, 20, 0, 0, 50, 10]

[0, 0, 15, 0, 0, 0]

[14, 0, 1, 0, 0, 0]

1285/3

(Новый план перевозок ставим в функцию цели первой транспортной задачи и таким образом получаем первое УПРАВЛЕНИЕ)

> f4z:=X[1,1]*z11+X[1,2]*z12+X[1,3]*z13+X[1,4]*z14+X[1,5]*z15+X[1,6]*z16+X[2,1]*z21+X[2,2]*z22+X[2,3]*z23+X[2,4]*z24+X[2,5]*z25+X[2,6]*z26+X[3,1]*z31+X[3,2]*z32+X[3,3]*z33+X[3,4]*z34+X[3,5]*z35+X[3,6]*z36+X[4,1]*z41+X[4,2]*z42+X[4,3]*z43+X[4,4]*z44+X[4,5]*z45+X[4,6]*z46+X[5,1]*z51+X[5,2]*z52+X[5,3]*z53+X[5,4]*z54+X[5,5]*z55+X[5,6]*z56+X[6,1]*z61+X[6,2]*z62+X[6,3]*z63+X[6,4]*z64+X[6,5]*z65+X[6,6]*z66;

f4z := 514

(Новый план перевозок ставим в функцию цели второй транспортной задачи и таким образом получаем второе УПРАВЛЕНИЕ)

> f5z:=Y[1,1]*z11+Y[1,2]*z12+Y[1,3]*z13+Y[1,4]*z14+Y[1,5]*z15+Y[1,6]*z16+Y[2,1]*z21+Y[2,2]*z22+Y[2,3]*z23+Y[2,4]*z24+Y[2,5]*z25+Y[2,6]*z26+Y[3,1]*z31+Y[3,2]*z32+Y[3,3]*z33+Y[3,4]*z34+Y[3,5]*z35+Y[3,6]*z36+Y[4,1]*z41+Y[4,2]*z42+Y[4,3]*z43+Y[4,4]*z44+Y[4,5]*z45+Y[4,6]*z46+Y[5,1]*z51+Y[5,2]*z52+Y[5,3]*z53+Y[5,4]*z54+Y[5,5]*z55+Y[5,6]*z56+Y[6,1]*z61+Y[6,2]*z62+Y[6,3]*z63+Y[6,4]*z64+Y[6,5]*z65+Y[6,6]*z66;

f5z := 257

Приложение 3

Листинг программы решения транспортной задачи в векторных координатах (Для трёх матриц)

> restart:

> b:=[50,18,12,80,15,15];

b := [50, 18, 12, 80, 15, 15]

> c:=[14,20,22,24,50,60];

c := [14, 20, 22, 24, 50, 60]

(Решить первую транспортную задачу, найдя цену перевозки и план перевозки)

>X:=Matrix(6,6,[[3,8,9,1,9,0],[3,4,5,0,9,6],[2,7,6,0,9,0],[9,1,9,4,7,2],[2,4,5,6,4,1],[1,4,5,7,8,7]]);

X := Matrix(6,6,{(1, 1) = 3, (1, 2) = 8, (1, 3) = 9, (1, 4) = 1, (1, 5) = 9, (2, 1) = 3, (2, 2) = 4, (2, 3) = 5, (2, 5) = 9, (2, 6) = 6, (3, 1) = 2, (3, 2) = 7, (3, 3) = 6, (3, 5) = 9, (4, 1) = 9, (4, 2) = 1, (4, 3) = 9, (4, 4) = 4, (4, 5) = 7, (4, 6) = 2, (5, 1) = 2, (5, 2) = 4, (5, 3) = 5, (5, 4) = 6, (5, 5) = 4, (5, 6) = 1, (6, 1) = 1, (6, 2) = 4, (6, 3) = 5, (6, 4) = 7, (6, 5) = 8, (6, 6) = 7},datatype = anything,storage = rectangular,order = Fortran_order,shape = [])

> proc(X,b,c)

>f1x,x11,x12,x13,x14,x15,x16,x21,x22,x23,x24,x25,x26,x31,x32,x33,x34,x35,x36,x41,x42,x43,x44,x45,x46,x51,x52,x53,x54,x55,x56,x61,x62,x63,x64,x65,x66;

Warning, premature end of input

> with(simplex):

Warning, the protected names maximize and minimize have been redefined and unprotected

>minimize(X[1,1]*x11+X[1,2]*x12+X[1,3]*x13+X[1,4]*x14+X[1,5]*x15+X[1,6]*x16+X[2,1]*x21+X[2,2]*x22+X[2,3]*x23+X[2,4]*x24+X[2,5]*x25+X[2,6]*x26+X[3,1]*x31+X[3,2]*x32+X[3,3]*x33+X[3,4]*x34+X[3,5]*x35+X[3,6]*x36+X[4,1]*x41+X[4,2]*x42+X[4,3]*x43+X[4,4]*x44+X[4,5]*x45+X[4,6]*x46+X[5,1]*x51+X[5,2]*x52+X[5,3]*x53+X[5,4]*x54+X[5,5]*x55+X[5,6]*x56+X[6,1]*x61+X[6,2]*x62+X[6,3]*x63+X[6,4]*x64+X[6,5]*x65+X[6,6]*x66, {x11+x12+x13+x14+x15+x16=b[1],x21+x22+x23+x24+x25+x26=b[2], x31+x32+x33+x34+x35+x36=b[3],x41+x42+x43+x44+x45+x46=b[4], x51+x52+x53+x54+x55+x56=b[5], x61+x62+x63+x64+x65+x66=b[6], x11+x21+x31+x41+x51+x61=c[1], x12+x22+x32+x42+x52+x62=c[2], x13+x23+x33+x43+x53+x63=c[3], x14+x24+x34+x44+x54+x64=c[4],x15+x25+x35+x45+x55+x65=c[5],x16+x26+x36+x46+x56+x66=c[6]},NONNEGATIVE);

{x11 = 0, x12 = 0, x13 = 0, x14 = 0, x15 = 0, x21 = 0, x22 = 0, x31 = 0, x32 = 0, x33 = 0, x36 = 0, x41 = 0, x51 = 0, x54 = 0, x55 = 0, x56 = 0, x64 = 0, x65 = 0, x66 = 0, x61 = 14, x16 = 50, x25 = 0, x26 = 0, x35 = 0, x43 = 0, x44 = 0, x52 = 0, x62 = 0, x34 = 12, x46 = 10, x24 = 12, x45 = 50, x63 = 1, x42 = 20, x23 = 6, x53 = 15}

> assign(%);

>f1x:=X[1,1]*x11+X[1,2]*x12+X[1,3]*x13+X[1,4]*x14+X[1,5]*x15+X[1,6]*x16+X[2,1]*x21+X[2,2]*x22+X[2,3]*x23+X[2,4]*x24+X[2,5]*x25+X[2,6]*x26+X[3,1]*x31+X[3,2]*x32+X[3,3]*x33+X[3,4]*x34+X[3,5]*x35+X[3,6]*x36+X[4,1]*x41+X[4,2]*x42+X[4,3]*x43+X[4,4]*x44+X[4,5]*x45+X[4,6]*x46+X[5,1]*x51+X[5,2]*x52+X[5,3]*x53+X[5,4]*x54+X[5,5]*x55+X[5,6]*x56+X[6,1]*x61+X[6,2]*x62+X[6,3]*x63+X[6,4]*x64+X[6,5]*x65+X[6,6]*x66;

f1x := 514

>[x11,x12,x13,x14,x15,x16];[x21,x22,x23,x24,x25,x26];[x31,x32,x33,x34,x35,x36];[x41,x42,x43,x44,x45,x46];[x51,x52,x53,x54,x55,x56];[x61,x62,x63,x64,x65,x66];f1x;

[0, 0, 0, 0, 0, 50]

[0, 0, 6, 12, 0, 0]

[0, 0, 0, 12, 0, 0]

[0, 20, 0, 0, 50, 10]

[0, 0, 15, 0, 0, 0]

[14, 0, 1, 0, 0, 0]

514

(Решить вторую транспортную задачу (с другими ценами), найдя цену перевозки и план перевозки)

>Y:=Matrix(6,6,[[3/2,8/2,9/2,1/2,9/2,0/2],[3/2,4/2,5/2,0/2,9/2,6/2],[2/2,7/2,6/2,0/2,9/2,0/2],[9/2,1/2,9/2,4/2,7/2,2/2],[2/2,4/2,5/2,6/2,4/2,1/2],[1/2,4/2,5/2,7/2,8/2,7/2]]);

Y := Matrix(6,6,{(1, 1) = 3/2, (1, 2) = 4, (1, 3) = 9/2, (1, 4) = 1/2, (1, 5) = 9/2, (2, 1) = 3/2, (2, 2) = 2, (2, 3) = 5/2, (2, 5) = 9/2, (2, 6) = 3, (3, 1) = 1, (3, 2) = 7/2, (3, 3) = 3, (3, 5) = 9/2, (4, 1) = 9/2, (4, 2) = 1/2, (4, 3) = 9/2, (4, 4) = 2, (4, 5) = 7/2, (4, 6) = 1, (5, 1) = 1, (5, 2) = 2, (5, 3) = 5/2, (5, 4) = 3, (5, 5) = 2, (5, 6) = 1/2, (6, 1) = 1/2, (6, 2) = 2, (6, 3) = 5/2, (6, 4) = 7/2, (6, 5) = 4, (6, 6) = 7/2},datatype = anything,storage = rectangular,order = Fortran_order,shape = [])

> proc(Y,b,c)

>f2y,y11,y12,y13,y14,y15,y16,y21,y22,y23,y24,y25,y26,y31,y32,y33,y34,y35,y36,y41,y42,y43,y44,y45,y46,y51,y52,y53,y54,y55,y56,y61,y62,y63,y64,y65,y66;

Warning, premature end of input

> with(simplex):

>minimize(Y[1,1]*y11+Y[1,2]*y12+Y[1,3]*y13+Y[1,4]*y14+Y[1,5]*y15+Y[1,6]*y16+Y[2,1]*y21+Y[2,2]*y22+Y[2,3]*y23+Y[2,4]*y24+Y[2,5]*y25+Y[2,6]*y26+Y[3,1]*y31+Y[3,2]*y32+Y[3,3]*y33+Y[3,4]*y34+Y[3,5]*y35+Y[3,6]*y36+Y[4,1]*y41+Y[4,2]*y42+Y[4,3]*y43+Y[4,4]*y44+Y[4,5]*y45+Y[4,6]*y46+Y[5,1]*y51+Y[5,2]*y52+Y[5,3]*y53+Y[5,4]*y54+Y[5,5]*y55+Y[5,6]*y56+Y[6,1]*y61+Y[6,2]*y62+Y[6,3]*y63+Y[6,4]*y64+Y[6,5]*y65+Y[6,6]*y66, {y11+y12+y13+y14+y15+y16=b[1],y21+y22+y23+y24+y25+y26=b[2], y31+y32+y33+y34+y35+y36=b[3],y41+y42+y43+y44+y45+y46=b[4], y51+y52+y53+y54+y55+y56=b[5], y61+y62+y63+y64+y65+y66=b[6], y11+y21+y31+y41+y51+y61=c[1], y12+y22+y32+y42+y52+y62=c[2], y13+y23+y33+y43+y53+y63=c[3], y14+y24+y34+y44+y54+y64=c[4],y15+y25+y35+y45+y55+y65=c[5],y16+y26+y36+y46+y56+y66=c[6]},NONNEGATIVE);

{y54 = 0, y55 = 0, y56 = 0, y64 = 0, y65 = 0, y66 = 0, y61 = 14, y16 = 50, y43 = 0, y44 = 0, y52 = 0, y62 = 0, y34 = 12, y46 = 10, y23 = 6, y63 = 1, y45 = 50, y42 = 20, y24 = 12, y53 = 15, y25 = 0, y26 = 0, y35 = 0, y14 = 0, y15 = 0, y21 = 0, y11 = 0, y12 = 0, y13 = 0, y22 = 0, y31 = 0, y32 = 0, y36 = 0, y41 = 0, y51 = 0, y33 = 0}

> assign(%);

>f2y:=Y[1,1]*y11+Y[1,2]*y12+Y[1,3]*y13+Y[1,4]*y14+Y[1,5]*y15+Y[1,6]*y16+Y[2,1]*y21+Y[2,2]*y22+Y[2,3]*y23+Y[2,4]*y24+Y[2,5]*y25+Y[2,6]*y26+Y[3,1]*y31+Y[3,2]*y32+Y[3,3]*y33+Y[3,4]*y34+Y[3,5]*y35+Y[3,6]*y36+Y[4,1]*y41+Y[4,2]*y42+Y[4,3]*y43+Y[4,4]*y44+Y[4,5]*y45+Y[4,6]*y46+Y[5,1]*y51+Y[5,2]*y52+Y[5,3]*y53+Y[5,4]*y54+Y[5,5]*y55+Y[5,6]*y56+Y[6,1]*y61+Y[6,2]*y62+Y[6,3]*y63+Y[6,4]*y64+Y[6,5]*y65+Y[6,6]*y66;

f2y := 257

>[y11,y12,y13,y14,y15,y16];[y16,y21,y22,y23,y24,y25,y26];[y31,y32,y33,y34,y35,y36];[y41,y42,y43,y44,y45,y46];[y51,y52,y53,y54,y55,y56];[y61,y62,y63,y64,y65,y66];f2y;

[0, 0, 0, 0, 0, 50]

[50, 0, 0, 6, 12, 0, 0]

[0, 0, 0, 12, 0, 0]

[0, 20, 0, 0, 50, 10]

[0, 0, 15, 0, 0, 0]

[14, 0, 1, 0, 0, 0]

257

(Решить третью транспортную задачу (с другими ценами), найдя цену перевозки и план перевозки)

>V:=Matrix(6,6,[[3/6,8/6,9/6,1/6,9/6,0/6],[3/6,4/6,5/6,0/6,9/6,6/6],[2/6,7/6,6/6,0/6,9/6,0/6],[9/6,1/6,9/6,4/6,7/6,2/6],[2/6,4/6,5/6,6/6,4/6,1/6],[1/6,4/6,5/6,7/6,8/6,7/6]]);

V := Matrix(6,6,{(5, 3) = 5/6, (5, 4) = 1, (5, 5) = 2/3, (5, 6) = 1/6, (6, 1) = 1/6, (6, 2) = 2/3, (6, 3) = 5/6, (6, 4) = 7/6, (6, 5) = 4/3, (6, 6) = 7/6, (4, 5) = 7/6, (4, 6) = 1/3, (5, 1) = 1/3, (5, 2) = 2/3, (1, 1) = 1/2, (1, 2) = 4/3, (1, 3) = 3/2, (1, 4) = 1/6, (1, 5) = 3/2, (2, 1) = 1/2, (2, 2) = 2/3, (2, 3) = 5/6, (2, 5) = 3/2, (2, 6) = 1, (3, 1) = 1/3, (3, 2) = 7/6, (3, 3) = 1, (3, 5) = 3/2, (4, 1) = 3/2, (4, 2) = 1/6, (4, 3) = 3/2, (4, 4) = 2/3},datatype = anything,storage = rectangular,order = Fortran_order,shape = [])

> proc(V,b,c)

>f3v,v11,v12,v13,v14,v15,v16,v21,v22,v23,v24,v25,v26,v31,v32,v33,v34,v35,v36,v41,v42,v43,v44,v45,v46,v51,v52,v53,v54,v55,v56,v61,v62,v63,v64,v65,v66;

Warning, premature end of input

> with(simplex):

>minimize(V[1,1]*v11+V[1,2]*v12+V[1,3]*v13+V[1,4]*v14+V[1,5]*v15+V[1,6]*v16+V[2,1]*v21+V[2,2]*v22+V[2,3]*v23+V[2,4]*v24+V[2,5]*v25+V[2,6]*v26+V[3,1]*v31+V[3,2]*v32+V[3,3]*v33+V[3,4]*v34+V[3,5]*v35+V[3,6]*v36+V[4,1]*v41+V[4,2]*v42+V[4,3]*v43+V[4,4]*v44+V[4,5]*v45+V[4,6]*v46+V[5,1]*v51+V[5,2]*v52+V[5,3]*v53+V[5,4]*v54+V[5,5]*v55+V[5,6]*v56+V[6,1]*v61+V[6,2]*v62+V[6,3]*v63+V[6,4]*v64+V[6,5]*v65+V[6,6]*v66, {v11+v12+v13+v14+v15+v16=b[1],v21+v22+v23+v24+v25+v26=b[2], v31+v32+v33+v34+v35+v36=b[3],v41+v42+v43+v44+v45+v46=b[4], v51+v52+v53+v54+v55+v56=b[5], v61+v62+v63+v64+v65+v66=b[6], v11+v21+v31+v41+v51+v61=c[1], v12+v22+v32+v42+v52+v62=c[2], v13+v23+v33+v43+v53+v63=c[3], v14+v24+v34+v44+v54+v64=c[4],v15+v25+v35+v45+v55+v65=c[5],v16+v26+v36+v46+v56+v66=c[6]},NONNEGATIVE);

{v25 = 0, v26 = 0, v35 = 0, v43 = 0, v44 = 0, v52 = 0, v62 = 0, v34 = 12, v46 = 10, v24 = 12, v23 = 6, v45 = 50, v63 = 1, v42 = 20, v53 = 15, v51 = 0, v54 = 0, v55 = 0, v56 = 0, v64 = 0, v65 = 0, v66 = 0, v61 = 14, v16 = 50, v14 = 0, v15 = 0, v21 = 0, v22 = 0, v31 = 0, v32 = 0, v33 = 0, v36 = 0, v41 = 0, v13 = 0, v11 = 0, v12 = 0}

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