Соответствующая система уравнений примет вид:
f11 = f111 + f112 + f113 = 6000, (4) *1
f21 = f211 +0f12 +0f13 = 0, (5) *2
f31 = f311 +0f12 +0f13 = 0, (6) *3
f12 = f121 +0f22 +0f23 = 0, (7) *4
f22 = f221 + f222 + f223 = 9000, (8) *5
f32 = f321 +0f22 +0f23 = 0, (9) *6
f13 = f131 +0f32 +0f33 = 0, (10) *7
f23 = f231 +0f32 +0f33 = 0, (11) *8
f33 = f331 + f332 + f333 = 12000, (12) *9
Рис. 14. Балансовая матрица, повторяющая три j-ых среза трёхмерной матрицы «обменов» рисунка 13, с обозначениями неизвестных переменных и переменных равных нулю
3 × (x111 +03 × (x11 +03 × (x113 × (x = 3 × (x121 + 3 × (x221 +03 × (x213 × (x, (16) *10
2 × (x111 +02 × (x11 +02 × (x112 × (x = 2 × (x131 +02 × (x31 + 2 × (x3312 × (x, (17) *11
4 × (0121 + 4 × (0221 +04 × (0214 × (0 = 4 × (0131 +04 × (031 + 4 × (03314 × (0, (18) *12
3 × (x112 +03 × (x12 +03 × (x123 × (x = 3 × (x122 + 3 × (x222 +03 × (x223 × (x, (21) *13
2 × (x112 +02 × (x12 +02 × (x122 × (x = 2 × (x132 +02 × (x32 + 2 × (x3322 × (x, (22) *14
4 × (0122 + 4 × (0222 +04 × (0224 × (0 = 4 × (0132 +04 × (032 + 4 × (03324 × (0, (23) *15
3 × (x113 +03 × (x13 +03 × (x133 × (x = 3 × (x123 + 3 × (x223 +03 × (x233 × (x, (26) *16
2 × (x113 +02 × (x13 +02 × (x132 × (x = 2 × (x133 +02 × (x33 + 2 × (x3332 × (x, (27) *17
4 × (0123 + 4 × (0223 +04 × (0234 × (0 = 4 × (0133 +04 × (033 + 4 × (03334 × (0, (28) *18
(x111 +0(x11 +0(x11(x = (x112 +0(x12 +0(x12(x, (32) *19
(x111 +0(x11 +0(x11(x = (x113 +0(x13 +0(x13(x, (33) *20
(x112 +0(x12 +0(x12(x = (x113 +0(x13 +0(x13(x, (34) *21
(0121 + (0221 +0(021(0 = (0122 + (0222 +0(022(0, (35) *22
(0121 + (0221 +0(021(0 = (0123 + (0223 +0(023(0, (36) *23
(0122 + (0222 +0(022(0 = (0123 + (0223 +0(023(0, (37) *24
(0131 +0(031 + (0331(0 = (0132 +0(032 + (0332(0, (38) *25
(0131 +0(031 + (0331(0 = (0133 +0(033 + (0333(0, (39) *26
(0132 +0(032 + (0332(0 = (0133 +0(033 + (0333(0. (40) *27
В результате получаем, сохраняя (повторяя) при этом прежние номера соответствующих уравнений:
f11 = f111 + f112 + f113 = 6000, (4) *1
f22 = f221 + f222 + f223 = 9000, (8) *5
f33 = f331 + f332 + f333 = 12000, (12) *9
3×x111 = 3×x221, (16) *10
2×x111 = 2×x331, (17) *11