Контрольная точка. Математическое моделирование (по вариантам)
Задание 1.
Ниже представлены 33 варианта. В каждом варианте:
· A — запасы трех поставщиков.
· B — потребности трех потребителей.
· C — матрица тарифов (стоимость перевозки единицы груза).
Решить задачу методом минимального тарифа и северо-западного угла.
Варианты задач (3x3)
|
№ |
Запасы (A) |
Потребности (B) |
Матрица тарифов (C) |
|
1 |
40, 60, 50 |
30, 70, 50 |
(2, 5, 3), (4, 1, 6), (7, 3, 2) |
|
2 |
100, 150, 50 |
80, 120, 100 |
(5, 2, 4), (3, 6, 1), (8, 4, 3) |
|
3 |
70, 80, 90 |
100, 60, 80 |
(1, 8, 4), (5, 3, 7), (2, 6, 5) |
|
4 |
50, 50, 50 |
40, 60, 50 |
(6, 4, 2), (3, 5, 8), (1, 7, 3) |
|
5 |
120, 80, 100 |
90, 110, 100 |
(3, 7, 5), (4, 2, 6), (8, 1, 4) |
|
6 |
200, 150, 250 |
150, 200, 250 |
(10, 5, 8), (7, 12, 4), (6, 9, 11) |
|
7 |
30, 40, 30 |
20, 50, 30 |
(9, 2, 6), (4, 8, 3), (7, 5, 1) |
|
8 |
85, 45, 70 |
60, 70, 70 |
(4, 3, 5), (2, 8, 6), (7, 1, 9) |
|
9 |
60, 90, 100 |
110, 70, 70 |
(5, 5, 2), (3, 4, 8), (6, 1, 7) |
|
10 |
150, 200, 150 |
100, 250, 150 |
(8, 10, 4), (5, 3, 9), (2, 7, 6) |
|
11 |
45, 55, 60 |
50, 60, 50 |
(3, 1, 4), (6, 2, 5), (2, 8, 7) |
|
12 |
90, 110, 100 |
120, 80, 100 |
(7, 3, 2), (5, 6, 4), (8, 9, 1) |
|
13 |
75, 75, 50 |
60, 80, 60 |
(2, 6, 8), (5, 3, 1), (4, 7, 9) |
|
14 |
130, 70, 100 |
110, 90, 100 |
(5, 4, 3), (2, 7, 6), (8, 5, 1) |
|
15 |
40, 40, 40 |
30, 50, 40 |
(4, 8, 2), (3, 1, 5), (6, 7, 9) |
|
16 |
180, 120, 200 |
150, 150, 200 |
(11, 4, 7), (8, 10, 3), (5, 6, 12) |
|
17 |
55, 65, 80 |
70, 60, 70 |
(6, 3, 5), (4, 9, 2), (1, 8, 7) |
|
18 |
100, 100, 100 |
120, 80, 100 |
(2, 5, 9), (7, 1, 4), (3, 6, 8) |
|
19 |
90, 60, 50 |
70, 70, 60 |
(8, 2, 4), (5, 9, 3), (1, 6, 7) |
|
20 |
250, 150, 100 |
200, 100, 200 |
(4, 6, 10), (3, 8, 2), (7, 5, 9) |
|
21 |
65, 75, 60 |
80, 40, 80 |
(1, 5, 3), (7, 2, 6), (4, 8, 5) |
|
22 |
110, 140, 150 |
130, 130, 140 |
(9, 4, 2), (3, 7, 5), (6, 8, 1) |
|
23 |
50, 80, 70 |
60, 90, 50 |
(5, 3, 7), (2, 6, 4), (8, 1, 9) |
|
24 |
140, 160, 100 |
150, 150, 100 |
(10, 2, 6), (5, 11, 4), (3, 7, 8) |
|
25 |
80, 60, 60 |
70, 70, 60 |
(4, 9, 3), (2, 5, 8), (7, 1, 6) |
|
26 |
35, 45, 55 |
40, 40, 55 |
(6, 2, 4), (1, 8, 5), (7, 3, 9) |
|
27 |
120, 180, 100 |
150, 100, 150 |
(3, 8, 5), (6, 2, 9), (4, 7, 1) |
|
28 |
95, 55, 50 |
70, 80, 50 |
(5, 1, 6), (3, 9, 4), (8, 2, 7) |
|
29 |
70, 70, 70 |
80, 60, 70 |
(2, 7, 4), (5, 3, 8), (6, 1, 9) |
|
30 |
160, 140, 100 |
130, 170, 100 |
(7, 4, 1), (9, 2, 6), (5, 8, 3) |
|
31 |
45, 65, 40 |
50, 50, 50 |
(4, 6, 2), (3, 8, 5), (1, 7, 9) |
|
32 |
100, 120, 80 |
110, 90, 100 |
(8, 3, 5), (2, 7, 4), (6, 1, 9) |
|
33 |
60, 60, 80 |
70, 70, 60 |
(3, 5, 2), (6, 1, 8), (4, 9, 7) |
Задание 2.
Решить задачу методом потенциалов
|
№ |
Запасы |
Потребности (Столбцы) |
|
Тарифы (по строкам) |
|
1 |
50, 60, 40 |
40, 70, 40 |
|
(10, 8, 5), (7, 6, 9), (4, 5, 2) |
|
2 |
100, 80, 120 |
90, 110, 100 |
|
(5, 9, 3), (8, 4, 7), (2, 6, 5) |
|
3 |
70, 90, 50 |
60, 80, 70 |
|
(12, 15, 10), (11, 10, 14), (9, 13, 8) |
|
4 |
30, 50, 40 |
40, 30, 50 |
|
(8, 6, 12), (10, 11, 7), (5, 9, 4) |
|
5 |
150, 100, 150 |
120, 180, 100 |
|
(20, 25, 15), (18, 14, 22), (10, 19, 12) |
|
6 |
60, 40, 80 |
50, 70, 60 |
|
(7, 5, 9), (8, 10, 6), (4, 3, 5) |
|
7 |
200, 150, 100 |
180, 120, 150 |
|
(15, 12, 18), (14, 11, 13), (9, 13, 10) |
|
8 |
45, 55, 60 |
50, 60, 50 |
|
(6, 4, 8), (7, 5, 3), (9, 2, 6) |
|
9 |
80, 70, 90 |
100, 60, 80 |
|
(11, 14, 10), (13, 12, 15), (9, 16, 11) |
|
10 |
120, 130, 110 |
140, 100, 120 |
|
(5, 8, 4), (7, 6, 9), (3, 5, 2) |
|
11 |
25, 35, 40 |
30, 40, 30 |
|
(10, 7, 12), (9, 11, 8), (6, 13, 5) |
|
12 |
95, 85, 70 |
80, 100, 70 |
|
(4, 6, 2), (5, 3, 7), (8, 4, 6) |
|
13 |
65, 75, 60 |
70, 80, 50 |
|
(14, 12, 16), (15, 11, 13), (10, 14, 9) |
|
14 |
110, 140, 150 |
130, 120, 150 |
|
(8, 5, 10), (11, 7, 12), (6, 9, 4) |
|
15 |
40, 30, 50 |
45, 35, 40 |
|
(9, 6, 11), (10, 8, 7), (5, 12, 6) |
|
16 |
180, 220, 200 |
250, 150, 200 |
|
(12, 10, 15), (14, 11, 13), (8, 16, 9) |
|
17 |
55, 45, 65 |
60, 50, 55 |
|
(7, 4, 9), (8, 6, 5), (3, 10, 7) |
|
18 |
130, 170, 100 |
150, 120, 130 |
|
(6, 9, 5), (8, 4, 10), (3, 7, 6) |
|
19 |
20, 40, 30 |
25, 35, 30 |
|
(11, 8, 14), (12, 9, 10), (7, 13, 6) |
|
20 |
75, 85, 90 |
100, 70, 80 |
|
(5, 7, 3), (8, 4, 9), (2, 6, 5) |
|
21 |
160, 140, 120 |
180, 140, 100 |
|
(15, 18, 12), (17, 14, 20), (11, 21, 13) |
|
22 |
35, 55, 45 |
40, 50, 45 |
|
(9, 6, 10), (8, 5, 7), (4, 11, 8) |
|
23 |
90, 60, 80 |
70, 90, 70 |
|
(6, 8, 4), (10, 7, 11), (5, 9, 3) |
|
24 |
50, 50, 50 |
60, 40, 50 |
|
(12, 10, 15), (13, 11, 9), (8, 14, 7) |
|
25 |
140, 120, 160 |
150, 150, 120 |
|
(7, 5, 9), (8, 4, 10), (3, 6, 5) |
|
26 |
25, 45, 30 |
35, 30, 35 |
|
(10, 8, 12), (11, 9, 7), (6, 13, 5) |
|
27 |
85, 95, 70 |
100, 80, 70 |
|
(5, 9, 4), (8, 6, 11), (3, 7, 5) |
|
28 |
115, 105, 130 |
120, 140, 90 |
|
(14, 16, 11), (13, 12, 15), (9, 18, 10) |
|
29 |
45, 35, 55 |
50, 40, 45 |
|
(8, 5, 10), (11, 7, 12), (6, 9, 4) |
|
30 |
190, 160, 150 |
200, 180, 120 |
|
(6, 9, 4), (8, 7, 10), (3, 5, 2) |
|
31 |
60, 70, 80 |
90, 60, 60 |
|
(12, 14, 10), (13, 11, 15), (9, 16, 11) |
|
32 |
25, 25, 25 |
20, 30, 25 |
|
(7, 5, 8), (9, 6, 4), (5, 10, 7) |
|
33 |
100, 100, 100 |
110, 90, 100 |
|
(4, 7, 2), (5, 3, 6), (8, 4, 5) |
Задание 3.
Решить задачу о назначении
Ниже представлены 33 варианта. В каждом варианте указаны стоимости выполнения работ (столбцы A, B, C, D) для четырех рабочих (строки 1, 2, 3, 4).
Варианты задач (Матрицы 4x4)
|
№ |
Р1 (A,B,C,D) |
Р2 (A,B,C,D) |
Р3 (A,B,C,D) |
Р4 (A,B,C,D) |
|
1 |
12, 10, 15, 13 |
14, 11, 13, 15 |
10, 15, 11, 14 |
13, 12, 14, 11 |
|
2 |
25, 20, 30, 24 |
28, 22, 26, 28 |
20, 30, 22, 28 |
26, 24, 28, 22 |
|
3 |
8, 5, 10, 7 |
10, 6, 8, 10 |
6, 11, 7, 10 |
9, 7, 10, 6 |
|
4 |
45, 40, 52, 43 |
49, 42, 47, 49 |
40, 54, 43, 50 |
47, 45, 51, 41 |
|
5 |
18, 14, 22, 17 |
20, 15, 19, 20 |
15, 23, 16, 21 |
19, 17, 21, 15 |
|
6 |
33, 28, 38, 31 |
36, 30, 34, 36 |
28, 40, 30, 37 |
35, 33, 39, 29 |
|
7 |
14, 10, 18, 12 |
16, 11, 14, 16 |
11, 19, 12, 17 |
15, 13, 18, 11 |
|
8 |
50, 44, 58, 48 |
54, 46, 51, 54 |
45, 60, 48, 56 |
53, 50, 57, 45 |
|
9 |
9, 5, 12, 7 |
11, 6, 9, 11 |
6, 14, 7, 12 |
10, 8, 13, 6 |
|
10 |
22, 17, 28, 20 |
25, 19, 23, 25 |
18, 29, 20, 26 |
23, 21, 27, 18 |
|
11 |
38, 32, 45, 36 |
42, 34, 39, 42 |
33, 48, 35, 43 |
41, 38, 46, 33 |
|
12 |
16, 11, 21, 14 |
19, 12, 16, 19 |
12, 23, 14, 20 |
17, 15, 21, 12 |
|
13 |
60, 53, 70, 58 |
65, 55, 61, 65 |
55, 75, 58, 68 |
64, 60, 69, 54 |
|
14 |
28, 22, 35, 26 |
32, 24, 29, 32 |
23, 38, 25, 34 |
31, 28, 36, 23 |
|
15 |
13, 8, 18, 11 |
16, 9, 13, 16 |
9, 20, 11, 17 |
14, 12, 18, 9 |
|
16 |
41, 35, 49, 39 |
45, 37, 42, 45 |
36, 52, 38, 48 |
44, 41, 50, 36 |
|
17 |
19, 13, 25, 17 |
22, 14, 19, 22 |
14, 27, 16, 24 |
20, 18, 26, 14 |
|
18 |
55, 48, 65, 53 |
60, 50, 56, 60 |
48, 70, 52, 63 |
59, 55, 64, 49 |
|
19 |
10, 5, 15, 8 |
13, 6, 10, 13 |
6, 18, 8, 14 |
11, 9, 16, 6 |
|
20 |
30, 24, 38, 28 |
34, 26, 31, 34 |
25, 42, 27, 37 |
33, 30, 39, 25 |
|
21 |
48, 41, 58, 46 |
53, 43, 49, 53 |
42, 62, 45, 56 |
51, 48, 57, 42 |
|
22 |
15, 9, 21, 13 |
18, 10, 14, 18 |
10, 24, 12, 19 |
16, 14, 22, 10 |
|
23 |
65, 57, 78, 62 |
70, 59, 66, 70 |
58, 82, 61, 74 |
69, 65, 76, 58 |
|
24 |
21, 15, 29, 19 |
25, 16, 21, 25 |
16, 32, 18, 27 |
23, 21, 30, 16 |
|
25 |
11, 6, 16, 9 |
14, 7, 11, 14 |
7, 19, 9, 15 |
12, 10, 17, 7 |
|
26 |
36, 29, 44, 34 |
40, 31, 37, 40 |
30, 48, 33, 43 |
39, 36, 45, 30 |
|
27 |
52, 45, 62, 50 |
57, 47, 53, 57 |
46, 66, 49, 60 |
55, 52, 61, 46 |
|
28 |
17, 11, 23, 15 |
20, 12, 16, 20 |
12, 26, 14, 21 |
18, 16, 24, 12 |
|
29 |
72, 64, 85, 69 |
77, 66, 73, 77 |
64, 89, 68, 81 |
76, 72, 83, 65 |
|
30 |
24, 18, 32, 22 |
28, 19, 24, 28 |
19, 35, 21, 30 |
26, 24, 33, 19 |
|
31 |
43, 36, 52, 41 |
48, 38, 44, 48 |
37, 57, 40, 51 |
46, 43, 53, 37 |
|
32 |
14, 9, 19, 12 |
17, 10, 14, 17 |
10, 22, 12, 18 |
15, 13, 20, 10 |
|
33 |
31, 25, 39, 29 |
35, 27, 32, 35 |
26, 43, 28, 38 |
34, 31, 40, 26 |
- Teacher: Медведева Ольга Федоровна
- Teacher: Рудина Татьяна Владимировна