7. Варианты домашних контрольных работ
Задание 1. Решить задачу ЛП графически и симплекс-методом. Если оптимальное решение не единственно, найти все оптимальные опорные решения.
1. |
|
|
2. |
|
3. |
|
|
4. |
|
5. |
|
|
6. |
|
7. |
|
|
8. |
|
9. |
|
|
10. |
|
11. |
|
|
12. |
|
13. |
|
|
14. |
|
15. |
|
|
16. |
|
17. |
|
|
18. |
|
19. |
|
|
20. |
|
21. |
|
|
22. |
|
23. |
|
|
24. |
|
25. |
|
|
26. |
|
27.
|
|
|
28. |
|
|
|
|
|
|
|
|
|
|
|
29. |
|
|
30. |
|
31. |
|
|
32. |
|
33. |
|
|
34. |
|
35. |
|
|
36. |
|
37. |
|
|
38. |
|
39. |
|
|
40. |
|
Задание 2. Построить двойственную задачу. Определить, является ли данный вектор оптимальным решением исходной задачи (использовать 2-ую теорему двойственности).
1. |
|
|
2. |
|
|||
|
|
|
|
|
|||
3. |
|
|
4. |
|
|||
|
|
|
|
|
|||
5. |
|
|
6. |
|
||||||||
|
|
|
|
|
||||||||
7. |
|
|
8. |
|
|
|||||||
|
|
|
|
|
|
|||||||
9. |
|
|
10. |
|
|
|||||||
|
|
|
|
|
|
|||||||
11. |
|
|
12. |
|
|
|
|
|
|
13. |
|
|
14. |
|
|
|
|
|
|
|
15. |
|
|
16. |
|
|
|||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
|
|
|
|
|
|
|
|||||||
17. |
|
|
18. |
|
|
||||||||
|
|
|
|
|
|
||||||||
19. |
|
|
20. |
|
|||||||||
|
|
|
|
|
|||||||||
|
21. |
|
|
22. |
|
|
|||
|---|---|---|---|---|---|---|---|---|---|
|
|
|
|
|
|
|
|||
|
23. |
|
|
24. |
|
|
|||
25. |
|
26. |
|
||||||
27. |
|
28. |
|
||||||
29. |
|
30. |
|
||||||
31. |
|
32. |
|
||||||
33. |
|
34. |
|
||||||
35. |
|
36. |
|
||||||
37. |
|
38. |
|
||||||
Задание 3. Решить транспортную задачу методом потенциалов.
1. |
16 |
30 |
17 |
10 |
16 |
4 |
|
2. |
15 |
1 |
22 |
19 |
1 |
20 |
|
30 |
27 |
26 |
9 |
23 |
6 |
|
|
21 |
18 |
11 |
4 |
3 |
20 |
|
13 |
4 |
22 |
3 |
1 |
10 |
|
|
26 |
29 |
23 |
26 |
24 |
20 |
|
3 |
1 |
5 |
4 |
24 |
10 |
|
|
21 |
10 |
3 |
19 |
27 |
20 |
|
7 |
7 |
7 |
7 |
7 |
|
|
|
19 |
19 |
19 |
19 |
4 |
|
3. |
17 |
20 |
29 |
26 |
25 |
15 |
|
4. |
20 |
26 |
24 |
26 |
29 |
13 |
|
3 |
4 |
5 |
15 |
24 |
15 |
|
|
15 |
20 |
29 |
26 |
23 |
17 |
|
19 |
2 |
22 |
4 |
13 |
15 |
|
|
4 |
10 |
27 |
30 |
7 |
17 |
|
20 |
27 |
1 |
17 |
19 |
15 |
|
|
9 |
16 |
29 |
20 |
3 |
13 |
|
11 |
11 |
11 |
11 |
16 |
|
|
|
12 |
12 |
12 |
12 |
12 |
|
5. |
21 |
22 |
2 |
13 |
7 |
18 |
|
6. |
10 |
17 |
9 |
20 |
30 |
15 |
|
27 |
10 |
4 |
24 |
9 |
12 |
|
|
13 |
4 |
24 |
26 |
26 |
15 |
|
3 |
16 |
25 |
5 |
4 |
17 |
|
|
22 |
24 |
30 |
27 |
29 |
19 |
|
28 |
11 |
17 |
10 |
29 |
13 |
|
|
25 |
12 |
11 |
24 |
23 |
11 |
|
8 |
8 |
8 |
8 |
28 |
|
|
|
9 |
24 |
9 |
9 |
9 |
|
7. |
30 |
24 |
11 |
12 |
25 |
21 |
|
8. |
5 |
15 |
3 |
6 |
10 |
9 |
|
26 |
4 |
29 |
20 |
24 |
19 |
|
|
23 |
8 |
13 |
27 |
12 |
11 |
|
27 |
14 |
14 |
10 |
18 |
15 |
|
|
30 |
1 |
5 |
24 |
25 |
14 |
|
6 |
14 |
28 |
8 |
2 |
25 |
|
|
8 |
26 |
7 |
28 |
9 |
16 |
|
15 |
15 |
15 |
15 |
20 |
|
|
|
8 |
9 |
13 |
8 |
12 |
|
9. |
9 |
17 |
29 |
28 |
8 |
22 |
|
10. |
30 |
2 |
5 |
6 |
15 |
16 |
|
13 |
21 |
27 |
16 |
29 |
13 |
|
|
5 |
29 |
9 |
5 |
7 |
15 |
|
20 |
30 |
24 |
7 |
26 |
17 |
|
|
16 |
24 |
14 |
6 |
26 |
14 |
|
11 |
19 |
30 |
6 |
2 |
18 |
|
|
13 |
28 |
4 |
25 |
8 |
15 |
|
7 |
7 |
7 |
7 |
42 |
|
|
|
6 |
6 |
13 |
20 |
15 |
|
11. |
12 |
11 |
25 |
17 |
21 |
17 |
|
12. |
2 |
24 |
4 |
2 |
3 |
28 |
|
22 |
18 |
14 |
8 |
1 |
14 |
|
|
20 |
10 |
15 |
27 |
7 |
13 |
|
9 |
13 |
2 |
28 |
15 |
21 |
|
|
15 |
15 |
12 |
25 |
19 |
15 |
|
26 |
21 |
3 |
4 |
27 |
43 |
|
|
2 |
6 |
3 |
5 |
5 |
30 |
|
19 |
22 |
23 |
17 |
14 |
|
|
|
27 |
16 |
25 |
11 |
7 |
|
13. |
15 |
6 |
25 |
11 |
12 |
9 |
|
14. |
22 |
24 |
25 |
23 |
19 |
24 |
|
13 |
14 |
20 |
27 |
30 |
18 |
|
|
1 |
21 |
10 |
7 |
19 |
14 |
|
16 |
7 |
19 |
10 |
21 |
23 |
|
|
2 |
26 |
18 |
30 |
27 |
19 |
|
1 |
29 |
23 |
25 |
18 |
26 |
|
|
22 |
10 |
29 |
26 |
23 |
17 |
|
11 |
22 |
31 |
6 |
6 |
|
|
|
22 |
9 |
12 |
13 |
18 |
|
15. |
6 |
11 |
20 |
17 |
8 |
12 |
|
16. |
7 |
10 |
16 |
27 |
19 |
17 |
|
1 |
25 |
3 |
18 |
17 |
17 |
|
|
30 |
18 |
8 |
29 |
15 |
19 |
|
9 |
39 |
16 |
30 |
31 |
18 |
|
|
3 |
18 |
28 |
19 |
15 |
11 |
|
23 |
15 |
4 |
3 |
28 |
13 |
|
|
9 |
12 |
2 |
25 |
21 |
13 |
|
10 |
8 |
12 |
14 |
16 |
|
|
|
5 |
15 |
11 |
9 |
20 |
|
17. |
4 |
21 |
12 |
8 |
1 |
21 |
|
18. |
5 |
3 |
24 |
10 |
25 |
24 |
|
20 |
8 |
25 |
15 |
23 |
21 |
|
|
30 |
2 |
22 |
16 |
7 |
15 |
|
17 |
1 |
11 |
5 |
3 |
23 |
|
|
30 |
24 |
27 |
29 |
10 |
16 |
|
23 |
10 |
24 |
6 |
5 |
23 |
|
|
15 |
17 |
21 |
2 |
3 |
24 |
|
22 |
22 |
22 |
11 |
11 |
|
|
|
12 |
13 |
14 |
31 |
9 |
|
19. |
21 |
19 |
11 |
12 |
12 |
24 |
|
20. |
25 |
28 |
20 |
15 |
7 |
16 |
|
26 |
29 |
14 |
1 |
26 |
12 |
|
|
27 |
5 |
11 |
23 |
10 |
12 |
|
39 |
1 |
22 |
8 |
25 |
18 |
|
|
1 |
25 |
14 |
16 |
16 |
14 |
|
53 |
23 |
40 |
26 |
28 |
16 |
|
|
8 |
6 |
4 |
16 |
18 |
18 |
|
11 |
13 |
26 |
10 |
10 |
|
|
|
7 |
8 |
4 |
11 |
30 |
|
21. |
14 |
25 |
18 |
19 |
23 |
33 |
|
22. |
8 |
1 |
19 |
1 |
15 |
18 |
|
2 |
17 |
16 |
24 |
2 |
25 |
|
|
8 |
27 |
30 |
7 |
7 |
23 |
|
29 |
3 |
7 |
15 |
22 |
25 |
|
|
10 |
20 |
19 |
26 |
20 |
17 |
|
5 |
20 |
17 |
23 |
10 |
17 |
|
|
18 |
28 |
25 |
7 |
22 |
22 |
|
33 |
11 |
11 |
11 |
34 |
|
|
|
21 |
21 |
9 |
9 |
20 |
|
23. |
30 |
20 |
27 |
15 |
26 |
33 |
|
24. |
11 |
10 |
15 |
8 |
7 |
16 |
|
25 |
6 |
28 |
20 |
5 |
33 |
|
|
12 |
14 |
29 |
20 |
20 |
15 |
|
19 |
24 |
11 |
29 |
23 |
33 |
|
|
18 |
7 |
5 |
25 |
28 |
24 |
|
1 |
4 |
6 |
6 |
8 |
11 |
|
|
24 |
4 |
30 |
24 |
26 |
15 |
|
22 |
22 |
22 |
22 |
22 |
|
|
|
15 |
15 |
15 |
15 |
10 |
|
25. |
30 |
10 |
27 |
15 |
26 |
30 |
|
26. |
11 |
10 |
15 |
8 |
7 |
16 |
|
25 |
6 |
28 |
20 |
5 |
33 |
|
|
12 |
11 |
29 |
20 |
20 |
15 |
|
19 |
24 |
11 |
29 |
23 |
33 |
|
|
18 |
7 |
5 |
25 |
28 |
20 |
|
1 |
4 |
6 |
6 |
8 |
11 |
|
|
24 |
4 |
30 |
24 |
26 |
15 |
|
22 |
18 |
22 |
22 |
22 |
|
|
|
15 |
15 |
11 |
15 |
10 |
|
27. |
30 |
20 |
27 |
15 |
26 |
33 |
|
28. |
11 |
10 |
15 |
8 |
7 |
15 |
|
25 |
6 |
28 |
20 |
5 |
30 |
|
|
12 |
14 |
29 |
20 |
20 |
15 |
|
19 |
24 |
11 |
29 |
23 |
30 |
|
|
18 |
7 |
5 |
25 |
28 |
20 |
|
1 |
4 |
6 |
6 |
8 |
11 |
|
|
24 |
4 |
30 |
24 |
26 |
12 |
|
20 |
22 |
18 |
22 |
22 |
|
|
|
11 |
15 |
11 |
15 |
10 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
29. |
20 |
20 |
21 |
15 |
26 |
33 |
|
30. |
11 |
10 |
15 |
8 |
7 |
16 |
|
25 |
6 |
28 |
20 |
5 |
30 |
|
|
12 |
14 |
29 |
20 |
20 |
10 |
|
19 |
24 |
11 |
26 |
23 |
23 |
|
|
18 |
7 |
5 |
25 |
28 |
20 |
|
1 |
4 |
6 |
6 |
8 |
11 |
|
|
24 |
4 |
30 |
24 |
26 |
15 |
|
14 |
22 |
17 |
22 |
22 |
|
|
|
13 |
11 |
15 |
12 |
10 |
|
31. |
30 |
10 |
27 |
15 |
26 |
20 |
|
32. |
11 |
10 |
15 |
8 |
7 |
12 |
|
25 |
6 |
28 |
20 |
5 |
30 |
|
|
12 |
11 |
29 |
20 |
20 |
15 |
|
19 |
24 |
11 |
29 |
23 |
31 |
|
|
18 |
7 |
5 |
25 |
28 |
18 |
|
1 |
4 |
6 |
6 |
8 |
11 |
|
|
24 |
4 |
30 |
24 |
26 |
15 |
|
20 |
16 |
22 |
18 |
16 |
|
|
|
15 |
15 |
9 |
11 |
10 |
|
33. |
30 |
20 |
27 |
15 |
26 |
33 |
|
34. |
11 |
10 |
15 |
8 |
7 |
15 |
|
25 |
6 |
28 |
20 |
5 |
30 |
|
|
12 |
14 |
29 |
20 |
20 |
15 |
|
19 |
24 |
11 |
29 |
23 |
30 |
|
|
18 |
7 |
5 |
25 |
28 |
20 |
|
1 |
4 |
6 |
6 |
8 |
11 |
|
|
24 |
4 |
30 |
24 |
26 |
12 |
|
20 |
22 |
18 |
22 |
22 |
|
|
|
11 |
15 |
11 |
15 |
10 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
ЗДАНИЕ 4.
А) Решить задачу одномерной оптимизации
для заданной точности , с помощью метода дихотомии.
Варианты заданий
-
№ вар
f(x)
a
b
А.1
-2.9*
+9.8*
3.5
5.5
А.2
-2.7* +9.7*
7.2
9.1
А.3
-2.1*
+8.7*
-0.5
1.1
А.4
2.1* -8.7*
3.8
6.1
А.5
-0.8*
+2.1*
+0.5*x-3.9
0.1
А.6
+4.*
-5.8
-2.1
А.7
-(
+4.68*
)-4.3
-1.9
А.8
1.5*
+1.7*
+0.3*x-4.1
-2.2
А.9
1.5* +1.7* +0.3*x
1.6
4.2
А.10
3.15*
-
3.98*
+1.12-1.6
1.3
А.11
1.75*ln(x+12)+4.36*
-5.35-3.9
-0.6
А.12
-3.5*ln(x+12)-4*
+5.35-6.9
-3.9
А.13
1.75*ln(x+11.34)*
+2.45-8.6
-6.4
А.14
1. 5*ln(x+9)* +2.3
2.1
4.5
А.15
1.1
2.2
А.16
-3.9
1.5
В)
Для заданной функции n
переменных f(x)
, точки
и n-мерного
вектора s
построить одномерное сечение
и
решить задачу минимизации одномерного
сечения :
Варианты заданий
-
№ вар
f(x)
s
В.17
(3.73; 2.5)
(1, 1)
В.18
(-3.4 ; -2.2)
(-1, 1)
В.19
(4.5; 1.25)
(1, -1)
В.20
(-4.5; -1.25)
(-1, -1)
В.21
(2.73; 3.5)
(1, 1)
В.22
(-3.4 ; -2.2)
(-1, 1)
В.23
(1.73; 4.5)
(1, -1)
В.24
(-3.4 ; -2.2)
(-1, -1)
В.25
(3.16; 2.05)
(1, 1)
В.26
(-3.4 ; -2.2)
(-1, 1)
В.27
(2.36; 1.5)
(1, -1)
В.28
(-3.4 ; -2.2)
(-1, 1)
В.29
(3.16; 2.05)
(1, -1)
В.30
(-3.4 ; -2.2)
(-1, -1)
В.31
(2.36; 1.5)
(1, 1)
В.32
(-3.4 ; -2.2)
(-1, 1)
В.33
(2.36; 1.5)
(1, -1)
В.34
(-3.4 ; -2.2)
(-1, 1)
В.35
(3.16; 2.05)
(1, -1)
В.36
(-3.4 ; -2.2)
(-1, -1)
В.37
(2.36; 1.5)
(1, 1)
В.38
(-3.4 ; -2.2)
(-1, 1)
Итоговая аттестация (Экзамен) выставляется по итогам работы в семестре.