Задание 1
Решить задачу линейного программирования обычным симплекс-методом и методом искусственного базиса (найти оба экстремума):
Вариант |
Задача |
Вариант |
Задача |
1 |
F=x1+4x2+x3max (min) |
16 |
F=2x12x22x3 max (min) |
2 |
F=2x1+3x2x3 max (min) |
17 |
F=3x12x22x3 max (min) |
3 |
F=x1x2+x3 max (min) |
18 |
F=2x1+8x2+3x3 max (min) |
4 |
F=5x1+2x2+x3 max (min)
|
19 |
F=6x1+7x2+9x3 max (min) |
5 |
F=x18x23x3 max (min)
|
20 |
F=5x1+2x2+x3 max (min) |
6 |
F=x13x2x3 max (min) |
21 |
F=6x1x2+3x3 max (min) |
7 |
F=x1+4x2+3x3 max (min)
|
22 |
F=2x1+2x2x3 max (min) |
8 |
F=4x13x22x3 max (min)
|
23 |
F=x1+3x2+x3 max (min) |
9 |
F=4x1+x2+3x3 max (min) |
24 |
F=2x1+3x2+2x3 max (min) |
10 |
F=x13x22x3 max (min)
|
25 |
F=2x1+2x25x3 max (min) |
11 |
F=3x1+2x2+2x3 max (min) |
26 |
F=x1+2x2+2x3 max (min) |
12 |
F=3x1+2x2+3x3 max (min) |
27 |
F=5x1+7x2+9x3 max (min) |
13 |
F=x1+2x2+x3 max (min) |
28 |
F=x1+x24x3 max (min) |
14 |
F=2x1+x2+2x3 max (min) |
29 |
F=3x1+2x23x3 max (min) |
15 |
F=6x1+7x2+9x3 max (min) |
30 |
F=3x1+x2+2x3 max (min) |
Задание 2
Дана задача параметрического программирования:
Z=()x1+()x2max(min)
Решить задачу: а) графическим (геометрическим) методом; б) симплекс-методом.
Значения коэффициентов целевой функции
№ вари-анта
Значения |
1, 13, 22 |
2, 11, 25 |
3, 17, 21 |
4, 16, 27 |
5, 19, 26 |
6, 14, 28 |
7, 18, 24 |
8, 20, 29 |
9, 12, 30 |
10, 15, 23 |
1 |
1 |
2 |
1 |
3 |
2 |
2 |
1 |
3 |
2 |
|
1 |
2 |
1 |
2 |
1 |
3 |
1 |
3 |
1 |
3 |
|
2 |
2 |
1 |
2 |
1 |
3 |
1 |
3 |
4 |
1 |
|
1 |
1 |
1 |
1 |
2 |
1 |
1 |
1 |
1 |
2 |
|
a11 |
1 |
1 |
2 |
2 |
3 |
3 |
1 |
1 |
1 |
1 |
a12 |
2 |
2 |
1 |
1 |
1 |
1 |
1 |
1 |
2 |
2 |
b1 |
4 |
4 |
6 |
6 |
3 |
3 |
3 |
3 |
2 |
2 |
a21 |
1 |
1 |
1 |
1 |
1 |
1 |
2 |
2 |
2 |
2 |
a22 |
1 |
1 |
3 |
3 |
1 |
1 |
1 |
1 |
1 |
1 |
b2 |
1 |
1 |
11 |
11 |
2 |
2 |
7 |
7 |
1 |
1 |
a31 |
2 |
2 |
3 |
3 |
4 |
4 |
3 |
3 |
1 |
1 |
a32 |
3 |
3 |
2 |
2 |
1 |
1 |
2 |
2 |
1 |
1 |
b3 |
3 |
3 |
2 |
2 |
3 |
3 |
7 |
7 |
0 |
0 |
Диапазон измен. |
[5; 5] |
[10; 1] |
[10; 10] |
[0; 8] |
[6; 6] |
[8; 8] |
[4; 4] |
[3; 3] |
[7; 7] |
[3; 3/4] |