Составители:
Рубрика:
12
4. ВАРИАНТЫ ЗАДАНИЙ
Найти решение задачи линейного программирования симплекс-
методом.
1. Z = x
1
+ x
2
+ x
3
+ x
4
+ x
6
→ max
x
1
+ x
2
+ x
3
+ x
4
- x
5
- x
6
= 1 x
j
≥ 0,
x
2
+ x
3
- x
4
- x
5
- x
6
= 1 6,1j =
x
2
- x
6
= 2.
2. Z = x
1
+ x
3
+ x
5
+ x
6
→ max
x
1
+ 4x
2
+ x
3
+ 3x
4
- 2x
5
+ x
6
= 15 x
j
≥ 0,
x
1
+ 4x
2
- x
3
- x
4
+ x
6
= 5 6,1j =
2x
1
+ 6x
2
+ x
3
+ 4x
4
- 2x
5
+ x
6
= 22.
3. Z = x
1
- 2x
2
+ x
3
- 8x
4
+ x
5
+ x
6
→ max
x
1
+ 4x
2
+ x
3
+ 3x
4
- 2x
5
+ x
6
= 15 x
j
≥ 0,
x
1
+ 4x
2
- x
3
- x
4
+ x
6
= 5
6,1j =
2x
1
+ 6x
2
+ x
3
+ 4x
4
- 2x
5
+ x
6
= 22.
4. Z = x
1
+ x
3
+ x
6
→ max
x
1
+ x
2
+ x
3
+ x
4
- x
5
- x
6
= 1 x
j
≥ 0,
x
2
+ x
3
- x
4
- x
5
- x
6
= 1
6,1j =
x
2
- x
6
= 2.
5. Z = x
1
+ 2x
2
+ x
3
- 2x
4
+ x
5
- 2x
6
→ min
x
1
- x
2
+ x
3
- x
4
+ x
5
- x
6
= 7
2x
1
+ 3x
2
- 2x
3
- 3x
4
+ 2x
5
+ 3x
6
= 3
3x
1
+ 2x
2
- x
3
- 4x
4
+ 3x
5
+ 2x
6
= 10.
6. Z = x
1
- 4x
2
+ x
3
+ x
4
+ x
5
+x
6
→ min
- 2x
1
+ x
2
+ x
3
+ x
5
= 20
-x
1
- 2x
2
+ x
4
+ 3x
5
= 24
3x
1
- x
2
- 12x
5
+ x
6
= 18.
7. Z = 2x
1
- 6x
2
+ 3x
5
→ max
- 2x
1
+ x
2
+ x
3
+ x
5
= 20
- x
1
- 2x
2
+ x
4
+ 3x
5
= 24
3x
1
- x
2
- 12x
5
+ x
6
= 18.
8. Z = x
1
+ x
2
+ x
3
+ 2x
4
+ 3x
5
+ 2x
6
→ max
- 2x
1
+ x
2
+ x
3
+ x
5
= 20
- x
1
- 2x
2
+ x
4
+ 3x
5
= 24
3x
1
- x
2
- 12x
5
+ x
6
= 18.
4. ВАРИАНТЫ ЗАДАНИЙ
Найти решение задачи линейного программирования симплекс-
методом.
1. Z = x1 + x2 + x3 + x4 + x6 → max
x1 + x2 + x3 + x4 - x5 - x6 = 1 xj ≥ 0,
x2 + x3 - x4 - x5 - x6 = 1 j = 1,6
x2 - x6 = 2.
2. Z = x1 + x3 + x5 + x6 → max
x1 + 4x2 + x3 + 3x4 - 2x5 + x6 = 15 xj ≥ 0,
x1 + 4x2 - x3 - x4 + x6 = 5 j = 1,6
2x1 + 6x2 + x3 + 4x4 - 2x5 + x6 = 22.
3. Z = x1 - 2x2 + x3 - 8x4 + x5 + x6 → max
x1 + 4x2 + x3 + 3x4 - 2x5 + x6 = 15 xj ≥ 0,
x1 + 4x2 - x3 - x4 + x6 = 5 j = 1,6
2x1 + 6x2 + x3 + 4x4 - 2x5 + x6 = 22.
4. Z = x1 + x3 + x6 → max
x1 + x2 + x3 + x4 - x5 - x6 = 1 xj ≥ 0,
x2 + x3 - x4 - x5 - x6 = 1 j = 1,6
x2 - x6 = 2.
5. Z = x1 + 2x2 + x3 - 2x4 + x5 - 2x6 → min
x1 - x2 + x3 - x4 + x5 - x6 = 7
2x1 + 3x2 - 2x3 - 3x4 + 2x5 + 3x6 = 3
3x1 + 2x2 - x3 - 4x4 + 3x5 + 2x6 = 10.
6. Z = x1 - 4x2 + x3 + x4 + x5 +x6 → min
- 2x1 + x2 + x3 + x5 = 20
-x1 - 2x2 + x4 + 3x5 = 24
3x1 - x2 - 12x5 + x6 = 18.
7. Z = 2x1 - 6x2 + 3x5 → max
- 2x1 + x2 + x3 + x5 = 20
- x1 - 2x2 + x4 + 3x5 = 24
3x1 - x2 - 12x5 + x6 = 18.
8. Z = x1 + x2 + x3 + 2x4 + 3x5 + 2x6 → max
- 2x1 + x2 + x3 + x5 = 20
- x1 - 2x2 + x4 + 3x5 = 24
3x1 - x2 - 12x5 + x6 = 18.
12
