Решение оптимизационных задач графическим методом.
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Вариант задания определяется по номеру студента в журнале преподавателя
1. W = 2x1 – 5x2 → min;
3x1 + 4x2 ≤ 6;
2x1 + 3x2 ≤ 4.
2. W = x1 – 4x2 → min;
3x1 + 5x2 ≥ 8;
–3x1 + 10x2 ≤ 16.
3. W = x1 + x2 → max;
x1 + 3x2 ≤ 30;
2x1 + x2 ≤ 20.
4. W = 2x1 + 2x2 → min;
x1 + x2 ≥ 1;
–x1 + x2 ≤ 1.
5. W = 2x1 + 3x2 → max;
x1 ≥ 4;
x2 ≥ 3;
x1 + x2 ≤ 8.
6. W = x1 – 3x2 → min;
x1 + x2 ≤ 3;
–x1 + 2x2 ≤ 5.
7. W = x1 – 3x2 → min;
–x1 + 2x2 ≤ 6;
x1 + 2x2 ≤ 5.
8. W = 2x1 + 5x2 → max;
x1 + x2 ≤ 500;
x1 ≤ 400;
x2 ≤ 300.
8. W = x1 + 4x2 → max;
x1 + x2 ≤ 7;
x1 ≤ 3;
x2 ≤ 1.
9. W = 2x1 + x2 → max;
2x1 + 6x2 ≤ 15;
4x1 + 3x2 ≤ 11.
10. W = 2x1 + 2x2 → min;
x1 + x2 ≥ 4;
–x1 + 2x2 ≤ 8.
11. W = 3x1 + 2x2 → max;
x1 ≥ 1;
x2 ≥ 0,6;
0,1x1 + 0,4x2 ≤ 2.
12. W = x1 + x2 → max;
3x1 + x2 ≤ 20;
2x1 + 3x2 ≤ 30.
13. W = 5x1 + x2 → max;
3x1 + 6x2 ≤ 11;
x1 ≤ 2,75;
3x2 ≤ 1,1.
14. W = x1 – 2x2 → min;
x1 + 10x2 ≤ 1;
–2x1 + 24x2 ≤ 1.
15. W = x1 + 3x2 → max;
4x1 + 8x2 ≤ 17;
x1 ≤ 3;
x2 ≤ 2.
16. W = 2x1 + 3x2 → min;
5x1 + 2x2 ≥ 3;
–4x1 + 6x2 ≤ 9.
17. W = 4x1 + 6x2 → max;
x1 + 15x2 ≤ 32;
x1 ≤ 31;
x2 ≤ 2.
18. W = 4x1 – x2 → min;
4x1 + 6x2 ≤ 9;
–5x1 + 8x2 ≤ 4.
19. W = 2x1 + x2 → min;
5x1 + 3x2 ≥ 7;
–2x1 + 9x2 ≤ 21.
20. W = x1 + 5x2 → max;
2x1 + x2 ≤ 8;
x1 + 3x2 ≤ 7.
21. W = 3x1 – x2 → min;
2x1 + 5x2 ≤ 8;
–3x1 + 8x2 ≤ 4.
22. W = x1 + 3x2 → max;
16x1 + 4x2 ≤ 9;
x1 ≤ 1/3.
x2 ≤ 2/3.
23. W = 5x1 + 4x2 → max;
4x1 + x2 ≤ 9;
x1 + 3x2 ≤ 6.
24. W = 3x1 + x2 → min;
4x1 + x2 ≥ 5;
–3x1 + 10x2 ≤ 50.
25. W = 3x1 + 0,5x2 → max;
x1 ≤ 2;
x2 ≥ 1,8;
2x1 + 5x2 ≥ 12.