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Петербургский государственный университет путей сообщения им. императора Александра I
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[НЕСОРТИРОВАННОЕ]
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СБОРНИК ЗАДАЧ ПО МАТЕМАТИКЕ ДЛЯ ТРАНСПОРТНЫХ СП...doc
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►Содержание►

Вариант 10

    1. f(X) = x1 – 4x2 min

x1 + 2x2 4

x1 – 2x2 -1

0 x1 3

x2 0.

    1. f(X) = 4x1 + 6x2 max

2x1 + x2 16

x1 + x2 10

0 x1 7

0 x2 6.

3. f(X) = x1 + 2x2 min

x1 – x2 1

x1 + x2 -1

x1 0, x2 0.

4.f(X) = x1 – 4x2 + x3 min

x1 + 2x2 + x3 = 3

2x1 + x2 – x3 = 1

xj 0, j = 1,2,3.

5. f(X) = x1 – x2 + 3x3 max

x1 + x2 – 2x3 = 0

x1 + 2x2 – 3x3 = 1

xj 0, j = 1,2,3.

6. f(X) = x1 + 2x2 - x3 max

2x1 - x2 + 2x3 = 4

-x1 + 4x2 – 2x3 6

x1 + x2 + 2x3 6

xj 0, j = 1,2,3.

7. f(X) = x1 + 3x2 + 4x3 max

2x1 + x2 + 4x3 = 2

x1 + x2 -4x3 = 4

xj 0, j = 1,2,3.

8. f(X) = x1 + 2x2 + 3x3 min

2x1 + 2x2 - x3 2

x1 - x2 – 4x3 - 3

x1 + x2 - 2x3 6

2x1 + x2 - 2x3 3

xj 0, j = 1,2,3.

9. f(X) = x1 + 2x2 min

x1 – x2 1

x1 + x2 -1

x1 0, x2 0.

10. f(X) = x1 – 4x2 + x3 min

x1 + 2x2 + x3 = 3

2x1 + x2 – x3 = 1

xj 0, j = 1,2,3.

Вариант 11

  1. f(X) = 2x1 + 3x2 max

-2x1 + 2x2 6

x1 – 4x2 2

x1 – x2 5

x1 0, x2 0.

  1. f(X) = x1 + x2 + x3 + x4 min

2x1 + x2 – x3 + x4 =3

-2x1 + x2 + x3 – x4 = -1

xj 0, j = 1,2,3,4.

  1. f(X) = x1 + 3x2 max

x1 – x2 1

2x1 + x2 2

x1 0, x2 0.

4. f(X) = x1 + 8x2 + 10x3 max

x1 + x2 + 4x3 = 2

x1 – x2 + 2x3 = 1

xj 0, j = 1,2,3.

5. f(X) = x1 + 2x2 - x3 max

- x1 + 4x2 - 2x3 6

x1 + x2 + 2x3 6

2x1 - x2 + 2x3 = 4

xj 0, j = 1,2,3.

6. f(X) = 2x1 + x2 max

x1 + 3x2 - x3 6

x2 + 3x3 4

x1 - x2 + x3 1

xj 0, j = 1,2,3.

7. f(X) = x1 + 2x2 max

2x1 + x2 2

x1 + x2 = 4

x1 0, x2 0.

8. f(X) = x1 + x2 + x3 min

x1 + 2x2 - x3 1

2x1 - x2 + 4x3 6

x1 + x2 - x3 = -1

xj 0, j = 1,2,3.

9. f(X) = x1 + 3x2 max

x1 – x2 1

2x1 + x2 2

x1 0, x2 0.

10. f(X) = x1 + 8x2 + 10x3 max

x1 + x2 + 4x3 = 2

x1 – x2 + 2x3 = 1

xj 0, j = 1,2,3.

Вариант 12

  1. f(X) = x1 – x2 + x3 min

x1 + 2x2 – x3 + x4 = 3

x1 – 4x2 + x3 = -2

xj 0, j = 1,2,3,4.

  1. f(X) = x1 + x2 max

x1 + x3 = 2

x2 – x3 + x4 = 1

xj 0, j = 1,2,3,4.

  1. f(X) = x1 + 2x2 – x3 min

2x1 – x2 + x3 5

x1 + 2x3 = 4

x1 – 2x2 = 1

xj 0, j = 1,2,3.

  1. f(X) = 6x1 + 3x2 max

2x1 + 3x2 16

2x1 + x2 15

x1 0, x2 0.

  1. f(X) = -4x1 - 7x2 -8x3 -5x4 max

x1 + x2 + 2x4 4

2x1 + x2 + 2x3 6

xj 0, j = 1,2,3,4.

  1. f(X) = x1 + x2 - x3 -2x5 min

x1 – 2x2 + x4 = -3

x3 - 2x4 = 2

3x1 – x4 + x5 5

x2 + x3 3

xj 0, j = 1,2,3,4,5.

7. f(X) = x1 - 2x2 max

2x1 + 3x2 7

x1 + x2 = 2

x1 + 4x2 5

xj 0, j = 1,2.

8. f(X) = x1 - 2x2 + 3x3 min

3x1 + 5x2 8

2x1 – x2 + x3 = 2

x1 + x2 - 2x3 5

xj 0, j = 1,2,3.

9. f(X) = x1 + 2x2 – x3 min

2x1 – x2 + x3 5

x1 + 2x3 = 4

x1 – 2x2 = 1

xj 0, j = 1,2,3.

10. f(X) = 6x1 + 3x2 max

2x1 + 3x2 16

2x1 + x2 15

x1 0, x2 0.

Вариант 13

  1. f(X) = x1 + x2 max

0 x1 1

0 x2 2

0 x1 + x2 3

-1 x1 – x2 0.

2. f(X) = x1 + 2x2 + x3 max

x1 + x2 + 2x3 = 12

x1 + x2 2

x1 + 2x2 3

xj 0, j = 1,2,3.

3. f(X) = 2x1 + x2 max

x1 + x2 150

0.01x1 + 0.03x2 1

x1 0, x2 0.

  1. f(X) = 12x1 + x2 min

2x1 – x2 14

x1 + x2 6

xj 0, j = 1,2.

5. f(X) = x1 + 3x2 + 4x3 + 2x4 min

x1 - x2 + 4x3 + 5x4 27

2x1 + 3x2 - x3 + 4x4 24

xj 0, j = 1,2,3,4.

6. f(X) = x1 + 2x2 + x3 max

x1 + x2 + 2x3 =12

x1 + x2 2

x1 + 2x2 3

xj 0, j = 1,2,3.

7. f(X) = 2x1 - 9x2 min

3x1 + 2x2 7

x1 + x2 2

x1 + 5x2 = 4

xj 0, j = 1,2.

8. f(X) = x1 - 2x2 + 5x3 max

x1 + 2x2 - x3 = 2

x1 + 4x2 + x3 5

x2 + x3 4

xj 0, j = 1,2,3.

9. f(X) = 2x1 + x2 max

x1 + x2 150

0.01x1 + 0.03x2 1

x1 0, x2 0.

10. f(X) = 12x1 + x2 min

2x1 – x2 14

x1 + x2 6

xj 0, j = 1,2.

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