ВТОРОЙ ВОПРОС Найти графическим методом решение задачи линейного программирования (в соответствии с вариантом)
Задача 1
z= 2x1 + 3x2→max;
x1 + 2x2 ≥4;
2x1 -x2 ≥9;
5x1+ 3x2 ≤ 30;
4x1 - l- 7x2≤28;
x1 ≥ 0, x2 ≥ 0.
Задача2
z= 3x1 - 3x2→max;
x1 - 4x2 ≤ 4;
3x1 + 2x2 ≤ 6;
-x1 + x2 ≥ 7;
x1 + 2x2 ≤ 2;
x1 ≥ 0, x2 ≥ 0.
Задача3
z= 3x1 + 4x2→max;
-2x1 + x2 ≤ 1;
4x1+ 6x2 ≤ 12;
6x1 + 3x2 ≤ 9;
x1 + x2 ≥ 6;
2x1 – 4x2 ≥ 2;
x1 ≥ 0, x2 ≥ 0.
Задача4
z= x1 + 2x2→max;
x1 + x2 ≤ 4;
3x1 + x2 ≥ 4;
x1 + 5x2 ≥ 4;
x1 ≤ 3;
x2 ≤ 3;
x1 ≥ 0,
x2 ≥ 0.
Задача5
z= x1 + x2→max;
-4x1 + x2 ≤ 1;
2x1 - 3x2 ≤ 6;
2x1 + x2 ≤ 8;
-x1 +x2≤7;
x1 + 2x2 ≥ 2;
x1 ≥ 0, x2 ≥ 0.
Задача6
z= 2x1 + x2→max;
2x1- x2 ≥ 4;
3x1 + 2x2 ≥ 3;
3x1 - x2 ≤ 6;
7x1 + x2 ≤ 7;
x1 ≥ 0, x2 ≥ 0.
Задача7
z = x1 + x2 →max;
-4x1 + x2 ≤ 2;
2x1 - 3x2 ≤ 3;
2x1 + x2 ≤ 8;
x1 - 4x2≤4;
x1 ≥0, x2≥0.
Задача 8
z = 7x1 + 6x2 →max;
2x1+ 5x2 ≥ 10;
5x1 + 2x2≥ 10;
x1 ≤6;
x2≤5;
x1 ≥ 0, x2 ≥ 0.
Задача 9
z = x1+ x2 - x3 + x5 + 15→min;
-3x1 + x2 + x3 = 3;
4x1 + 2x2 - x4 = 12;
2x1 _ x2 + x5 = 2;
x1, x2, x3, x4, x5 ≥0.
Задача 10
z = x1 + 2x2 + x4 + 3x5 + 6→ max;
x1 - 2x2 + x3 = 1;
2x1 + x2 — x4 = 8;
x1 + 2x2 + x5 = 3;
x1, x2, x3, x4, x5 ≥ 0.
Задача 11
z = x1 + 5x2→min;
x1 - 2x2 ≤ 2;
-2x1 - 3x2 ≤ -4;
-2x1 + x2≤ 2;
x1 ≥ 0, x2 ≥ 0.
Задача 12
z = 3x1 + x2→max;
-x1 + x2 ≥ 1;
x1 + 3x2 ≤ 15;
-2x1 + x2 ≤ 4;
x1 ≥0,x2 ≥0.
Задача 13
z =x1 + 2x2 + x4 + x5 + 3 → max;
- x1 - 2x2 + x3 = 1;
2 x1 + x2-x4 = 4;
x1 + 2x2 + x5 = 5;
x1, x2, x3, x4, x5 → 0.
Задача 14
z= 3x1 + 2x2 →min;
x1 - 2x2 ≤ 1;
-2x1 - 3x2 ≤ -2;
-2 x1 + x2 ≤ 4;
x1 ≥ 0, x2 ≥ 0.
Задача 15
z= 3x1 + 4x2 → max;
x1 + 2x2 ≤ 4;
-2x1 - 2x2 ≥ 2;
2 x1 + 4x2 ≤ 8;
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x1 + 3x2 ≤ 6;
4x1 - 2x2 ≤ 4;
x1 ≥0, x2≥ 0.
Задача 16
z = 5x1 + x2 → min;
x1 + 7x2 ≥ 7;
5 x1 + 2x2≥ 10;
-2x1 + x2 ≤ 6;
7x1 + x2 ≥ 7;
2x1 + 5x2 ≥ 10; 2 x1 ≤ 12;
x2≤7;
x1 ≥ 0, x2 ≥ 0.
Задача 17
z= 3x1 - x2 + 2x3 - x4 - 3 → min;
- x1 + 2x2-x3 = 1;
2x1 - x2 + x5 = 5;
x1 + x2 - x4 = 2;
x1, x2, x3, x4, x5≥0
Задача18
z= -6x1 + 8х2→ min;
9x1 + Зх2 ≥ 9;
-2x1 + 2х2 ≤ 4;
2x1- Зх2 ≤ -5;
x1 ≥ 0, х2 ≥ 0.
Задача19
z= -2x1 + 4х2 + 6→min;
x1 - 3x2 ≤ 1;
x1 + х2 ≤ 5;
-x1 + x2 ≤ 2;
x1 ≥ 0, х2 ≥ 0.
Задача20
z = 2x1 + 2х2→mах;
x1 - х2 ≥ - 4;
6x1 + 7х2 ≤ 42;
Зx1 – 2x2 ≤ 6;
х2≤4;
x1 ≥ 0, х2 ≥ 0.
Задача21
z= 5x1 - Зх2→min;
Зx1 + 2х2 ≥ 6;
2x1 - Зх2 ≥ - 6;
x1 - х2 ≤ 4;
4x1 + 7х2 ≤ 14;
x1 ≥ 0,х2 ≥ 0.
Задача22
z= 5x1 + Зх2→min;
2x1 + 2х2 ≥ 6;
2x1 – 2x2 ≥ -6;
x1 + 2х2 ≤ 4;
4x1 + Зх2 ≤ 12;
x1 ≥ 0, х2 ≥ 0.
Задача23
z = 2x1 - Зх2→min;
Зx1 + 2х2 ≥ 6;
x1 - 0,5x2 ≤ 2;
x1 + 2,5х2 ≤ 5;
x1 ≥ 0, х2 ≥ 0.
Задача24
z = 2x1 - 4х2→mах;
8x1 – 5x2 ≤ 16;
x1 + Зх2 ≥ 3;
2x1 + 5х2 ≤ 10;
x1 ≥ 0, х2 ≥ 0.
Задача25
z = x1 + 2х2 →min;
-Зx1 + 2х2 ≤ 9;
Зx1 + 4х2 ≥ 28;
2x1 + х2 ≤ 8;
x1 ≥ 0, х2 ≥ 0.
Задача26
z = x1 + Зх2→mах;
-Зx1 + 4х2 ≤ 12;
Зx1 + Зх2 ≤ 9;
Зx1 - 4х2 ≤ 3;
2x1 + Зх2 ≤ 6;
x1 ≥ 0, х2 ≥ 0.
Задача27
z = 2x1 - 4х2→min;
4x1 + Зх2 ≤ 12;
x1 + Зх2 ≥ 6;
2x1 + 5х2 ≤ 10;
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x1 ≥ 0, х2 ≥ 0.
Задача28
z = 2x1 + Зх2→mах;
2x1 - 4х2 ≥ 8;
x1 + х2 ≥ 4;
Зx1 + 6х2 ≤ 12;
x1 ≥ 0, х2 ≥ 0.
Задача29
z = x1 + 4х2→mах;
- x1 + х2 ≤ 5;
x1 + х2 ≤ 8;
Зx1 + 2х2 ≤ 18;
x1 ≥ 0, х2 ≥ 0.
Задача 30
z = 4 x1 + 2х2→min;
x1 + 4х2 ≥ 8;
5x1 + Зх2 ≥ 15;
7x1 + х2 ≥ 7;
Зx1 + 5х2 ≥ 15;
x1 ≥ 0, х2 ≥ 0.
Задача 31
z = 2x1 + х2→mах;
-x1 + 2х2 ≤ 14;
7x1 + 4х2 ≤ 28;
4x1 - Зх2 ≤ 12;
5x1 + 2х2 ≥ 10;
10x1 - 8х2 ≥ 2;
x1 ≥ 0, х2 ≥ 0.
Задача 32
z = x1 - Зх2→ min;
x1 + х2 ≤ 3;
- x1 + 2х2 ≤ 5;
x1 ≥ 0, х2 ≥ 0.
Задача33
z = x1 + 2х2→min;
-Зx1 +4х2 ≤ 12;
x1 + 4х2 ≥ 4;
Зx1 - 4х2 ≥ 10;
x1 ≥ 0, х2 ≥ 0.
Задача34
z = x1 + х2→mах;
З x1 + х2 ≤ 20;
2x1 + Зх2 ≤ 30;
x1 ≥ 0, х2 ≥ 0;
Задача35
z = x1 + х2→mах;
x1 + Зх2 ≤ 30;
2x1 + х2 ≤ 20;
x1 ≥ 0, х2 ≥ 0.
Задача36
z = 2x1 + х2→mах;
2x1 + 6х2 ≤ 15;
4x1 + Зх2 ≤ 11;
x1 ≥ 0, х2 ≥ 0.
Задача 37
Z = 2x1 + 2х2→max;
0,2x1 + Зх2 ≤ 24;
0,5x1 + 0,1x2 ≤ 5;
Зx1 + 2x2 ≤ 30;
x1 ≥ 0, х2 ≥ 0.
Задача 38
z = x1 + x2→max;
Зx1 + х2 ≤ 20;
2x1 + Зх2 ≤ 30;
x1 ≥ 0, х2 ≥ 0.
Задача 39
z = x1 - Зх2→min;
- x1 + 2х2 ≤ 6;
x1 + 2х2 ≤ 5;
x1 ≥ 0, х2 ≥ 0.
Задача 40
z = 2 x1 + х2→max;
2x1 + 6х2 ≤ 15;
4x1 + 3x2 ≤ 11;
x1 ≥ 0, х2 ≥ 0;
Задача 41
z = 2x1 + 2х2→min;
x1 + x2 ≥ 4;
-x1 + 2х2 ≤ 8;
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5x1 + 2х2 ≤ 10;
x1 ≥ 0, х2 ≥ 0.
Задача 42
z = x1 - 4х2→min;
3x1 + 5х2 ≥ 8;
-Зx1 + 10х2 ≤ 16;
x1 ≥ 0, х2 ≥ 0.
Задача 43
z = Зx1 + 2х2 →max;
x1 ≥ 1;
x2 ≥0,6;
0,1x1 + 0,4x2 ≤ 2;
x1 ≥ 0, x2 ≥ 0.
Задача 44
z = x1 + 2х2→max;
-Зx1 + 2х2 ≤ 9;
Зx1 + 4х2 ≥ 28;
2x1 + x2 ≤ 8;
x1 ≥ 0, x2 ≥ 0.
45
z = x1 + x2→max;
-4x1 + x2 ≤ 1;
2x1 – 3x2 ≤ 6;
2x1 + x2 ≤ 8;
-x1 + x2 ≤ 7;
x1 + 2x2 ≥ 2;
x1 ≥ 0, x2 ≥ 0.
46
z = x1 + x2→max;
3x1 + x2 ≤ 20;
2x1 + 3x2 ≤ 30;
x1 ≥ 0,x2 ≥ 0.
47
z = x1 +x2-x3 +x5 + 15→min;
-3x1 + x2 + x3 = 3;
4x1 + 2x2 - x4 = 12;
2x1 – x2 + x5 = 2;
x1, x2, x3, x4, x5 ≥ 0
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x = 3x1 + 2x2 →max; |
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0,1x1 + 0,4x2 ≤4; |
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Зx1 + 5x2 ≤ 15; |
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x1 + x2 ≥ 1; |
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x2 ≥ 0,6; |
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x1 ≥1. |
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z = 5x1 + x2 →max; | |||
3x1 + 6x2 ≤ 11; | |||
x1 ≤ 2,75; | |||
3x2 ≤ 1,1; | |||
x1 ≥ о, x2 ≥ 0. | |||
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