СРС 2 ВСК 2. Задачи

1.

СРС 2 ВСК 2
Задачи 1.1 – 1.30. Решить графически следующие задачи ЛП.
1.1
f x1 2x2 min ;
x1 x 2 1,
x x 2,
1 2
x1 2 x 2 0,
x1 0, x 2 0
1.2
f 5x1 3x2 max ;
3 x1 5 x 2 15,
5 x1 2 x 2 10,
x 0, x 0
2
1
1.3
f x1 3x2 max ;
x1 x 2 1,
2 x x 2,
1
2
x1 x 2 0,
x1 0, x 2 0
1.4
f 2x1 3x2 max ;
3 x1 2 x 2 6,
x1 x 2 1,
x 0, x 0
2
1

2.

1.5
f 2x1 3x2 min ;
3 x1 2 x 2 6,
x1 4 x 2 4,
x 0, x 0
2
1
1.6
f x1 x2 max ;
x1 2 x 2 10,
x 2 x 2,
1
2
2 x1 x 2 10,
x1 0, x 2 0
1.7
f 3 p1 2 p2 max ;
2 p1 3 p 2 21,
4 p1 p 2 17,
p 0, p 0
2
1
1.8
f 2 p1 3 p2 min ;
p1 3 p 2 12,
2 p1 p 2 10,
p 0, p 0
2
1
1.9
f 2x1 3x2 max ;
2 x1 4 x 2 9,
5 x1 x 2 6,
x 0, x 0
2
1
1.10
f 4x1 6x2 max ;
2 x1 3 x 2 7,
2 x x 5,
1
2
2 x1 4 x 2 9,
x1 0, x 2 0

3.

1.11
1.13
f 5x1 2x2 max ;
x1 3 x 2 3,
2 x x 2,
1
2
3 x1 2 x 2 6,
x1 0, x 2 0
1.12 f 2x1 8x2 max(min)
f 2x1 3x2 min ;
x1 x 2 12,
3x1 3x 2 15,
x 0, x 0
2
1
1.14
x1 2 x 2 4,
3x1 x 2 3,
x 0, x 0
2
1
f 3x1 4x2 min ;
x1 x 2 20,
x 4 x 20,
1
2
x1 10,
0 x 2 5

4.

1.15
f 6x1 2x2 min ;
2 x1 4 x 2 9,
3 x1 x 2 6,
x 0, x 0
2
1
1.16
f x1 x2 min ;
x1 x 2 1,
2 x x 10,
1 2
x1 0,
0 x 2 2
1.17
f x1 x2 min ;
2 x1 x 2 2,
x 2 x 2,
1
2
x1 x 2 5,
x1 0, x 2 0
1.18
f 5x1 3x2 max ;
3 x1 5 x 2 15,
5 x1 2 x 2 10,
x 0, x 0
2
1

5.

1.19
f x1 x2 min ;
2 x1 x 2 4,
x x 2,
1 2
x1 x 2 5,
x1 0, x 2 0
1.20
f x1 2x2 max ;
3 x1 2 x 2 6,
x 2 x 4,
1
2
3 x1 2 x 2 12,
x1 0, x 2 0
1.21
f 2x1 x2 max ;
x1 x 2 2,
x 2 x 7,
1
2
4 x1 3 x 2 6,
x1 0, x 2 0
1.22
f 7 x1 5x2 min ;
x1 x 2 3,
x 5 x 5,
1
2
2 x1 x 2 4,
x1 0, x 2 0

6.

1.23
f x1 x2 max ;
1.24
3 x1 x 2 1,
x1 3 x 2 5,
x 0, x 0
2
1
x1 3 x 2 6,
3 x1 x 2 6,
x 0, x 0
2
1
1.25
f 8 x1 4 x2 max ;
4 x1 x 2 9,
2 x1 x 2 5,
x 0, x 0
2
1
f 2 x1 x2 min
1.26
f x1 2x2 max ;
x1 2 x2 6,
3x1 5 x2 15,
x 0
2

7.

1.27
1.29
f x1 2x2 max ;
3x1 2 x 2 6,
x1 3x 2 3,
x 0
2
f 2x1 4x2 max ;
2 x1 x2 6,
3x 2 x 12,
1
2
x2 4,
x1 , x2 0.
1.28
f 2 x1 x2 max
2 x1 x 2 2,
x1 x 2 2,
x 0, x 0
2
1
1.30 f =5x1 + 4x2 → max
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