Контрольная работа

1. Решить задачу линейного программирования графическим методом:

ƒ= x₁ + ax₂→max

x₁ +2x₂ ≤ 10

3x₁ + 2x₂ ≤ 18

x₁ – x₂ ≥ - b

cx₁ – x₂ ≤ 8c + 3

N	a	b	c	N	a	b	c	N	a	b	c	N	a	b	c
1	5	7	2	6	-1/4	10	2	11	-5/6	8	1/4	16	-3/4	13/2	½
2	1	6	3	7	4	12	½	12	3	13/2	2	17	3/2	7	2
3	-1	6	1/8	8	5/4	9	1/3	13	1	9	1	18	3	6	1
4	5	9	1	9	-1	6	½	14	-1/3	10	2	19	4	8	¾
5	3/4	7	1	10	5/6	7	1	15	7/4	6	3	20	-1	15/2	1/3

2. Решить задачу линейного программирования графическим методом:

Для всех вариантов x₁≥ 0 x₂≥0

1. x1 +6x2≤ 12, 5x1+8x2 ≤ 40 5,5x1+2x2 ≤ 22 ƒ( x ) = 7x1 +4x2→max	2. -x1+2x2≤ 2 3x1+2x2≤ 6 ƒ( x ) = x1 +4x2→max	3. x1-2x2 ≤ 2 -2x1+x2≤ 2 x1+ x2 ≤ 3 ƒ( x ) = x1 +2x2→max	4. 3x1 +5x2≤11, 4x1+x2 ≤ 8 ƒ( x ) = x1 +4x2→max
5. 3x1 +2x2≤5, x2 ≤ 2 ƒ( x ) = x1 +x2→max	6. 3x1 +2x2≤8, x1+4 x2 ≤ 10 ƒ( x ) = 3x1 +4x2→max	7. 5x1 - 2x2≤3, x1+ x2 ≤ 1 ƒ( x ) = x1 -2x2→max	8. x1+2x2 ≤ 10 -4x1+3x2≤ 12 3x1- 4x2 ≤ 12 ƒ( x ) = x1 +x2→max
9. 2x1 +20x2≤ 20, 4x1+8x2 ≤ 16, 12x1+3x2 ≤ 24, ƒ( x ) = x1 +3x2→max	10. 2x1 +5x2≤ 20, 6x1+7x2 ≤ 42, 10x1+3x2 ≤ 30, ƒ( x ) = 4x1 +4x2→max	11. x1 -2x2≤ 2, -2x1+x2 ≤ 2 x1+x2 ≤ 3 ƒ( x ) = x1 +2x2→max	12. 2x1 +5x2≤ 20, 6x1+5x2 ≤ 30 x1-2x2 ≤ 3 ƒ( x ) = 4x1 +2x2→max
13. x1 +4x2≤ 12, x1+2x2 ≤ 10, 2x1+x2 ≤ 12, ƒ( x ) =3x1 +8x2→max	14. 8x1 +2x2≤ 89, x1≤ 22, 5x2 ≤ 90, ƒ( x ) = 4x1 +3x2→max	15. 3x1 -2x2≤ 3, -5x1- 4x2 ≤ -10, 2x1+ x2 ≤ 5, ƒ( x ) = 3x1 - x2→max	16. x1 +4x2≤ 12, 2x1+3x2 ≤ 12, x1 ≤ 4, ƒ( x ) = 4x1+12x2→max
17. 2x1 +18x2≤ 18, 3x1+7x2 ≤21, 4x1+5x2 ≤ 20, ƒ( x ) =2x1 +4x2→max	18. x1 +3x2≤ 15, x1+x2 ≤ 6, 2x1+x2 ≤ 10, ƒ( x ) =x1 +4x2→max	19. 2x1 +2x2≤ 12, 3,5x1+2x2 ≤ 14, 11x1+3x2 ≤ 33, ƒ( x ) =6x1 +2x2→max	20. 2x1 +7x2≤ 14, 3x1+5x2 ≤ 15, 10x1+6x2 ≤ 30, ƒ( x ) =3x1 +2x2→max
21. 3x1 +11x2≤ 33, 3x1+4x2 ≤24, 20x1+4x2 ≤ 40, ƒ( x ) =3x1 +6x2→max	22. 2x1 + x2≤ 6, x1+2x2 ≤10, 3x1- x2 ≤ 3, ƒ( x ) =3x1 +4x2→max	23. 4x1 + 5x2≤ 20, 2x1+ x2 ≤ 6, x1- x2 ≤ 2, ƒ( x ) =3x1 +x2→max	24. 31 +11x2≤ 33, 7x1+6x2 ≤42, 8x1+2x2 ≤ 24, ƒ( x ) =3x1 +6x2→max
25. 2x1 +5x2≤ 20, 6x1+7x2 ≤42, 10x1+3x2 ≤ 30, ƒ( x ) =7x1 +4x2→max	26. x1 + 4x2≤ 12, x1+2x2 ≤10, 2x1+ x2 ≤ 12, ƒ( x ) =3x1 +2x2→max	27. x1 +4x2≤ 12, 2x1+3x2 ≤12, x1≤ 4, ƒ( x ) =4x1 +12x2→max	28. 3x1 +2x2≤ 5, x2 ≤2, ƒ( x ) =x1 +x2→max