6.Решить задачу графическим методом

Вариант	Задача	Вариант	Задача
1	Z(X)=2x1+3x2→max, -2x1+ x2≤2, x1- 3x2≥-9, 4x1+3x2≤24, x1≥0, x2≥0	9	Z(X)=2x1- x2→max, -x1+ x2≤2, 2x1+3x2≥16, x1 + x2≤10, 2x1 + x2≤8, x1≥0, x2≥0
2	Z(X)=5x1 - 3x2→min, 4x1 - x2≥0, -x1 + x2≤3, 2x1 - 3x2≤6, x1≥0, x2≥0	10	Z(X)=3x1+2x2→max, 2x1 - x2≥0, -x1+ 2x2≤3, x2≤3, x1≥0, x2≥0
3	Z(X)=2x1+3x2→max, -6x1+ x2≤3, -5x1+9x2≤45, x1 - 3x2≤3, x1≥0, x2≥0	11	Z(X)=2x1+4x2→min, 2x1 + x2≥9, x1+ 2x2≤15, x1+ 2x2≥9, 2x1 + x2≤15, x1≥0, x2≥0
4	Z(X)=2x1+2x2→max, -3x1+2x2≤4, -x1+2x2≤8, x1 + x2≤10, 4x1 - x2≤20, x1≥0, x2≥0	12	Z(X)= x1 - 3x2→min, -x1+2x2≤12, 2x1 - x2≤6, -x1 + x2≤3, 2x1 + x2≤6
5	Z(X)=2x1+4x2→max, -3x1+2x2≤6, x1+2x2≥10, x1 - 5x2≤5, x1 + x2≤4, x1≥0, x2≥0	13	Z(X)=3x1 - x2→max, -3x1+ 2x2≤6, 2x1 -3x2≤6, x1 ≤6, x2≤6, x1≥0, x2≥0
6	Z(X)=15x1+10x2→max, 6x1 - x2≥3, -x1 + 2x2≤8, 3x1 + 2x2≤24, x1 - x2≤3, x1 + 2x2≥2, x1≥0, x2≥0	14	Z(X)= x1 - 2x2→min, 2x1 - x2≥-2, -x1+2x2≤7, -4x1+3x2≥-12, x1 +3x2≥18, x1≥0, x2≥0
7	Z(X)=3x1+2x2→max, 3x1 - x2≥0, x1 - x2≥-2, 4x1 - x2≤16, 2x1 - x2≤6, x1≥0, x2≥0	15	Z(X)=3x1+6x2→max, -4x1+ x2≥0, x1 - x2≥-3, 2x1 -3x2≤6, x1≥0, x2≥0
8	Z(X)=2x1 + 5x2→min, 2x1 + x2≥4, -x1 + x2≤4, x1 +2x2≤14, -x1 +3x2≥5, x1≥0, x2≥0	16	Z(X)=5x1+5x2→max, -2x1 + x2≤2, -x1+3x2≥9, x1 + x2≥3, x1≥0, x2≥0
17	Z(X)= - x1 - x2→min, -3x1+2x2≤4, -x1+ 2x2≤8, x1 + x2≥10, 4x1 - x2≤20, x1≥0, x2≥0	25	Z(X)= x1 -4x2→min, x1 - 3x2≤0, x1 - x2≥0, 2x1 + x2≥6, 2x1 +3x2≤18, x1≥0, x2≥0
18	Z(X)=5x1+5x2→ min, 2x1 - 3x2≤0, -5x1+9x2≤45, x1-2x2≤4, x1≥0, x2≥0	26	Z(X)=-5x1+ x2→min, 2x1-3x2≥0, x1+3x2≥9, x1- 3x2≤3, -x1+3x2≤3, x1≥0, x2≥0
19	Z(X)=4x1+ 2x2→ min, -3x1+2x2≤6, x1+2x2≥10, x1-3x2≤6, x1+ x2≥3, x1≥0, x2≥0	27	Z(X)=4x1+ 3x2→ min, 2x1+ 3x2≥0, 2x1+ x2≥4, 3x1- x2≥0, 2x1+ 3x2≤12, x2≥0
20	Z(X)=-3x1 - x2→min, 4x1 - x2≥0, 2x1 - x2≤0, x1 + x2≤3, x1≥0, x2≥0	28	Z(X)=2x1+3x2→min, x1+ x2≥2, x1- x2≤0, 3x1+ x2≥6, 3x1- x2≥6,
21	Z(X)=2x1+3x2→max, x1+ 2x2≥2, x1+ x2≥2, 2x1+ x2≥4, 2x1 - 3x2≤0 x1≥0	29	Z(X)=3x1 - x2→min, 2x1 - x2≤4, -x1 + x2≤2, 3x1 -2x2≥0, x1- x2≤0
22	Z(X)=4x1+ 6x2→ max, 4x1-5x2≥0, 2x1- 3x2≤0, 2x1+3x2≥6, 2x1 + x2≥2,	30	Z(X)=3x1+4x2→max, 4x1- x2≥0, -x1+ x2≤3, 3x1 +2x2≥6, 2x1 - 5x2≥0, x1≥0, x2≥0
23	Z(X)=-x1 +4x2→min, 2x1 - 3x2≤6, 3x1 - 2x2≤6, 2x1 + 3x2≥0, x1 + x2≥-1, x2≥0	24	Z(X)= x1 +4x2→min, 2x1+3x2≥6, -2x1+3x2≥6, x1 + x2≤3, 2x1 - 3x2≤0, x1≥0, x2≥0

7. Решить задачу а)графическим методом;

б) методом искусственного базиса.

В-т	Задание	В-т	Задание
1	Z(X)=2x1+8x2+3x3+4x4→min, 13x1-3x2+2x3-7x4=8, -7x1-2x2 - x3+4x4=-2, xj≥0, j=1, 2, 3, 4	13	Z(X)=-2x1+x2+3x3-2x4→min, 3x1-x2-4x3 + x4=2, 5x1-x2-7x3+2x4=6, xj≥0, j=1, 2, 3, 4
2	Z(X)=2x1+3x2-x3+4x4→min, 2x1+3x2 +7x4=21, -x1-2x2+x3-5x4=-12, xj≥0, j=1, 2, 3, 4	14	Z(X)=-2x1 + 2x2-3x3 - 7x4→min, -x1 - 8x2 + x3 + 6x4=-2, 3x1+27x2- 4x3-22x4=-22, xj≥0, j=1, 2, 3, 4
3	Z(X)=4x1+13x2+3x3+6x4→min, -5x1+ 3x2 - x3+2x4=-1, 9x1- 4x2 +2x3- 3x4=-2, xj≥0, j=1, 2, 3, 4	15	Z(X)=2x1+x2-4x3+3x4→max, -2x1 + 3x3- 4x4=-2, 3x1+x2- 5x3+2x4=7, xj≥0, j=1, 2, 3, 4
4	Z (X)=x1 + x2+ 3x3 + x4→min, 5x1 - 6x2 + x3-2x4=2, x1-14x2+2x3-5x4=2, xj≥0, j=1, 2, 3, 4	16	Z (X)=2x1+6x2 + x3+ x4→max, -4x1 +5x2 +2x3- x4=-2, 5x1- 8x2 - 3x3+x4=7, xj≥0, j=1, 2, 3, 4
5	Z(X)= 11x2 + x3+4x4→min, 4x1 - 5x2 + x3 - x4=1, 11x1-11x2+ 3x3- 2x4=11, xj≥0, j=1, 2, 3, 4	17	Z(X)=2x1+5x2+ x3+x4→max, 5x1-2x2­-3x3+x4=1, 3x2+2x3+x4=6, xj≥0, j=1, 2, 3, 4
6	Z(X)=4x1+ 4x2-3x3+2x4→min, 2x1+13x2-4x3+3x4=19, 3x1 + 7x2 - x3+2x4=16, xj≥0, j=1, 2, 3, 4	18	Z (X)=9x1+2x2+4x3-8x4→max, 4x1+3x2+2x3-7 x4=12, 2x1+2x2+ x3-4x4=4, xj≥0, j=1, 2, 3, 4
7	Z(X)=12x1+8x2+5x3+4x4→min, -6x1 + x2 - x3+2x4=-2, 11x1 - x2+2x3-3x4=7, xj≥0, j=1, 2, 3, 4	19	Z (X)= x1-2x2- x3+3x4→max, -4x1+2x2 -x3 + x4=2, 6x1+6x2-x3+2x4=10, xj≥0, j=1, 2, 3, 4
8	Z (X)=x1-19x2-5x3-7 x4→min, 5x1 - 4x2 + x3 - x4=-1, -6x1+ 7x2-3x3+2x4=10, xj≥0, j=1, 2, 3, 4	20	Z(X)=2x1+x2 - x3-2x4→min, 2x1+x2-3x3­+ x4=6, x1+ x2+2x3- x4=7, xj≥0, j=1, 2, 3, 4
9	Z(X)=7x1+3x2+3x3 +2x4→min, -10x1 - x2 +2x3+3x4=-2, 6x1+2x2+3x3 + x4=18, xj≥0, j=1, 2, 3, 4	21	Z(X)=2x1+ 3x2+6x3-18x4→min, -4x1+ 6x2 - x3+ 2x4=-8, 4x1-14x2+ 2x3- 5x4=12, xj≥0, j=1, 2, 3, 4
10	Z (X)=3x1+4x2 + 2x3+7x4→min, 2x1 - x2 +10x3 - 5x4=10, -x1 + x2 - 6x3+4x4=-2, xj≥0, j=1, 2, 3, 4	22	Z(X)=3x1- x2- 3x3 + x4→max, 2x1-2x3+3x3+3x4=9, -x1+ x2- 2x3 + x4=-6, xj≥0, j=1, 2, 3, 4
11	Z (X)=-22x1+19x2 - 5x3 -6x4→max, 4x1-13x2 + 7x3 - x4=-1, -4x1+18x2-10x3+2x4=6, xj≥0, j=1, 2, 3, 4	23	Z (X)=x1-2x2 + 3x4→max, 3x1­ +x2+x3+ x4=10, 2x1-3x2+x3-2x4=8, xj≥0, j=1, 2, 3, 4
12	Z (X)=3x1+2x2+ 5x3+4x4→min, 8x1- 7x2+3x3 - 2x4=4, x1+ 4x2+2x3+3x4=20, xj≥0, j=1, 2, 3, 4	24	Z (X)=3x1+3x2+4x3­-6x4→max, 3x1­ + x2 + x3 - x4=3, x1 + x2+2x3-2x4=4, xj≥0, j=1, 2, 3, 4
25	Z(X)=2x1+10x2+4x3+2x4→min, x1 + 2x2+2x3 -2x4=2, -x1 + x2 + x3+ x4=3, xj≥0, j=1, 2, 3, 4	28	Z(X)=2x1+6x2+4x3 +3x4→max, 2x1+3x2+2x3 + x4=6, x1+2x2 + x3 + x4=4, xj≥0, j=1, 2, 3, 4
26	Z(X)=2x1+3x2+4x3 -6x4→max, x1 + x2+2x3+2x4=8, 2x1+ x2 + x3+3x4=6, xj≥0, j=1, 2, 3, 4	29	Z(X)=-2x1+6x2- 3x3+6x4→min, x1+3x2+3x3 + x4=6, -2x1+2x2 - x3+2x4=6, xj≥0, j=1, 2, 3, 4
27	Z(X)=7x1 - 10x3 +6x4→min, x1+2 x2- 2x3 - 2x4=3, x1- 5x2 - 5x3+3x4=8, xj≥0, j=1, 2, 3, 4	30	Z(X)=4x1+12x2+4x3+8x4→max, x1 + 4x2 + x3 +2x4=12, 2x1 + 3x2+3x3 + x4=12, xj≥0, j=1, 2, 3, 4