用分枝定界法求解下列问题:max z=3x1+x2+3x3, s.t.-x1+2x2+x3≤4, 4x2-3x3≤2, x1-3x2+2x3≤3, x1,x2,x3≥0
用分枝定界法求解下列问题:max z=3x1+x2+3x3,
s.t.-x1+2x2+x3≤4,
4x2-3x3≤2,
x1-3x2+2x3≤3,
x1,x2,x3≥0且x1,x3为整数.
用分枝定界法求解下列问题:max z=3x1+x2+3x3,
s.t.-x1+2x2+x3≤4,
4x2-3x3≤2,
x1-3x2+2x3≤3,
x1,x2,x3≥0且x1,x3为整数.
用分枝定界法求解下列整数线性规划问题:
(1)max z=x1+x2,
(2)max z=9x1+6x2+6x3,
s.t.
4x1+9x3≤15,
xj≥0(j=1,2,3),
x1,x2为整数;
(3)min x0=3x1+2x2-10,
s.t.
xj≥0(j=1,2,3,4).
x2,x3为整数
用分枝定界法求解下列问题:max z=5x1+8x2,
s.t.x1+x2≤6,
5x1+9x2≤45,
x1,x2≥0且均为整数.
用分枝定界法求解下列问题:max z=7x1+9x2,
s.t.-x1+3x2≤6,
7x1+x2≤35,
x1,x2≥0且x1为整数.
用隐枚举法求解下列问题:max z=3x1+2x2-5x3-2x4+3x5,
s.t.x1+x2+x3+2x4+x5≤4,
7x1+3x3-4x4+3x5≤8,
11x1-6x2+3x4-3x5≥3,
xj=0或1(j=1,2,…,5).
用割平面法求解下列整数线性规划问题:
(1)max z=x1+x2,
s.t.2x1+x2≤6,
4x1+5x2≤20,
x1,x2≥0且为整数;
(2)min x0=-3x1+x2,
s.t.3x1-2x2≤3,
5x1+4x2≥10,
2x1+x2≤5,
x1,x2≥0且为整数.
用两阶段法求解下列问题:
(1) min f=2x1+x2-x3-x4,
s.t.x1-x2+2x3-x4=2,
2x1+x2-3x3+x4=6,
x1+x2+x3+x4=7,
xj≥0(j=1,2,3,4);
(2)max z=10x1+15x2+12x3,
s.t.5x1+3x2+x3≤9,
-5x1+6x2+15x3≤15,
2x1+x2+x3≥5,
x1,x2,x3≥0;
(3)max z=2x1-x2+2x3,
s.t.x1+x2+x3≥6,
-2x1+x3≥2,
2x2-x3≥0,
x1,x2,x3≥0;
(4)max z=5x1+3x2+6x3,
s.t.x1+2x2+x3≤18,
2x1+x2+3x3≤16,
x1+x2+x3=10,
x1,x2≥0,x3无符号限制.
用割平面法求解下列整数线性规划问题:max z=4x1+5x2+x3,
s.t.3x1+2x2≤10,
x1+4x2≤11,
3x1+3x2+x3≤13,
xj≥0且为整数(j=1,2,3).
用割平面法求解下列整数线性规划问题:max z=3x2, s.t.3x1+2x2≤7, x1-x2≥-2, x1,x2≥0且为整数.
用割平面法求解下列整数线性规划问题:max z=3x2,
s.t.3x1+2x2≤7,
x1-x2≥-2,
x1,x2≥0且为整数.