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: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).
用分解算法求解下列线性规划问题:
max z=6x1+7x2+3x3+5x4+x5+x6,
s.t.x1+x2+x3+x4+x5+x6≤50,
x1+x2≤10,
x2≤8,
5x3+x4≤12,
x5+x6≥5,
x5+x6≤50,
xi≥0(i=1,2,…,6).
用有界变量单纯形法求解下列线性规划问题:
(1)min x0=2x1+x2+3x3-2x4+10x5,
s.t.x1+x3-x4+2x5=5,
x2+2x3+2x4+x5=9,
0≤x1≤7,0≤x2≤10,0≤x3≤1,
0≤x4≤5,0≤x5≤3;
(2)max z=3x1+5x2+6x3,
s.t.x1+2x2+3x3≤21,
2x1+x2+x3≤12,
2≤x1≤4,3≤x2≤5,1≤x3≤3.