求解有界变量线性规划问题: min x0=-x1-2x2, s.t.-2x1+x2+x3=12, -x1+x2+x4=5, x1-x2+x5=1, 0≤x1≤1,0≤
求解有界变量线性规划问题:
min x0=-x1-2x2,
s.t.-2x1+x2+x3=12,
-x1+x2+x4=5,
x1-x2+x5=1,
0≤x1≤1,0≤x3≤9,
0≤xj≤4(j=2,4,5).
求解有界变量线性规划问题:
min x0=-x1-2x2,
s.t.-2x1+x2+x3=12,
-x1+x2+x4=5,
x1-x2+x5=1,
0≤x1≤1,0≤x3≤9,
0≤xj≤4(j=2,4,5).
求解有界变量线性规划问题:
min x0=-2x1-x2,
s.t.x1+x2+x3=5,
-x1+x2+x4=0,
6x1+2x2+x5=21,
0≤x1≤3,0≤x2≤2,x3,x4,x5≥0.
求解有界变量线性规划问题:
min x0=-2x1-x2,
s.t. x1+x2+x3=5,
-x1+x2+x4=0,
6x1+2x2+x5=21,
0≤x1≤3,2≤x2≤5,
x3≥1,x4≥0,x5≥0.
求解下列有界变量线性规划问题:
(1)min x0=3x1+4x2-2x3-5x4+3x5+2x6-x7,
s.t.x1+x4+2x5-x6+x7=13,
x2-x4+x5+x6+2x7=9,
x3+2x4+2x5+2x6-x7=5,
0≤xj≤5(j=1,2,…,7);
(2)min f=x1+2x2+x3-x4+2x5+x6-x7,
s.t.x1+2x4-2x5+x6-8x7=0,
x2+x4+x5-x6+x7=11,
x3+3x4-x5-2x6+2x7=6,
0≤xj≤4(j=1,2,…,7).
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.
用有界变量对偶单纯形法求解下列问题:
(1)min x0=3x1+2x2+3x3+2x4,
s.t.x1+x2+x3+3x4=16,
2x1+x2+3x3+2x4=12,
0≤(x1,x2,x3,x4)T≤(5,5,3,4)T;
(2)max z=x1+2x2,
s.t.-2x1+x2+x3=8,
-x1+x2+x4=3,
x1-x2+x5=3,
2≤x1≤3,3≤x2≤8,x3≥0,x4≥0,x5≥0.
min cx.
s.t.Ax=b,
0≤x≤Me.
试验证:对上述问题必可起动对偶仿射尺度算法.
min cx.
s.t.Ax=b,
0≤x≤Me.
试验证:对上述问题必可起动对偶仿射尺度算法.
求解线性规划问题:
min x0=8x1+2x2+4x3+7x4+5x5-10,
s.t.-3x1-3x2+x3+2x4+3x5≤-2,
-5x1-3x2-2x3-x4+x5≤-4,
求解线性规划问题:
min x0=3x1+2x2,
s.t.
xj≥0(j=1,2,3,4),
x2和x3只取整数值.