用p分算法求解下列问题: min f=5x1+3x2+8x3-5x4, s.t.x1+x2+x3+x4≥25, 5x1+x2≤20, 5x1-x2≥5, x3+x4=20
用p分算法求解下列问题:
min f=5x1+3x2+8x3-5x4,
s.t.x1+x2+x3+x4≥25,
5x1+x2≤20,
5x1-x2≥5,
x3+x4=20,
xi≥0(i=1,2,3,4).
用p分算法求解下列问题:
min f=5x1+3x2+8x3-5x4,
s.t.x1+x2+x3+x4≥25,
5x1+x2≤20,
5x1-x2≥5,
x3+x4=20,
xi≥0(i=1,2,3,4).
现在用原仿射尺度算法求解如下问题:
min f=x2-x3,
s.t.2x1-x2+2x3=2,
x1+2x2=5,
用原仿射尺度算法求解:
min f=-2x1+x2,
s.t.x1-x2+x3=15,
x2+x4=5,
x1,x2,x3,x4≥0.
用对偶单纯形法求解下列问题:
(1)min f=4x1+12x2+18x3,
s.t.x1+3x3≥3,
2x2+2x3≥5,
xj≥0(j=1,2,3);
(2)min f=3x1+2x2+x3,
s.t.x1+x2+x3≤6,
x1-x3≥4,
x2-x3≥3,
xi≥0(i=1,2,3);
(3)min f=-2x1+4x2+x3+6x4-9x5-5x6,
s.t.x1-2x4+x5-2x6=-3,
x2+x4-3x5-x6=-14.
x3-x4-x5+x6=-5,
xj≥0(j=1,2,…,6).
用对偶单纯形法求解下列线性规划问题:min f=3x1+2x2+x3,
s.t.x1+x2+x3≤6,
x1-x3≥4,
x2-x3≥3,
x1,x2,x3≥0.
用改进单纯形法求解下列问题:
(1)max z=4x1+3x2+6x3,
s.t. 3x1+x2+3x3≤30,
2x1+2x2+3x3≤40,
xj≥0(j=1,2,3);
(2) min f=-2x1+x2-x3,
s.t.3x1+x2+x3≤60,
x1-x2+2x3≤10,
x1+x2-x3≤20,
xj≥0(j=1,2,3).
用隐枚举法求解下列0-1规划问题:
(1)min x0=2x1+5x2+3x3+4x4,
s.t.-4x1+x2+x3+x4≥0,
-2x1+4x2+2x3+4x4≥4,
x1+x2-x3+x4≥1,
xj=0或1 (j=1,2,3,4);
(2)max z=2x1-x2+5x3-3x4+4x5,
s.t.3x1-2x2+7x3-5x4+4x5≤6,
x1-x2+2x3-4x4+2x5≤0,
xj=0或1(j=1,2,…,5).
求解线性规划问题
min f=-x4+x5,
s.t. x1-x4+4x5=-5,
x2+x4-3x5=1,
x3-2x4+5x5=-1,
xj≥0(j=1,2,…,5).
求解下列线性规划问题:
min 4x1+6x2+18x3 s.t. x1 +3x3≥3, x2+2x3≥5, x1,x2,x3≥0.
用乘子法求解下列问题: (1)min x12+x22 s.t. x1≥1; (2)min
s.t.x1≥0, x2≥1