Question

求高手解决线性规划问题 已知 0<=X1<=15 0<=x1+x2<=20 0<=x1+x2+x3<=23 0<=x1+x2+x3+x4<=25

已知 0<=X1<=15
0<=x1+x2<=20
0<=x1+x2+x3<=23
0<=x1+x2+x3+x4<=25
0<=X1+x2+x3+x4+x5<=27
x1+x2+x3+x4+x5+x6=27
(其中X1至X6均为不小于0数)
求：Y=11*X1+18*X2+13*X3+17*X4+20*X5+10*X6 的最小值
急！！！！！！

其中X1 X2 X3 X4 X5 X6 均为自然数（0也包括在内）！
不好意思，前面题目打错了，下面是原题：麻烦了！！
已知 6<=X1<=15
11<=x1+x2<=20
14<=x1+x2+x3<=23
16<=x1+x2+x3+x4<=25
23<=X1+x2+x3+x4+x5<=27
x1+x2+x3+x4+x5+x6=27
(其中X1至X6均为不小于0数)
求：Y=11*X1+18*X2+13*X3+17*X4+20*X5+10*X6 的最小值
急！！！！！！

其中X1 X2 X3 X4 X5 X6 均为自然数（0也包括在内）！

Answer 1

用lingo求解代码如下：
@bnd(6,x1,15);
11<=x1+x2;
14<=x1+x2+x3;
16<=x1+x2+x3+x4;
23<=x1+x2+x3+x4+x5;
x1+x2<=20;
x1+x2+x3<=23;
x1+x2+x3+x4<=25;
x1+x2+x3+x4+x5<=27;
x1+x2+x3+x4+x5+x6=27;
@gin(x1);@gin(x2);@gin(x3);@gin(x4);@gin(x5);@gin(x6);
min=11*x1+18*x2+13*x3+17*x4+20*x5+10*x6;

结果
Global optimal solution found.
Objective value: 309.0000
Extended solver steps: 0
Total solver iterations: 0

Variable Value Reduced Cost
X1 15.00000 11.00000
X2 0.000000 18.00000
X3 8.000000 13.00000
X4 0.000000 17.00000
X5 0.000000 20.00000

x1=15,x2=x3=x4=x5=0,x6=4,最小值为309

追问

不好意思，前面题目打错了，下面是原题：麻烦了！！
已知 6<=X1<=15
11<=x1+x2<=20
14<=x1+x2+x3<=23
16<=x1+x2+x3+x4<=25
23<=X1+x2+x3+x4+x5<=27
x1+x2+x3+x4+x5+x6=27
(其中X1至X6均为不小于0数)
求：Y=11*X1+18*X2+13*X3+17*X4+20*X5+10*X6 的最小值
急！！！！！！

其中X1 X2 X3 X4 X5 X6 均为自然数（0也包括在内）！

追答

程序改为：
@bnd(6,x1,15);
x1+x2>=11;
x1+x2+x3>=14;
x1+x2+x3+x4>=16;
x1+x2+x3+x4+x5>=23;
x1+x2<=20;
x1+x2+x3<=23;
x1+x2+x3+x4<=25;
x1+x2+x3+x4+x5<=27;
x1+x2+x3+x4+x5+x6=27;
@gin(x1);@gin(x2);@gin(x3);@gin(x4);@gin(x5);@gin(x6);
min=11*x1+18*x2+13*x3+17*x4+20*x5+10*x6;

结果变为：
Global optimal solution found.
Objective value: 309.0000
Extended solver steps: 0
Total solver iterations: 0

Variable Value Reduced Cost
X1 15.00000 11.00000
X2 0.000000 18.00000
X3 8.000000 13.00000
X4 0.000000 17.00000
X5 0.000000 20.00000
X6 4.000000 10.00000

x1=15，x2=x3=x4=x5=0,x6=24,最小值为309.

Answer 2

答案270 X6=27 其余都的0

追问

不好意思，前面题目打错了，下面是原题：麻烦把解题代码也发过来！！
已知 6<=X1<=15
11<=x1+x2<=20
14<=x1+x2+x3<=23
16<=x1+x2+x3+x4<=25
23<=X1+x2+x3+x4+x5<=27
x1+x2+x3+x4+x5+x6=27
(其中X1至X6均为不小于0数)
求：Y=11*X1+18*X2+13*X3+17*X4+20*X5+10*X6 的最小值
急！！！！！！

其中X1 X2 X3 X4 X5 X6 均为自然数（0也包括在内）！