Question

运筹学线性规划问题~~~跪求过程和答案 谢谢！

max=3a+2b+c+4d
s.t 4a+3b+2c+5d<=8
a,b,c,d范围[0,1]
求最适可行解

Answer 1

不知道这个最适可行解什么意思，看成0-1规划来求解。按目标函数中个系数的大小顺序重新排列个变量，本题为最大化问题，可按从小到大顺序排列。然后用0-1规划的方法来求解，方法参见胡运权 运筹学教程 第三版 P141 可得最适可行解为[0 1 1 0]（不确定）

Answer 2

Global optimal solution found.
Objective value: 6.250000
Infeasibilities: 0.000000
Total solver iterations: 1
Model Class: LP
Total variables: 4
Nonlinear variables: 0
Integer variables: 0
Total constraints: 2
Nonlinear constraints: 0
Total nonzeros: 8
Nonlinear nonzeros: 0
Variable Value Reduced Cost
A 0.7500000 0.000000
B 0.000000 0.2500000
C 0.000000 0.5000000
D 1.000000 -0.2500000
Row Slack or Surplus Dual Price
1 6.250000 1.000000
2 0.000000 0.7500000

Answer 3

Objective value: 6.000000
Variable Value Reduced Cost
A 0.000000 -3.000000
B 1.000000 -2.000000
C 0.000000 -1.000000
D 1.000000 -4.000000