运筹学试验一：线性规划 LINGO 程序说明：LP

LINGO 程序说明

3.1 程序名: linearp1（求极小问题）

linearp1运行实例:

5

,,1 ,0 1

2 2

6 .t .s 215min 532143212

1 =≥=-++=-+-+=j x x x x x x x x x x x z j

在model window 中输入以下语句：

min=5*x1+21*x3;

x1-x2+6*x3-x4=2;

x1+x2+2*x3-x5=1;

按运行按钮在solution report 窗口得到以下结果：

Global optimal solution found at iteration: 2 Objective value: 7.750000

Variable Value Reduced Cost X1 0.5000000 0.000000 X3 0.2500000 0.000000 X2 0.000000 0.5000000 X4 0.000000 2.750000 X5 0.000000 2.250000

Row Slack or Surplus Dual Price 1 7.750000 -1.000000 2 0.000000 -2.750000 3 0.000000 -2.250000

3.2 程序名: linearp2（求极大问题）

linearp2运行实例： max 100150..2160

100

120

,0

x y

s t x y x y x y ++≤≤≤≥

在model window 中输入以下语句：

max=100*x+150*y; ! this is a commnent;

x<=100;

y<=120;

x+2*y<=160;

按运行按钮在solution report 窗口得到以下结果：

Global optimal solution found at iteration: 2

Objective value: 14500.00

Variable Value Reduced Cost X 100.0000 0.000000

Y 30.00000 0.000000

Row Slack or Surplus Dual Price

1 14500.00 1.000000

2 0.000000 25.00000

3 90.00000 0.000000

4 0.000000 75.00000

max=100*x1+180*x2+70*x3; 40*x1+50*x2+60*x3<=10000; 3*x1+6*x2+2*x3<=600;

x1<=130;

x2<=80;

x3<=200;