求出全部货物总重量与总利润
求实际运送货物件数
求实际运送货物总重量
求出全部货物重量乘积
求出所有货物重量最大值与最小值
求出所有货物利润最大值和最小值
TOTALW = @SUM(ITEM : WEIGHT);
TOTALP = @SUM(ITEM : PROFIT);SIGMA_X = @SUM(ITEM : X);
SIGMA_W = @SUM(ITEM : WEIGHT*X);
P = @PROD(ITEM : WEIGHT);MAX_W = @SUM(ITEM : WEIGHT);
MIN_W = @SUM(ITEM : WEIGHT);MAX_P = @SUM(ITEM : PROFIT);
MIN_P = @SUM(ITEM : PROFIT);
举例：
!Name: 背包问题模型
!Date: 2022-03-16
!Desc: 10件货物的背包问题
;MODEL:SETS:ITEM/1 2 3 4 5 6 7 8 9 10/:WEIGHT, PROFIT,X;ENDSETSDATA:WEIGHT = 6 3 4 5 1 2 3 5 4 2;
PROFIT = 540 200 180 350 60 150 280 450 320 120;ENDDATAMAX = @SUM(ITEM(I):PROFIT(I)*x(I));@SUM(ITEM(I):WEIGHT(I)*X(I))<=30;
@FOR(ITEM(I):@BIN(X(I)));TOTALW = @SUM(ITEM : WEIGHT);
TOTALP = @SUM(ITEM : PROFIT);SIGMA_X = @SUM(ITEM : X);
SIGMA_W = @SUM(ITEM : WEIGHT*X);
P = @PROD(ITEM : WEIGHT);MAX_W = @SUM(ITEM : WEIGHT);
MIN_W = @SUM(ITEM : WEIGHT);MAX_P = @SUM(ITEM : PROFIT);
MIN_P = @SUM(ITEM : PROFIT);END
结果显示：
Global optimal solution found.Objective value: 2410.000Objective bound: 2410.000Infeasibilities: 0.000000Extended solver steps: 0Total solver iterations: 0Elapsed runtime seconds: 0.08Model Class: MILPTotal variables: 12Nonlinear variables: 0Integer variables: 10Total constraints: 4Nonlinear constraints: 0Total nonzeros: 42Nonlinear nonzeros: 0Variable Value Reduced CostTOTALW 35.00000 0.000000TOTALP 2650.000 0.000000SIGMA_X 8.000000 0.000000SIGMA_W 30.00000 0.000000P 86400.00 0.000000MAX_W 35.00000 0.000000MIN_W 35.00000 0.000000MAX_P 2650.000 0.000000MIN_P 2650.000 0.000000WEIGHT( 1) 6.000000 0.000000WEIGHT( 2) 3.000000 0.000000WEIGHT( 3) 4.000000 0.000000WEIGHT( 4) 5.000000 0.000000WEIGHT( 5) 1.000000 0.000000WEIGHT( 6) 2.000000 0.000000WEIGHT( 7) 3.000000 0.000000WEIGHT( 8) 5.000000 0.000000WEIGHT( 9) 4.000000 0.000000WEIGHT( 10) 2.000000 0.000000PROFIT( 1) 540.0000 0.000000PROFIT( 2) 200.0000 0.000000PROFIT( 3) 180.0000 0.000000PROFIT( 4) 350.0000 0.000000PROFIT( 5) 60.00000 0.000000PROFIT( 6) 150.0000 0.000000PROFIT( 7) 280.0000 0.000000PROFIT( 8) 450.0000 0.000000PROFIT( 9) 320.0000 0.000000PROFIT( 10) 120.0000 0.000000X( 1) 1.000000 -540.0000X( 2) 1.000000 -200.0000X( 3) 0.000000 -180.0000X( 4) 1.000000 -350.0000X( 5) 0.000000 -60.00000X( 6) 1.000000 -150.0000X( 7) 1.000000 -280.0000X( 8) 1.000000 -450.0000X( 9) 1.000000 -320.0000X( 10) 1.000000 -120.0000Row Slack or Surplus Dual Price1 2410.000 1.0000002 0.000000 0.0000003 0.000000 0.0000004 0.000000 0.0000005 0.000000 0.0000006 0.000000 0.0000007 0.000000 0.0000008 0.000000 0.0000009 0.000000 0.00000010 0.000000 0.00000011 0.000000 0.000000
用lingo产生一个向量[1 4 9 16 25 36]
model:sets:A/1..6/:x;
endsets@for(A(i): x(i)=i^2);end
显示结果：
Feasible solution found.Total solver iterations: 0Elapsed runtime seconds: 0.06Model Class: . . .Total variables: 0Nonlinear variables: 0Integer variables: 0Total constraints: 0Nonlinear constraints: 0Total nonzeros: 0Nonlinear nonzeros: 0Variable ValueX( 1) 1.000000X( 2) 4.000000X( 3) 9.000000X( 4) 16.00000X( 5) 25.00000X( 6) 36.00000Row Slack or Surplus1 0.0000002 0.0000003 0.0000004 0.0000005 0.0000006 0.000000用lingo产生一个60维的向量X，Xi=i^0.5
model:sets:A/1..60/:x;
endsets@for(A(i): x(i)=@sqrt(i));end
显示结果：
Feasible solution found.Total solver iterations: 0Elapsed runtime seconds: 0.06Model Class: . . .Total variables: 0Nonlinear variables: 0Integer variables: 0Total constraints: 0Nonlinear constraints: 0Total nonzeros: 0Nonlinear nonzeros: 0Variable ValueX( 1) 1.000000 X( 2) 1.414214 X( 3) 1.732051X( 4) 2.000000 X( 5) 2.236012 X( 6) 2.449490X( 7) 2.645751 X( 8) 2.828427 X( 9) 3.000000X( 10) 3.162278 X( 11) 3.316625 X( 12) 3.464102X( 13) 3.605551 X( 14) 3.741657 X( 15) 3.872983 X( 16) 4.000000X( 17) 4.123106X( 18) 4.242641X( 19) 4.358899X( 20) 4.472136X( 21) 4.582576X( 22) 4.690416X( 23) 4.795832X( 24) 4.898979X( 25) 5.000000X( 26) 5.099020X( 27) 5.196152X( 28) 5.291503X( 29) 5.385165X( 30) 5.477226X( 31) 5.567764X( 32) 5.656854X( 33) 5.744563X( 34) 5.830952X( 35) 5.916080X( 36) 6.000000X( 37) 6.082763X( 38) 6.164414X( 39) 6.244998X( 40) 6.324555X( 41) 6.403124X( 42) 6.480741X( 43) 6.557439X( 44) 6.633250X( 45) 6.708204X( 46) 6.782330X( 47) 6.855655X( 48) 6.928203X( 49) 7.000000X( 50) 7.071068X( 51) 7.141428X( 52) 7.211103X( 53) 7.280110X( 54) 7.348469X( 55) 7.416198X( 56) 7.483315X( 57) 7.549834X( 58) 7.615773X( 59) 7.681146X( 60) 7.745967
model:sets:A/1..10/:x;
endsets@for(A(i)|i#LE#5:x(i)=i^2);@for(A(i)|i#GT#5:x(i)=@sqrt(i));end
结果：
Feasible solution found.Total solver iterations: 0Elapsed runtime seconds: 0.06Model Class: . . .Total variables: 0Nonlinear variables: 0Integer variables: 0Total constraints: 0Nonlinear constraints: 0Total nonzeros: 0Nonlinear nonzeros: 0Variable ValueX( 1) 1.000000X( 2) 4.000000X( 3) 9.000000X( 4) 16.00000X( 5) 25.00000X( 6) 2.449490X( 7) 2.645751X( 8) 2.828427X( 9) 3.000000X( 10) 3.162278Row Slack or Surplus1 0.0000002 0.0000003 0.0000004 0.0000005 0.0000006 0.0000007 0.0000008 0.0000009 0.00000010 0.000000
model:sets:A/1..10/:x;
endsets@for(A(i)|i#LE#5:x(i)=i^2);@for(A(i)|i#GT#5:x(i)=@sqrt(i));P = @prod(A(i)|i#LE#5: x(i));S = @sum(A(i)|i#GT#5: x(i)*x(i));end
实现结果：
Feasible solution found.Total solver iterations: 0Elapsed runtime seconds: 0.07Model Class: . . .Total variables: 0Nonlinear variables: 0Integer variables: 0Total constraints: 0Nonlinear constraints: 0Total nonzeros: 0Nonlinear nonzeros: 0Variable ValueP 14400.00S 40.00000X( 1) 1.000000X( 2) 4.000000X( 3) 9.000000X( 4) 16.00000X( 5) 25.00000X( 6) 2.449490X( 7) 2.645751X( 8) 2.828427X( 9) 3.000000X( 10) 3.162278| 完整格式 |
|---|
| @FOR(S(I)[|logical_condition]: expression); |
| @SUM(S(I)[logical_condition]: expression); |
| @MAX(S(I)[logical_condition]: expression); |
| @MIN(S(I)[logical_condition]: expression); |
| @PROD(S(I)[logical_condition]: expression); |
五个整数，不相同，和100
如果乘积最大，五个整数应该是多少？
model:sets:A/1..5/:x;
endsetsmax = @prod(A:x);@sum(A:x)=100;@for(A: @GIN(x));X(1)>=0+1;X(2)>=X(1)+1;X(3)>=X(2)+1;X(4)>=X(3)+1;X(5)>=X(4)+1;end
实现结果：
Local optimal solution found.Objective value: 3160080.Objective bound: 3160080.Infeasibilities: 0.000000Extended solver steps: 0Total solver iterations: 24Elapsed runtime seconds: 1.35Model Class: PINLPTotal variables: 5Nonlinear variables: 5Integer variables: 5Total constraints: 7Nonlinear constraints: 1Total nonzeros: 19Nonlinear nonzeros: 5Variable Value Reduced CostX( 1) 18.00000 -175560.0X( 2) 19.00000 -166320.0X( 3) 20.00000 -158004.0X( 4) 21.00000 -150480.0X( 5) 22.00000 -143640.0Row Slack or Surplus Dual Price1 3160080. 1.0000002 0.000000 0.0000003 17.00000 0.0000004 0.000000 0.0000005 0.000000 0.0000006 0.000000 0.0000007 0.000000 0.000000如果乘积最小，五个整数应该是多少？
model:sets:A/1..5/:x;
endsetsmin = @prod(A:x);@sum(A:x)=100;@for(A: @GIN(x));X(1)>=0+1;@FOR(A(I)|I#LT#5: X(I)+1);end
实现结果：
Local optimal solution found.Objective value: 2160.000Objective bound: 2160.000Infeasibilities: 0.000000Extended solver steps: 0Total solver iterations: 35Elapsed runtime seconds: 0.26Model Class: PINLPTotal variables: 5Nonlinear variables: 5Integer variables: 5Total constraints: 7Nonlinear constraints: 1Total nonzeros: 19Nonlinear nonzeros: 5Variable Value Reduced CostX( 1) 1.000000 0.000000X( 2) 2.000000 0.000000X( 3) 3.000000 0.000000X( 4) 4.000000 0.000000X( 5) 90.00000 -516.0000Row Slack or Surplus Dual Price1 2160.000 -1.0000002 0.000000 -540.00003 0.000000 -2340.0004 0.000000 -720.00005 0.000000 -180.00006 0.000000 0.0000007 85.00000 0.000000一个40英尺的集装箱最大载重22吨，内部最大容积54立方米，现有六种货物，每种货物一件，重量、体积和运费如下表所示，问如何装在运送货物才能使得运费收入最大（嘉定不考虑货物的形状）？
| 货物 | 重量/T | 体积/立方米 | 运费/元 |
|---|---|---|---|
| A | 6 | 12 | 500 |
| B | 10 | 18 | 900 |
| C | 8 | 20 | 700 |
| D | 5 | 33 | 1600 |
| E | 12 | 25 | 1500 |
| F | 14 | 21 | 1200 |
二维背包问题：
!Name: 背包问题模型
!Date: 2022-03-16
!Desc: 10件货物的背包问题
;MODEL: SETS:ITEM:WEIGHT, VOLUMN, PRICE,X;ENDSETSDATA:ITEM WEIGHT VOLUMN PRICE =
A 6 12 500
B 10 18 900
C 8 20 700
D 5 33 1600
E 12 25 1500
F 14 21 1200
;ENDDATAMAX = @SUM(ITEM(I):PRICE(I)*X(I));@SUM(ITEM(I):WEIGHT(I)*X(I))<=22;
@SUM(ITEM: VOLUMN*X)<=54;
@FOR(ITEM(I):@BIN(X(I)));TOTALW = @SUM(ITEM : WEIGHT);
TOTALP = @SUM(ITEM : PRICE);SIGMA_X = @SUM(ITEM : X);
SIGMA_W = @SUM(ITEM : WEIGHT*X);END
实际结果：
Global optimal solution found.Objective value: 2800.000Objective bound: 2800.000Infeasibilities: 0.000000Extended solver steps: 0Total solver iterations: 0Elapsed runtime seconds: 0.08Model Class: MILPTotal variables: 8Nonlinear variables: 0Integer variables: 6Total constraints: 5Nonlinear constraints: 0Total nonzeros: 32Nonlinear nonzeros: 0Variable Value Reduced CostTOTALW 55.00000 0.000000TOTALP 6400.000 0.000000SIGMA_X 2.000000 0.000000SIGMA_W 19.00000 0.000000WEIGHT( A) 6.000000 0.000000WEIGHT( B) 10.00000 0.000000WEIGHT( C) 8.000000 0.000000WEIGHT( D) 5.000000 0.000000WEIGHT( E) 12.00000 0.000000WEIGHT( F) 14.00000 0.000000VOLUMN( A) 12.00000 0.000000VOLUMN( B) 18.00000 0.000000VOLUMN( C) 20.00000 0.000000VOLUMN( D) 33.00000 0.000000VOLUMN( E) 25.00000 0.000000VOLUMN( F) 21.00000 0.000000PRICE( A) 500.0000 0.000000PRICE( B) 900.0000 0.000000PRICE( C) 700.0000 0.000000PRICE( D) 1600.000 0.000000PRICE( E) 1500.000 0.000000PRICE( F) 1200.000 0.000000X( A) 0.000000 -500.0000X( B) 0.000000 -900.0000X( C) 0.000000 -700.0000X( D) 1.000000 -1600.000X( E) 0.000000 -1500.000X( F) 1.000000 -1200.000Row Slack or Surplus Dual Price1 2800.000 1.0000002 3.000000 0.0000003 0.000000 0.0000004 0.000000 0.0000005 0.000000 0.0000006 0.000000 0.0000007 0.000000 0.000000一节某种型号的铁路车棚车厢内部最大容积130立方米，最大载重60吨，现有60中货物，每种一件，重量体积运费如下，如何装运货物才能运费收入最大（不考虑货物形状）？
| 货物 | 重量 | 体积 | 运费 |
|---|---|---|---|
| 1 | 6 | 14 | 500 |
| 2 | 8 | 4 | 900 |
| 3 | 10 | 8 | 700 |
| 4 | 12 | 20 | 900 |
| 5 | 14 | 11 | 1000 |
| 6 | 16 | 14 | 1100 |
| 7 | 18 | 17 | 1200 |
| 8 | 6 | 20 | 1300 |
| 9 | 12 | 23 | 1400 |
| 10 | 14 | 26 | 1500 |
| 11 | 26 | 14 | 1600 |
| 12 | 28 | 16 | 1700 |
| 13 | 9 | 10 | 1800 |
| 14 | 12 | 12 | 1200 |
| 15 | 14 | 14 | 1600 |
| 16 | 16 | 16 | 800 |
| 17 | 18 | 18 | 800 |
| 18 | 20 | 6 | 600 |
| 19 | 22 | 12 | 1400 |
| 20 | 14 | 9 | 1200 |
| 21 | 4 | 12 | 1000 |
| 22 | 8 | 14 | 800 |
| 23 | 20 | 16 | 600 |
| 24 | 11 | 18 | 400 |
| 25 | 14 | 20 | 2800 |
| 26 | 17 | 22 | 3200 |
| 27 | 20 | 14 | 1700 |
| 28 | 23 | 4 | 500 |
| 29 | 26 | 8 | 700 |
| 30 | 14 | 10 | 900 |
| 31 | 16 | 12 | 1100 |
| 32 | 18 | 14 | 1300 |
| 33 | 20 | 16 | 1500 |
| 34 | 22 | 18 | 1700 |
| 35 | 24 | 20 | 1900 |
| 36 | 26 | 22 | 2100 |
| 37 | 28 | 24 | 2300 |
| 38 | 10 | 26 | 2500 |
| 39 | 12 | 28 | 1300 |
| 40 | 14 | 30 | 1500 |
| 41 | 16 | 12 | 1700 |
| 42 | 18 | 14 | 1900 |
| 43 | 20 | 16 | 2100 |
| 44 | 22 | 8 | 2300 |
| 45 | 24 | 10 | 2500 |
| 46 | 26 | 11 | 2700 |
| 47 | 28 | 14 | 2900 |
| 48 | 30 | 26 | 3100 |
| 49 | 12 | 28 | 3300 |
| 50 | 14 | 30 | 3500 |
| 51 | 16 | 12 | 3200 |
| 52 | 8 | 14 | 1500 |
| 53 | 10 | 16 | 1400 |
| 54 | 11 | 8 | 1300 |
| 55 | 14 | 10 | 1200 |
| 56 | 16 | 11 | 1100 |
| 57 | 11 | 14 | 1000 |
| 58 | 10 | 16 | 900 |
| 59 | 5 | 11 | 800 |
| 60 | 6 | 10 | 700 |
!Name: 背包问题模型
!Date: 2022-03-16
!Desc: 10件货物的背包问题
;MODEL: SETS:ITEM:WEIGHT, VOLUMN, PRICE,X;ENDSETSDATA:ITEM WEIGHT VOLUMN PRICE =
1 6 14 500
2 8 4 900
3 10 8 700
4 12 20 900
5 14 11 1000
6 16 14 1100
7 18 17 1200
8 6 20 1300
9 12 23 1400
10 14 26 1500
11 26 14 1600
12 28 16 1700
13 9 10 1800
14 12 12 1200
15 14 14 1600
16 16 16 800
17 18 18 800
18 20 6 600
19 22 12 1400
20 14 9 1200
21 4 12 1000
22 8 14 800
23 20 16 600
24 11 18 400
25 14 20 2800
26 17 22 3200
27 20 14 1700
28 23 4 500
29 26 8 700
30 14 10 900
31 16 12 1100
32 18 14 1300
33 20 16 1500
34 22 18 1700
35 24 20 1900
36 26 22 2100
37 28 24 2300
38 10 26 2500
39 12 28 1300
40 14 30 1500
41 16 12 1700
42 18 14 1900
43 20 16 2100
44 22 8 2300
45 24 10 2500
46 26 11 2700
47 28 14 2900
48 30 26 3100
49 12 28 3300
50 14 30 3500
51 16 12 3200
52 8 14 1500
53 10 16 1400
54 11 8 1300
55 14 10 1200
56 16 11 1100
57 11 14 1000
58 10 16 900
59 5 11 800
60 6 10 700;ENDDATAMAX = @SUM(ITEM(I):PRICE(I)*X(I));@SUM(ITEM(I):WEIGHT(I)*X(I))<=60;
@SUM(ITEM: VOLUMN*X)<=130;
@FOR(ITEM(I):@BIN(X(I)));TOTALW = @SUM(ITEM : WEIGHT);
TOTALP = @SUM(ITEM : PRICE);SIGMA_X = @SUM(ITEM : X);
SIGMA_W = @SUM(ITEM : WEIGHT*X);END
实现结果：
Global optimal solution found.Objective value: 14000.00Objective bound: 14000.00Infeasibilities: 0.000000Extended solver steps: 0Total solver iterations: 0Elapsed runtime seconds: 0.09Model Class: MILPTotal variables: 62Nonlinear variables: 0Integer variables: 60Total constraints: 5Nonlinear constraints: 0Total nonzeros: 302Nonlinear nonzeros: 0Variable Value Reduced CostTOTALW 959.0000 0.000000TOTALP 92100.00 0.000000SIGMA_X 5.000000 0.000000SIGMA_W 60.00000 0.000000WEIGHT( 1) 6.000000 0.000000WEIGHT( 2) 8.000000 0.000000WEIGHT( 3) 10.00000 0.000000WEIGHT( 4) 12.00000 0.000000WEIGHT( 5) 14.00000 0.000000WEIGHT( 6) 16.00000 0.000000WEIGHT( 7) 18.00000 0.000000WEIGHT( 8) 6.000000 0.000000WEIGHT( 9) 12.00000 0.000000WEIGHT( 10) 14.00000 0.000000WEIGHT( 11) 26.00000 0.000000WEIGHT( 12) 28.00000 0.000000WEIGHT( 13) 9.000000 0.000000WEIGHT( 14) 12.00000 0.000000WEIGHT( 15) 14.00000 0.000000WEIGHT( 16) 16.00000 0.000000WEIGHT( 17) 18.00000 0.000000WEIGHT( 18) 20.00000 0.000000WEIGHT( 19) 22.00000 0.000000WEIGHT( 20) 14.00000 0.000000WEIGHT( 21) 4.000000 0.000000WEIGHT( 22) 8.000000 0.000000WEIGHT( 23) 20.00000 0.000000WEIGHT( 24) 11.00000 0.000000WEIGHT( 25) 14.00000 0.000000WEIGHT( 26) 17.00000 0.000000WEIGHT( 27) 20.00000 0.000000WEIGHT( 28) 23.00000 0.000000WEIGHT( 29) 26.00000 0.000000WEIGHT( 30) 14.00000 0.000000WEIGHT( 31) 16.00000 0.000000WEIGHT( 32) 18.00000 0.000000WEIGHT( 33) 20.00000 0.000000WEIGHT( 34) 22.00000 0.000000WEIGHT( 35) 24.00000 0.000000WEIGHT( 36) 26.00000 0.000000WEIGHT( 37) 28.00000 0.000000WEIGHT( 38) 10.00000 0.000000WEIGHT( 39) 12.00000 0.000000WEIGHT( 40) 14.00000 0.000000WEIGHT( 41) 16.00000 0.000000WEIGHT( 42) 18.00000 0.000000WEIGHT( 43) 20.00000 0.000000WEIGHT( 44) 22.00000 0.000000WEIGHT( 45) 24.00000 0.000000WEIGHT( 46) 26.00000 0.000000WEIGHT( 47) 28.00000 0.000000WEIGHT( 48) 30.00000 0.000000WEIGHT( 49) 12.00000 0.000000WEIGHT( 50) 14.00000 0.000000WEIGHT( 51) 16.00000 0.000000WEIGHT( 52) 8.000000 0.000000WEIGHT( 53) 10.00000 0.000000WEIGHT( 54) 11.00000 0.000000WEIGHT( 55) 14.00000 0.000000WEIGHT( 56) 16.00000 0.000000WEIGHT( 57) 11.00000 0.000000WEIGHT( 58) 10.00000 0.000000WEIGHT( 59) 5.000000 0.000000WEIGHT( 60) 6.000000 0.000000VOLUMN( 1) 14.00000 0.000000VOLUMN( 2) 4.000000 0.000000VOLUMN( 3) 8.000000 0.000000VOLUMN( 4) 20.00000 0.000000VOLUMN( 5) 11.00000 0.000000VOLUMN( 6) 14.00000 0.000000VOLUMN( 7) 17.00000 0.000000VOLUMN( 8) 20.00000 0.000000VOLUMN( 9) 23.00000 0.000000VOLUMN( 10) 26.00000 0.000000VOLUMN( 11) 14.00000 0.000000VOLUMN( 12) 16.00000 0.000000VOLUMN( 13) 10.00000 0.000000VOLUMN( 14) 12.00000 0.000000VOLUMN( 15) 14.00000 0.000000VOLUMN( 16) 16.00000 0.000000VOLUMN( 17) 18.00000 0.000000VOLUMN( 18) 6.000000 0.000000VOLUMN( 19) 12.00000 0.000000VOLUMN( 20) 9.000000 0.000000VOLUMN( 21) 12.00000 0.000000VOLUMN( 22) 14.00000 0.000000VOLUMN( 23) 16.00000 0.000000VOLUMN( 24) 18.00000 0.000000VOLUMN( 25) 20.00000 0.000000VOLUMN( 26) 22.00000 0.000000VOLUMN( 27) 14.00000 0.000000VOLUMN( 28) 4.000000 0.000000VOLUMN( 29) 8.000000 0.000000VOLUMN( 30) 10.00000 0.000000VOLUMN( 31) 12.00000 0.000000VOLUMN( 32) 14.00000 0.000000VOLUMN( 33) 16.00000 0.000000VOLUMN( 34) 18.00000 0.000000VOLUMN( 35) 20.00000 0.000000VOLUMN( 36) 22.00000 0.000000VOLUMN( 37) 24.00000 0.000000VOLUMN( 38) 26.00000 0.000000VOLUMN( 39) 28.00000 0.000000VOLUMN( 40) 30.00000 0.000000VOLUMN( 41) 12.00000 0.000000VOLUMN( 42) 14.00000 0.000000VOLUMN( 43) 16.00000 0.000000VOLUMN( 44) 8.000000 0.000000VOLUMN( 45) 10.00000 0.000000VOLUMN( 46) 11.00000 0.000000VOLUMN( 47) 14.00000 0.000000VOLUMN( 48) 26.00000 0.000000VOLUMN( 49) 28.00000 0.000000VOLUMN( 50) 30.00000 0.000000VOLUMN( 51) 12.00000 0.000000VOLUMN( 52) 14.00000 0.000000VOLUMN( 53) 16.00000 0.000000VOLUMN( 54) 8.000000 0.000000VOLUMN( 55) 10.00000 0.000000VOLUMN( 56) 11.00000 0.000000VOLUMN( 57) 14.00000 0.000000VOLUMN( 58) 16.00000 0.000000VOLUMN( 59) 11.00000 0.000000VOLUMN( 60) 10.00000 0.000000PRICE( 1) 500.0000 0.000000PRICE( 2) 900.0000 0.000000PRICE( 3) 700.0000 0.000000PRICE( 4) 900.0000 0.000000PRICE( 5) 1000.000 0.000000PRICE( 6) 1100.000 0.000000PRICE( 7) 1200.000 0.000000PRICE( 8) 1300.000 0.000000PRICE( 9) 1400.000 0.000000PRICE( 10) 1500.000 0.000000PRICE( 11) 1600.000 0.000000PRICE( 12) 1700.000 0.000000PRICE( 13) 1800.000 0.000000PRICE( 14) 1200.000 0.000000PRICE( 15) 1600.000 0.000000PRICE( 16) 800.0000 0.000000PRICE( 17) 800.0000 0.000000PRICE( 18) 600.0000 0.000000PRICE( 19) 1400.000 0.000000PRICE( 20) 1200.000 0.000000PRICE( 21) 1000.000 0.000000PRICE( 22) 800.0000 0.000000PRICE( 23) 600.0000 0.000000PRICE( 24) 400.0000 0.000000PRICE( 25) 2800.000 0.000000PRICE( 26) 3200.000 0.000000PRICE( 27) 1700.000 0.000000PRICE( 28) 500.0000 0.000000PRICE( 29) 700.0000 0.000000PRICE( 30) 900.0000 0.000000PRICE( 31) 1100.000 0.000000PRICE( 32) 1300.000 0.000000PRICE( 33) 1500.000 0.000000PRICE( 34) 1700.000 0.000000PRICE( 35) 1900.000 0.000000PRICE( 36) 2100.000 0.000000PRICE( 37) 2300.000 0.000000PRICE( 38) 2500.000 0.000000PRICE( 39) 1300.000 0.000000PRICE( 40) 1500.000 0.000000PRICE( 41) 1700.000 0.000000PRICE( 42) 1900.000 0.000000PRICE( 43) 2100.000 0.000000PRICE( 44) 2300.000 0.000000PRICE( 45) 2500.000 0.000000PRICE( 46) 2700.000 0.000000PRICE( 47) 2900.000 0.000000PRICE( 48) 3100.000 0.000000PRICE( 49) 3300.000 0.000000PRICE( 50) 3500.000 0.000000PRICE( 51) 3200.000 0.000000PRICE( 52) 1500.000 0.000000PRICE( 53) 1400.000 0.000000PRICE( 54) 1300.000 0.000000PRICE( 55) 1200.000 0.000000PRICE( 56) 1100.000 0.000000PRICE( 57) 1000.000 0.000000PRICE( 58) 900.0000 0.000000PRICE( 59) 800.0000 0.000000PRICE( 60) 700.0000 0.000000X( 1) 0.000000 -500.0000X( 2) 0.000000 -900.0000X( 3) 0.000000 -700.0000X( 4) 0.000000 -900.0000X( 5) 0.000000 -1000.000X( 6) 0.000000 -1100.000X( 7) 0.000000 -1200.000X( 8) 0.000000 -1300.000X( 9) 0.000000 -1400.000X( 10) 0.000000 -1500.000X( 11) 0.000000 -1600.000X( 12) 0.000000 -1700.000X( 13) 0.000000 -1800.000X( 14) 0.000000 -1200.000X( 15) 0.000000 -1600.000X( 16) 0.000000 -800.0000X( 17) 0.000000 -800.0000X( 18) 0.000000 -600.0000X( 19) 0.000000 -1400.000X( 20) 0.000000 -1200.000X( 21) 0.000000 -1000.000X( 22) 0.000000 -800.0000X( 23) 0.000000 -600.0000X( 24) 0.000000 -400.0000X( 25) 0.000000 -2800.000X( 26) 0.000000 -3200.000X( 27) 0.000000 -1700.000X( 28) 0.000000 -500.0000X( 29) 0.000000 -700.0000X( 30) 0.000000 -900.0000X( 31) 0.000000 -1100.000X( 32) 0.000000 -1300.000X( 33) 0.000000 -1500.000X( 34) 0.000000 -1700.000X( 35) 0.000000 -1900.000X( 36) 0.000000 -2100.000X( 37) 0.000000 -2300.000X( 38) 1.000000 -2500.000X( 39) 0.000000 -1300.000X( 40) 0.000000 -1500.000X( 41) 0.000000 -1700.000X( 42) 0.000000 -1900.000X( 43) 0.000000 -2100.000X( 44) 0.000000 -2300.000X( 45) 0.000000 -2500.000X( 46) 0.000000 -2700.000X( 47) 0.000000 -2900.000X( 48) 0.000000 -3100.000X( 49) 1.000000 -3300.000X( 50) 1.000000 -3500.000X( 51) 1.000000 -3200.000X( 52) 1.000000 -1500.000X( 53) 0.000000 -1400.000X( 54) 0.000000 -1300.000X( 55) 0.000000 -1200.000X( 56) 0.000000 -1100.000X( 57) 0.000000 -1000.000X( 58) 0.000000 -900.0000X( 59) 0.000000 -800.0000X( 60) 0.000000 -700.0000Row Slack or Surplus Dual Price1 14000.00 1.0000002 0.000000 0.0000003 20.00000 0.0000004 0.000000 0.0000005 0.000000 0.0000006 0.000000 0.0000007 0.000000 0.000000本小节主要讲了lingo定义原始集合及其属性的语法规则，还有在数据段给常量赋值的多种形式、还有五个集合遍历函数及在集合遍历函数中使用条件筛选集合元素其简化形式、纯粹的语法问题，虽然简单但仍需要认真掌握。
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