数学建模实例讲稿_数学建模实例
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线性规划模型
4.1 奶制品的生产与销售[1] 例2 奶制品的生产销售计划（P88~92）
% plan.m c = [-24-16-44-32 3 3]
A = [4 3 0 0 4 3;4 2 0 0 6 4;1 0 0 0 1 0] b = [600;480;100]
aeq = [0 0 1 0-0.8 0;0 0 0 1 0-0.75] beq = zeros(2,1)xLB = zeros(6,1)xUB = inf * ones(6,1)
[x,fval] = linprog(c,A,b,aeq,beq,xLB,xUB)
非线性规划模型
12.1 供应与选址[2]
（1）编写M文件liaoch.m定义目标函数
% liaoch.m
function f=liaoch(x)
a=[1.25 8.75 0.5 5.75 3 7.25];b=[1.25 0.75 4.75 5 6.5 7.75];d=[3 5 4 7 6 11];e=[20 20];f1=0;for i=1:6
s(i)=sqrt((x(13)-a(i))^2+(x(14)-b(i))^2);f1=s(i)*x(i)+f1;end f2=0;for i=7:12
s(i)=sqrt((x(15)-a(i-6))^2+(x(16)-b(i-6))^2);f2=s(i)*x(i)+f2;end
f = f1 + f2;
（2）工地分布及需求量示意图
>> a=[1.25 8.75 0.5 5.75 3 7.25];>> b=[1.25 0.75 4.75 5 6.5 7.75];>> scatter(a,b)（3）编写主程序xuanzhi.m % xuanzhi.m
A=[1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0];b=[20;20];
Aeq=[eye(6)eye(6)zeros(6,4)];beq=[3 5 4 7 6 11]'
VLB=[zeros(12,1);-inf;-inf;-inf;-inf];x0=[3 0 4 5 4 0 0 5 0 2 2 11 3 4 7 6.5];
[x,fval,exitflag]=fmincon(@liaoch, x0, A, b, Aeq, beq,VLB)
（4）结果为 x =
Columns 1 through 6
3.0000 0 4.0000 7.0000 6.0000
0
Columns 7 through 12
0 5.0000 0 0.0000 0 11.0000
Columns 13 through 16
3.2549 5.6523 7.2500 7.7500
fval =
85.2660
exitflag =
统计回归模型
10.1牙膏的销售量[1]
>> x1 = [-0.05 0.25 0.60 0 0.25 0.20 0.15 0.05-0.15 0.15 0.20 0.10 0.40 0.45 0.35 0.30 0.50 0.50 0.40-0.05-0.05-0.10 0.20 0.10 0.50 0.60-0.05 0 0.05 0.55];>> y = [7.38 8.51 9.52 7.50 9.33 8.28 8.75 7.87 7.10 8.00 7.89 8.15 9.10 8.86 8.90 8.87 9.26 9.00 8.75 7.95 7.65 7.27 8.00 8.50 8.75 9.21 8.27 7.67 7.93 9.26];>> scatter(x1,y), title('图1 y对x1的散点图')>> x2 = [5.50 6.75 7.25 5.50 7.00 6.50 6.75 5.25 5.25 6.00 6.50 6.25 7.00 6.90 6.80 6.80 7.10 7.00 6.80 6.50 6.25 6.00 6.50 7.00 6.80 6.80 6.50 5.75 5.80 6.80];>> scatter(x2,y), title('图2 y对x2的散点图')>> x = [ones(size(x1));x1;x2;x2.^2];>> X = x.';>> Y = y.';>> [b,bint,r,rint,stats] = regre(Y,X,0.05)b =
17.3244
1.3070
-3.6956
0.3486
bint =
5.7282
0.6829
-7.4989
0.0379
r =
-0.0988
-0.0795
-0.1195
-0.0441
0.4660
-0.0133
0.2912
0.2735
-0.2351
0.1031
-0.4033
0.1747
0.0400
-0.1504
0.1284
0.1637 28.9206 1.9311 0.1077 0.6594
-0.0527
-0.1907
-0.0870
-0.0165
-0.1292
-0.3002
-0.2933
-0.1679
-0.2177
0.1116
0.3035
0.0693
0.2474
0.2270
rint =
-0.5270
-0.5309
-0.5106
-0.4731
0.0813
-0.4609
-0.1374
-0.0870
-0.5960
-0.3280
-0.8190
-0.2618
-0.4032
-0.5933
-0.3207
-0.2841
-0.4830
-0.6248
-0.5348
-0.4423
-0.5609
-0.7181
-0.7243
-0.5548
-0.6449
-0.2994 0.3294 0.3718 0.2716 0.3848 0.8507 0.4343 0.7197 0.6340 0.1258 0.5341 0.0125 0.6112 0.4832 0.2925 0.5775 0.6116 0.3776 0.2434 0.3609 0.4092 0.3024 0.1177 0.1377 0.2190 0.2095 0.5226
-0.1037
0.7106
-0.3714
0.5099
-0.1807
0.6755
-0.1890
0.6430
stats =
0.9054
82.9409
0.0000 >> x3=x1.*x2；
>> z=[ones(size(x1));x1;x2;x2.^2;x3];>> z1=z.';>> [b,bint,r,rint,stats] = regre(Y,z1,0.05)b =
29.1133
11.1342
-7.6080
0.6712
-1.4777
bint =
13.7013
44.5252
1.9778
20.2906
-12.6932
-2.5228
0.2538
1.0887
-2.8518
-0.1037
r =
-0.0441
-0.1229
0.0299
-0.0745
0.3841
-0.0472
0.2331
0.0287
-0.0661
0.0297
-0.4372
0.1763
0.0356
-0.1382
0.1027
0.1270
0.0048
-0.1435
-0.1016
0.0050
-0.0389
-0.1334
-0.3272
-0.3274
-0.2102
0.1412
0.3250
0.1096
0.2342
0.2455
rint =
-0.4425
-0.5408
-0.3101
-0.4736
0.0245
-0.4640
-0.1674
-0.2369
-0.3751
-0.3691
-0.8118
-0.2306
-0.3788
-0.5521
-0.3172
-0.2917
-0.3944
-0.5490
-0.5193
-0.3926 0.3542 0.2951 0.3698 0.3247 0.7437 0.3695 0.6337 0.2943 0.2430 0.4284-0.0627 0.5832 0.4499 0.2757 0.5226 0.5456 0.4039 0.2621 0.3160 0.4026
-0.4360
0.3582
-0.5045
0.2378-0.7212
0.0667-0.6326
-0.0221-0.6085
0.1881
-0.2398
0.5223
-0.0484
0.6984
-0.2988
0.5181
-0.1650
0.6335
-0.1391
0.6302
stats =
0.9209
72.7771
0.0000
0.0426 >> y=17.3244+1.3070*x1-3.6956*6.5+0.3486*6.5^2;>> plot(x1,y),title('图3 模型（3）y与x1的关系'),grid on >> y=29.1133+11.1342*x1-7.6080*6.5+0.6712*6.5^2-1.4777*x1*6.5;>> plot(x1,y),title('图4 模型（5）y与x1的关系'),grid on >> y=17.3244+1.3070*0.2-3.6956*x2+0.3486*x2.^2;>> xi=linspace(5,8,100);>> p=[0.3486,-3.6956,17.3244+1.3070*0.2];>> yi=polyval(p,xi);>> plot(xi,yi),title('图5 模型（3）y与x2的关系'),grid on >> y=29.1133+11.1342*0.2-7.6080*x2+0.6712*x2.^2-1.4777*x2*0.2;>> p=[0.6712,-1.4777*0.2-7.6080,29.1133+11.1342*0.2];>> xi=linspace(5,8,100);>> yi=polyval(p,xi);>> plot(xi,yi),title('图6 模型（5）y与x2的关系'),grid on >> y=30.2267-7.7558*x2+0.6712*x2.^2;>> xi=linspace(5,8,100);>> p=[0.6712,-7.7558,30.2267];>> yi=polyval(p,xi);>> plot(xi,yi)>> y=32.4535-8.0513*x2+0.6712*x2.^2;>> p=[0.6712,-8.0513,32.4535];>> yi=polyval(p,xi);>> hold on >> plot(xi,yi), title('图7 y与x2的关系(7)与(8)的图形'),grid on >> x = [x1;x2];>> rstool(x.',Y,'quadratic',0.05)Variables have been created in the current workspace.10.5教学评估[1]
%jiaoxue.m
X1=[4.46 4.11 3.58 4.42 4.62 3.18 2.47 4.29 4.41 4.59 4.55 4.67 3.71 4.28 4.24]';
X2=[4.42 3.82 3.31 4.37 4.47 3.82 2.79 3.92 4.36 4.34 4.45 4.64 3.41 4.45 4.38]';X3=[4.23 3.29 3.24 4.34 4.53 3.92 3.58 4.05 4.27 4.24 4.43 4.52 3.39 4.10 4.35]';
X4=[4.10 3.60 3.76 4.40 4.67 3.62 3.50 3.76 4.75 4.39 4.57 4.39 4.18 4.07 4.48]';
X5=[4.56 3.99 4.39 3.63 4.63 3.50 2.84 2.76 4.59 2.64 4.45 3.48 4.06 3.76 4.15]';
X6=[4.37 3.82 3.75 4.27 4.57 4.14 3.84 4.11 4.11 4.38 4.40 4.21 4.06 4.43 4.50]';
Y=[4.11 3.38 3.17 4.39 4.69 3.25 2.84 3.95 4.18 4.44 4.47 4.61 3.17 4.15 4.33]';
X=[X1 X2 X3 X4 X5 X6];stepwise(X,Y)
参考文献
[1]姜启源, 谢金星, 叶俊.数学模型(第三版).北京: 高等教育出版社, 2003 [2]宋来忠, 王志明.数学建模与实验.北京: 科学出版社, 2005
