数学建模培训 课后十九小题详细答案.doc

1.M文件：function y = myfun(x) y = 1./(x.*(x.2 - 3*x + 2 ).(1/3);命令窗口输入：warning off allQ = quad(myfun,2,100000)Q = quad(myfun,2,10000000)Q = quad(myfun,2,1000000000000000)warning on 求出Q = 1.4389Q = 1.4396Q =1.4393因此，可以将1.4396作为此定积分的值。2.syms t h f=exp(t+h)*cos(t+h)+(t+h)2*sin(t+h); g=int(f,t,1,10); ezplot(g)xlim(-10 10)3. y,z=cylinder(1:0.2:9,100);mesh(sqrt(16-(sqrt(y.2+z.2)-5).2),y,z);hold on;mesh(-sqrt(16-(sqrt(y.2+z.2)-5).2),y,z);4.（1）程序： x=(h,t)3*sec(h)*cos(t);y=(h,t)3*sec(h)*sin(t);z=(h,t)2*tan(h);ezmesh(x,y,z)（2）ezsurf(x,y)x*y)5. ezplot(sin(x)+cos(y)=1)6（1）程序： syms x; diff(log(x+2)/(1-x),3)结果：ans = (6/(1-x)3+6*(x+2)/(1-x)4)/(x+2)*(1-x)-2*(2/(1-x)2+2*(x+2)/(1-x)3)/(x+2)2*(1-x)-2*(2/(1-x)2+2*(x+2)/(1-x)3)/(x+2)+2*(1/(1-x)+(x+2)/(1-x)2)/(x+2)3*(1-x)+2*(1/(1-x)+(x+2)/(1-x)2)/(x+2)2（2）程序：a=0,0.5,2,4;cha=diff(a)结果：cha =0.5000 1.5000 2.00007.（1）程序：x,y=solve(x2+y-6,y2+x-6)结果：x = 2 -3 1/2+1/2*21(1/2) 1/2-1/2*21(1/2) y = 2 -3 1/2-1/2*21(1/2) 1/2+1/2*21(1/2)（2）程序：x,y=solve(exp(x+sin(y)+cos(y)-10,tan(x)+10*log(y)-5)结果：x = 1.8015294326165098294767777230651 y = 2.52359037310675957610708054928828x=sym(x); diff(x3+6*x2+8*x-1)ans = -26 -43 -8 11 -12 78 -26 -44 -7 13 -14 78 -75 4 solve(3*x2+12*x+8=0) ans = -2+2/3*3(1/2) -2-2/3*3(1/2) ezplot(x3+6*x2+8*x-1,-200,200)9. 目标函数：minz=0*x1+0.1*x2+0.6*x3+0.7*x4+0.8*x5;目标方程：x1+2*x2=100; 3*x3+2*x4+x5=100;结果： Feasible solution found. Total solver iterations: 0 Variable Value MINZ 80.00000 X1 100.0000 X2 0.000000 X3 0.000000 X4 0.000000 X5 100.0000 Row Slack or Surplus 1 0.000000 2 0.000000 3 0.000000从以上结果可以得出：当x1=10010.目标函数：maxz=1.15*x4A+1.25*x3B+1.4*x2C+1.06*x5D;目标方程：x1A+x1D=100000; x2A+x2C+x2D-1.06*x1D=0; x3A+x3B+x3D-1.15*x1A-1.06*x2D=0; x4A+x4D-1.15*x2A-1.06*x3D=0; x5D-1.15*x3A-1.06*x4D=0; x3B=40000; x2C=30000;结果： Feasible solution found. Total solver iterations: 0 Variable Value MAXZ 133822.6 X4A 0.000000 X3B 0.000000 X2C 0.000000 X5D 126247.7 X1A 0.000000 X1D 100000.0 X2A 0.000000 X2D 106000.0 X3A 0.000000 X3D 112360.0 X4D 119101.6 Row Slack or Surplus 1 0.000000 2 0.000000 3 0.000000 4 0.000000 5 0.000000 6 0.000000 7 40000.00 8 30000.00投资方案：第一年：x1A=0,x1D=100000第二年：x2A=0,x2C=30000,x2D=106000第三年：x3a=0,x3B=0,x3D=112360第四年：x4A=0,x4D=119101第五年：x5D=126247.7使到第五年末拥有的资金的本利总额为最大为133822.6。11. （1）设使用A为x1台时，B使用x2台时，C使用x3台时：目标函数：max=3000*x1+2000*x2+2900*x3;目标方程：8*x1+2*x2+10*x3=300; 10*x1+5*x2+8*x3=400; 2*x1+13*x2+10*x3=420;结果：Global optimal solution found. Objective value: 135266.7 Total solver iterations: 4 Variable Value Reduced Cost X1 22.53333 0.000000 X2 23.20000 0.000000 X3 7.333333 0.000000 Row Slack or Surplus Dual Price 1 135266.7 1.000000 2 0.000000 30.00000 3 0.000000 266.6667 4 0.000000 46.66667从以上结果分析可知：当x1=22.53333,x2=23.2,x3= 7.333333时，使生产盈利最大为135266.7。（2）目标函数：max=3000*x1+2000*x2+2900*x3;目标方程：8*x1+2*x2+10*x3=300; 10*x1+5*x2+8*x3=460; 2*x1+13*x2+10*x3=420; gin(x1); gin(x2); gin(x1);Global optimal solution found. Objective value: 145740.0 Extended solver steps: 0 Total solver iterations: 5 Variable Value Reduced Cost X1 30.00000 -680.0000 X2 27.00000 -1420.000 X3 0.6000000 0.000000 Row Slack or Surplus Dual Price 1 145740.0 1.000000 2 0.000000 290.0000 3 20.20000 0.000000 4 3.000000 0.000000综合考虑方案（1）和（2），方案（2）经济效益为145740.0不合理。（3）目标函数：max=3000*x1+2000*x2+2900*x3+21000*x4+1870*x5;目标方程：8*x1+2*x2+10*x3+12*x4+4*血=300; 10*x1+5*x2+8*x3+5*x4+4*x5=460; 2*x1+13*x2+10*x310*x4+12*x5=50;x2=800000;(100*x1+50*x2)*10=10000;10000*x1+5000*x2+(100*x1+50*x2)*10syms x;q=sqrt(100-(x+2.5)2);int(g,x,0,7.5)ans=25*pi=25/8*15(1/2)=50*asin(1/4)double(ans)ans=53.8027s=4* double(ans)s=215.210915. 建一个moutain.m文档：x=0:400:5600；y=0:400:4800;z=1350 1370 1390 1400 1410 960 940 880 800 690 570 430 290 210 1501370 1390 1410 1430 1440 1140 1110 1050 950 820 690 540 380 300 2101380 1410 1430 1450 1470 1320 1280 1200 1080 940 780 620 460 370 3501420 1430 1450 1480 1500 1550 1510 1430 1300 1200 980 850 750 550 5001430 1450 1460 1500 1550 1600 1550 1600 1600 1600 1550 1500 1500 1550 1550950 1190 1370 1500 1200 1100 1550 1600 1550 1380 1070 900 1050 1150 1200910 1090 1270 1500 1200 1100 1350 1450 1200 1150 1010 880 1000 1050 1100880 1060 1230 1390 1500 1500 1400 900 1100 1060 950 870 900 936 950830 980 1180 1320 1450 1420 400 1300 700 900 850 810 380 780 750740 880 1080 1130 1250 1280 1230 1040 900 500 700 780 750 650 550650 760 880 970 1020 1050 1020 830 800 700 300 500 550 480 350510 620 730 800 850 870 850 780 720 650 500 200 300 350 320370 470 550 600 670 690 670 620 580 450 400 300 100 150 250figure(1);mashz(x,y,z)xlzbel(X), ylzbel(Y),zlzbel(Z)xi=0:10:5600;yi=0:10:4800;figure(2)z1i=interp2(x,y,z,xi,yi,nearest);surfc(xi,yi,zli)xlzbel(X), ylzbel(Y),zlzbel(Z)figure(3)z2i=interp2(x,y,z,xi,yi);surfc(xi,yi,z2i)xlzbel(X), ylzbel(Y),zlzbel(Z)figure(4)z3i=interp2(x,y,z,xi,yi,cubic);surfc(xi,yi,z3i)xlzbel(X), ylzbel(Y),zlzbel(Z)figure(5)subplot(1,3,1),contour(xi,yi,z1i,10,r);subplot(1,3,2),contour(xi,yi,z2i,10,r);subplot(1,3,3),contour(xi,yi,z3i,10,r);16. syms x1 x2 x3;A=1,4,5;4,2,6;5,6,3; x=x1;x2;x3; t=x1,x2,x3; f=t*A*x f = (x1+4*x2+5*x3)*x1+(4*x1+2*x2+6*x3)*x2+(5*x1+6*x2+3*x3)*x317. Global optimal solution found. Objective value: 6330.000 Total solver iterations: 6 Variable Value Reduced Cost X1 0.000000 95.00000 X2 0.000000 10.00000 X3 60.00000 0.000000 X4 9.000000 0.000000 X5 30.00000 0.000000 Row Slack or Surplus Dual Price 1 6330.000 1.000000 2 0.000000 -5.000000 3 39.00000 0.000000 4 0.000000 40.00000 5 0.000000 35.00000该报告说明：进行6步找到全局最优解，目标函数值为6330，变量分别为x1=95,x2=10,x3=60,x4=9,x5=30.19.结果1：Descriptive StatisticsMeanStd. DeviationN瘦肉量14.93291.1044824眼肌面积25.91883.1781124腿肉量5.0171.3850524腰肉量1.6375.2004824该表中输入了3个自变量和一个因变量的一般统计结果，包括平均值Mean，方差和个案数N为24.结果2：Correlations瘦肉量眼肌面积腿肉量腰肉量Pearson Correlation瘦肉量1.000.261.861.603眼肌面积.2611.000.249.164腿肉量.861.2491.000.346腰肉量.603.164.3461.000Sig. (1-tailed)瘦肉量.109.000.001眼肌面积.109.121.222腿肉量.000.121.049腰肉量.001.222.049.N瘦肉量24242424眼肌面积24242424腿肉量24242424腰肉量24242424该表中列出了各个变量之间的相关性，从该表中可以看出自变量腿肉量x2和因变量瘦肉量y的相关性最大。结果3：Variables Entered/RemovedbModelVariables EnteredVariables RemovedMethod1腰肉量, 眼肌面积, 腿肉量a.Entera. All requested variables entered.b. Dependent Variable: 瘦肉量该表格输出的是被引入或从回归方程中被剔除的各个变量。结果4：Model SummaryModelRR SquareAdjusted R SquareStd. Error of the Estimate1.921a.848.825.46152a. Predictors: (Constant), 腰肉量, 眼肌面积, 腿肉量该表格输出的是常用统计量，从该表格可以看出，关系数R=0.92