数学建模实验二.docx
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数学建模实验二.docx
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数学建模实验二
实验2实验报告
2013326601054夏海浜13信科1班
一、完成教材(2013高教版)实验;
P213
1.求解线性规划问题
clear
f=[3,2,-8,5];
A=[-3,6,-5,2;7,-3,-1,3];
b=[-3,-1];
Aeq=[1,8,1,-1];
Beq=[-2];
LB=[0;;0];
[X,fval,exitflag,output,lambda]=linprog(f,A,b,Aeq,Beq,LB)
2.某快餐店一周中每天需要不同数目的雇员,设周一至少a1员,周二至少a2人,周三至少a3人,周四至少a4员,周五至少a5人,周六至少a6人,周日至少a7人,有规定雇员连续工作五天,每人每天的工资为C元,问快餐店怎样雇佣才能满足条件,又能使总聘用费最少。
clear
f=[100,100,100,100,100,100,100];
A=[-1,0,0,-1,-1,-1,-1;-1,-1,0,0,-1,-1,-1;-1,-1,-1,0,0,-1,-1;-1,-1,-1,-1,0,0,-1;-1,-1,-1,-1,-1,0,0;0,-1,-1,-1,-1,-1,0;0,0,-1,-1,-1,-1,-1];
b=[-16,-15,-16,-19,-14,-12,-18];
[X,fval]=linprog(f,A,b)
ans=
1221
P218
3.求函数f(x)=x^2+4x+4的最小值。
clear
fun='x^2+4*x+4'
ezplot(fun,[-12,8])
[X,fval,exitflag,output]=fminbnd(fun,-12,8)
>>Untitled8
fun=
x^2+4*x+4
X=
-2
fval=
0
exitflag=
1
output=
iterations:
5
funcCount:
6
algorithm:
'goldensectionsearch,parabolicinterpolation'
message:
'优化已终止:
当前的x满足使用1.000000e-04的OPTIONS.TolX的终止条件
'
4.在区间【-10,10】上,求函数f(x)=(x-2)^4*sin(x)-(x-1)^2*cos(x)的最小值
clear
fun='(x-2)^4*sin(x)-(x-1)^2*cos(x)'
ezplot(fun,[-10,10])
[X,fval,exitflag,output]=fminbnd(fun,-10,10)
>>Untitled9
fun=
(x-2)^4*sin(x)-(x-1)^2*cos(x)
X=
-2.2939
fval=
-247.6956
exitflag=
1
output=
iterations:
13
funcCount:
14
algorithm:
'goldensectionsearch,parabolicinterpolation'
message:
'优化已终止:
当前的x满足使用1.000000e-04的OPTIONS.TolX的终止条件
P222
1.求有约束的线性优化问题:
minf(x)=1/3*(x1+)^3+x2,约束条件为x1-1>=0,x2>=0.
min=1/3*(x1+1)^3+x2;
x1>=1;
end
运行结果:
Localoptimalsolutionfound.
Objectivevalue:
2.666667
Infeasibilities:
0.000000
Extendedsolversteps:
5
Totalsolveriterations:
44
VariableValueReducedCost
X11.0000000.000000
X20.0000001.000000
RowSlackorSurplusDualPrice
12.666667-1.000000
20.000000-4.000000
2.求有约束的非线性规划问题:
minf(x)=2x1^2+2x2^2-2x1x2-4x1-6x2,
约束条件为:
x1+x2<=2,
X1+5x2<=5,
X1>=0,
X2>=0,
解:
解:
min=2*x1^2+2*x2^2-2*x1*x2-4*x1-6*x2;
x1+x2<=2;
x1+5*x2<=5;
end
运行结果:
Localoptimalsolutionfound.
Objectivevalue:
-7.161290
Infeasibilities:
0.4440892E-15
Extendedsolversteps:
5
Totalsolveriterations:
30
VariableValueReducedCost
X11.1290320.000000
X20.77419350.000000
RowSlackorSurplusDualPrice
1-7.161290-1.000000
20.9677419E-010.000000
30.0000001.032258
二、lingo完成PPT上练习题;
1.
max=5*x1+8*x2;
x1+x2<=6;
5*x1+9*x2<=45;
x1>=0;
x2>=0;
end
Globaloptimalsolutionfound.
Objectivevalue:
41.25000
Infeasibilities:
0.000000
Totalsolveriterations:
2
VariableValueReducedCost
X12.2500000.000000
X23.7500000.000000
RowSlackorSurplusDualPrice
141.250001.000000
20.0000001.250000
30.0000000.7500000
42.2500000.000000
53.7500000.000000
2.
min=3*x^2+2*y^2+z^2+2*x*y-y*z-0.8*y*z;
x+y+z=1;
1.3*x+1.2*y+1.08*z>=1.12;
x>=0;x<=0.75;
y>=0;y<=0.75;
z>=0;z<=0.75;
end
Globaloptimalsolutionfound.
Objectivevalue:
0.2479167
Objectivebound:
0.2479167
Infeasibilities:
0.000000
Extendedsolversteps:
1
Totalsolveriterations:
93
VariableValueReducedCost
X0.0000000.000000
Y0.39583330.000000
Z0.60416670.000000
RowSlackorSurplusDualPrice
10.2479167-1.000000
20.000000-0.4958333
30.7500000E-020.000000
40.000000-0.2958333
50.75000000.000000
60.39583330.000000
70.35416670.000000
80.60416670.000000
90.14583330.000000
3.
sets:
D/1..7/:
a;
endsets
f=a(7);
a
(1)=1;
a
(2)=1;
@for(D(i)|i#ge#3:
a(i)=a(i-1)+a(i-2));
end
Feasiblesolutionfound.
Totalsolveriterations:
0
VariableValue
F13.00000
A
(1)1.000000
A
(2)1.000000
A(3)2.000000
A(4)3.000000
A(5)5.000000
A(6)8.000000
A(7)13.00000
RowSlackorSurplus
10.000000
20.000000
30.000000
40.000000
50.000000
60.000000
70.000000
80.000000
1.
min=-x1-5*x2;
x1-x2>=-2;
5*x1+6*x2<=30;
x1<=4;
x1>=0;
x2>=0;
@gin(x1);
@gin(x2);
end
Globaloptimalsolutionfound.
Objectivevalue:
-17.00000
Objectivebound:
-17.00000
Infeasibilities:
0.000000
Extendedsolversteps:
0
Totalsolveriterations:
0
VariableValueReducedCost
X12.000000-1.000000
X23.000000-5.000000
RowSlackorSurplusDualPrice
1-17.00000-1.000000
21.0000000.000000
32.0000000.000000
42.0000000.000000
52.0000000.000000
63.0000000.000000
2.
max=3*x1-2*x2+5*x3;
x1+2*x2-x3<=2;
x1+4*x2+x3<=4;
x1+x2<=3;
4*x2+x3<=6;
@bin(x1);
@bin(x2);
@bin(x3);
end
Globaloptimalsolutionfound.
Objectivevalue:
8.000000
Objectivebound:
8.000000
Infeasibilities:
0.000000
Extendedsolversteps:
0
Totalsolveriterations:
0
VariableValueReducedCost
X11.000000-3.000000
X20.0000002.000000
X31.000000-5.000000
RowSlackorSurplusDualPrice
18.0000001.000000
22.0000000.000000
32.0000000.000000
42.0000000.000000
55.0000000.000000
3.
min=13*x1+9*x2+10*x3+11*x4+12*x5+8*x6;
x1+x4=400;
x2+x5=600;
x3+x6=500;
0.4*x1+1.1*x2+x3<=800;
0.5*x4+1.2*x5+1.3*x6<=900;
@gin(x1);
@gin(x2);
@gin(x3);
@gin(x4);
@gin(x5);
@gin(x6);
end
Globaloptimalsolutionfound.
Objectivevalue:
13800.00
Objectivebound:
13800.00
Infeasibilities:
0.000000
Extendedsolversteps:
0
Totalsolveriterations:
0
VariableValueReducedCost
X10.00000013.00000
X2600.00009.000000
X30.00000010.00000
X4400.000011.00000
X50.00000012.00000
X6500.00008.000000
RowSlackorSurplusDualPrice
113800.00-1.000000
20.0000000.000000
30.0000000.000000
40.0000000.000000
5140.00000.000000
650.000000.000000
4.
sets:
cities/s,a1,a2,a3,
b1,b2,c1,c2,t/:
l;
roads(cities,cities)/
s,a1s,a2s,a3
a1,b1a1,b2a2,b1
a2,b2a3,b1a3,b2
b1,c1b1,c2b2,c1b2,c2
c1,tc2,t/:
d;
endsets
data:
d=633
658674
6789
56;
enddata
l
(1)=0;
@for(cities(i)|
i#gt#@index(s):
l(i)=@min(
roads(j,i):
l(j)+d(j,i)));
end
Feasiblesolutionfound.
Totalsolveriterations:
0
VariableValue
L(S)0.000000
L(A1)6.000000
L(A2)3.000000
L(A3)3.000000
L(B1)10.00000
L(B2)7.000000
L(C1)15.00000
L(C2)16.00000
L(T)20.00000
D(S,A1)6.000000
D(S,A2)3.000000
D(S,A3)3.000000
D(A1,B1)6.000000
D(A1,B2)5.000000
D(A2,B1)8.000000
D(A2,B2)6.000000
D(A3,B1)7.000000
D(A3,B2)4.000000
D(B1,C1)6.000000
D(B1,C2)7.000000
D(B2,C1)8.000000
D(B2,C2)9.000000
D(C1,T)5.000000
D(C2,T)6.000000
RowSlackorSurplus
10.000000
20.000000
30.000000
40.000000
50.000000
60.000000
70.000000
80.000000
90.000000
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