运筹学导论8版高级篇习题答案.pdf

C ( )

13

13.1A

2.(1,0) (0,2) Q , 0<λ<1, λ(1,0)+(1?λ)(0,2)=(λ,2?2λ) Q .

13.1B

2.(b) , x 1>1,0

(d) .

(f)

.

运筹学导论8版高级篇习题答案.pdf

C.14

3.(a) , det(B )=?

4.

(d) , 3 .

13.1C

1.

B ?1=

0.3?0.20.1

0.1

x 1x 2x 3x 4 z 1.5?0.50021.5x 300.5102x 4

0.5

1

1.5

, .4. z =34.

max z =2x 1+5x 2s .t .x 1 4,x 2 6,x 1+x 2 8,x 1,x 2 0.

, * .

2 C( )

13.2A

1.(a)P1 .(b)B=(P2,P4) .

2. X B,

{z j?c j}=c B B?1B?c B=c B I?c B=c B?c B=0 7. , n?m.

10. , , .

11.(a) x j=1α, x j.(b) x j=βα, x j.

13.2B

2.(b)(x1,x2,x3)=(1.5,2,0),z=5.

13.3A

2.(b)(x1,x2,x3,x4,x5,x6)=(0,1,0.75,1,0,1),z=22.

13.4A

2.max w=Y b s.t.Y A c,Y 0.

13.4B

5. 1:(b1,b2,b3)=(4,6,8)? =34.

2:(c1,c2)=(2,5)? =34.

7.min w=Y b s.t.Y A=C,Y .

13.5A

1.?27 t<1.

2.(a)

t

(x2,x3,x6)=(5,30,10)0 t 13

(x2,x3,x1)=(254,904,5)13 t 52

(x2,x4,x1)=(52,15,20)52 t<∞

5.{z j?c j}j=1,4,5=

4?3t

2

?3t2

2

,1?t2,2?t

2

+t2

2

. 0 t 1, .

13.5B

1.(a)t1=10,B1=(P2,P3,P4).

2. t=0 ,(x1,x2,x4)=(0.4,1.8,1). 0 t 1.5, . t>1.5,

.

C( ) 3

14

14.1A

1.(a) 0.15 0.25.(b)0.571.(c)0.821.

2.n 2

3.3.n >253.

14.1B

3.

532

.4. p =Liz , John 3p , Jim .Ann 6p . 4 , p +3p +3p +3p +6p =1.(a)

3

13

.(b)

7

13

.(c)

6

13

. 14.1C

3.(a)0.375.(b)0.6.7.0.9545.

14.2A

2.(a)K =20.

3.P { 1100}=0.3.

14.3A

3.(a)P {50 70}=0.6667.

(b) =2.67.(c) =$22.33.

14.3B

1. =3.667 =1.556.

14.3C

1.(a)P(x 1=1)=P(x 2=1)=0.4,P(x 1=2)=P(x 2=2)=0.2,P(x 1=3)=P(x 2=

3)=0.4.

(b) P(x 1,x 2)=P(x 1)P(x 2).

14.4A

1. 12

10

.

2.0.0547.

4 C( )

14.4B

1.0.8646.

3.(a)P{n=0}=0.(b)P{n 3};1.

14.4C

1.λ=12 / .P{t 5 }=0.63.

14.4D

2.0.001435.

15

15.1A

1.(a) 537 , 1000 .

15.1B

2.y?=317.82 ,R?=46.82 .

3.y?=316.85 ,R?=58.73 . 15.1-2 ,y?=319.44 ,R?=93.61 .

15.1-2 , R? , .

15.2A

3.0.43 p 0.82.

6.32 .

15.2B

1. x<4.53, 9?x , .

15.3A

2. x<4.61, 4.16?x , .

16

16.1A

1.(a)P{H}=P{T}=0.5. 0 R 0.5,Jim 10 0.5 R 1,Jan

10 .

7. 0 R 0.5,L=1 0.5 R 1,L=2 .

0 R 0.2, =0 0.2 R 0.9, =1

; 0.9 R 1, =2 . R L. L=1 ,

C( ) 5 R , L=2, , , .

16.2A

1.(a) .

16.3A

4. C.1

5.

运筹学导论8版高级篇习题答案.pdf

C.15

16.3B

1.t=?1λln(1?R), λ=4 .

R t( )

1––0

20.05890.0151760.015176

30.67330.2796780.294855

40.47990.1634340.458288

2.t=a+(b?a)R.

4.(a)0 R 0.2:d=0;0.2 R 0.5:d=1;0.5 R 0.9:d=2;0.9 R 1:

d=3;

).

9. 0 R p, x=0; x=( ln(1?R)

ln q

16.3C

1.y=?15ln(0.0589×0.6733×0.4799×0.9486)=0.803 .

2.t=x1+x2+x3+x4, x i=10+10R i,i=1,2,3,4.

16.4A

1. 16.4-1 , 4. , 50

, .

16.5A

2.(a) .(b) .

3.(a)1.48 .(b)7.4 .

6 C( )

16.6A

2. 15.07 μ 2

3.27.

17

17.1A

2.S1:

S2:

S3:

S4:

S5:

S1S2S3S4S5

S10.40.6000

S20.10.30.600

S30.100.50.40

S40.40000.6

S510000 17.2A

2.

S1S2S3S4S5

00100

S1S2S3S4S5

S10.40.6000

S20.10.30.600

S30.100.50.40

S40.40000.6

S510000

(2 2 ) (P2)

S1S2S3S4S5

S10.220.420.3600

S20.130.150.480.240

S30.250.060.250.20.24

S40.760.24000

S50.40.6000

2 =(00100)P2

C( ) 7

(2 )

S10.25

S20.06

S30.25

S40.2

S50.24

P{ ,S4,2 }=0.2.

17.3A

1.(a) excelMarkovChains.xls, , 3.

(b) 1,2,3 , 4 .

17.4A

1.(a)

S C R

S0.80.20

C0.30.50.2

R0.10.10.8

(π1,π2,π3)=(π1,π2,π3)P

π1+π2+π3=1

S0.502.0

C0.254.0

R0.254.0

=2×0.5+1.6×0.25+0.4×0.25=$1500

(b) μSS=2 , .

5.(a)

0.950.040.01

0.060.90.04

00.10.9

(b)

0.4411752.2666728

0.3676462.7200089

0.1911765.2307892

44.12% ,36.76% ,19.11% .

8 C( )

(c) =0.12($5000×0.3676+12000×0.1911)×70000000

=$34711641097.07

14.(a) =(i,j,k)=( ?2 , ?1 , ),

i,j,k=(0 1)

, , (1-0-0) (0-0-1).

0-0-01-0-00-1-00-0-11-1-01-0-10-1-11-1-1

0-0-00.1000.90000

1-0-00.2000.80000

0-1-000.20000.800

0-0-1000.20000.80

1-1-000.30000.700

1-0-1000.30000.70

0-1-100000.3000.7

1-1-100000.5000.5

(b)

0-0-00.014859

1-0-00.066865

0-1-00.066865

0-0-10.066865

1-1-00.178306

1-0-10.178306

0-1-10.178306

1-1-10.249629

3 =1(0.066865+0.066865+0.066865)

+2(0.178306+0.178306+0.178306)

+3(0.249629)=2.01932

=2.01932/3=0.67311

17.5A

1.(a)

12345

10000

:

12345

00.33330.33330.33330

0.333300.333300.3333

0.33330.3333000.3333

0.50000.5

00.33330.33330.33330

C( ) 9

(3 )

10.074070.214286

20.29630.214286

30.29630.214286

40.259260.142857

50.074070.214286

(b)a5=0.07407

(c)π5=0.214286

(d)μ5=4.6666

(I?N)?1Mu

1235

12110.66674.6666

211.6250.8750.33333.8333

310.8751.6250.33333.8333

410.50.51.33333.3333

5.(a)

A B C

A0.750.10.15

B0.20.750.05

C0.1250.1250.75

(b)

A0.394737

B0.307018

C0.298246

A:39.5%,B:30.7%,C:29.8%

(c)

(I?N)?1Mu

A C B

A5.714293.42857A9.14286

C2.857145.71429C8.57143

12C

A5.882352.35294A8.23529

B4.705885.88235B1.5882

A→B:9.14

A→C:8.23

17.6A

2.(a) 1 ,2 ,3 ,

10 C( )

P

123

100.300.7

2000.10.9

30001

0001

(b)

(I?N)?1Mu

123

110.30.0311.33

2010.0121.1

300131

1.33 .

8.(a)

P

1234F

10.20.8000

200.220.7800

3000.250.750

40000.30.7

F00001

(b)

(I?N)?1Mu

1234F

11.251.2821.3331.42915.29

201.2821.3331.42924.04

3001.3331.42932.76

40001.42941.43

(c) , 16 (4 ) .

=5.29, .

(d) , (c).

10.(a) 0,1,2,3,D( )

P

0123D

00.50.5000

10.400.600

20.3000.70

30.20000.8

D00001

(b) 12 .

C( )

11

(I ?N )?1

Mu 0123D 05.9522.9761.7861.2501213.9522.9761.7861.2519.9622.6191.311.7861.2526.963

1.19

0.595

0.357

1.25

3

3.39

(c)6.96 .

18

18.1A

1.(a) .

(b) x =0 .

(e)x =0 , x =0.63 , x =?0.63 .4.(x 1,x 2)=(?1,1) (2,4).

18.2A

1.(b)(?x 1,?x 2)=(

2.83,?2.5)?x 2.

18.2B

3. 2(x i ?

x 2n

x i

)=0,i =1,2,···,n ?1. x i =

n

√C ,i =1,2,···,n .

?f =2δn

√C 2?n .

6.(b) (x 1,x 2,x 3,x 4)=(?5

74,?1074

,15574,60

74

), .

18.2C

2. (x 1,x 2,x 3)=(?14.4,4.56,?1.44) (4.4,0.44,0.44).

19

19.1A

2.(c)x =2.5, ?=0.000001.

(e)x =2, ?=0.000001.

19.1B

1. ,?f (X )=?f (X 0)+H (X ?X 0).Hessie H X , f (X ) . , , . ,?f (X )=0, X =X 0?H ?1?f (X 0). X ?f (X )=0, X 0 ,X .

12 C( )

19.2A

2. x1=0,x2=3,z=17.

4. w j=x j+1,j=1,2,3,v1=w1w2,v2=w1w3,

max z=v1+v2?2w1?w2+1

s.t.v1+v2?2w1?w2 9

ln v1?ln w1?ln w2=0

ln v2?ln w1?ln w3=0

19.2B

1.x1=1,x2=0,z=4.

2.x1=0,x2=4,x3=0.7,z=?2.35.

19.2C

1.max z=x1+2x2+5x3

s.t.2x1+3x2+5x3+1.28y 10

9x21+16x23?y2=0

7x1+5x2+x3 12.4

x1,x2,x3,y 0

20

20.1A

1. C.16.

运筹学导论8版高级篇习题答案.pdf

C.16

20.1B

1. 1: .

C( ) 13

x12x13x24x32x34

min z15346

111=50

2?11?1=?40

3?111=20

4?1?1=?30

03010100

∞40∞∞∞

2 .

x 12x 13x 24x 32x 34

min z15346

111=20

2?11?1=?40

3?111=40

4?1?1=?20

∞10∞∞∞

20.1C

1. =9895 . 1 210 , 3 220 .

5. =24300 . .

1 2

10500

24500

30300

110000

201000

20.2A

1.(c) x2 M. ,

(x1,x2)=α1(0,0)+α2(10,0)+α3(20,10)+α4(20,M)+α5(0,M)

α1+α2+α3+α4+α5=1,αj 0,j=1,2,···,5

2. 1 (x1,x2)=α1(0,0)+α2(125,0)+α3(0,12)

2 (x4,x5)=β1(5,0)+β2(50,0)+β3(0,10)+β4(0,5)

α1=α2=0,α3=1?x1=0,x2=12

β1=0.4889,β2=0.5111,β3=β4=0?x4=28,x5=0

6. , .

(x1,x2,x3,x4)=(5

3,15

3

,0,20),z=195.

14 C( )

22

22.1A

2. 1 , . 2 , . 3 .

22.2A

1. 1 , $10000. 2 , . 3 . 4 .

$35520

4. 2 1,3 2,3 3.

22.3A

3. 1 $1, 2 $1, 3 $1 . =0.109375.

23

23.1A

2. , 1 , 2 , 3 , 1 2 , 1 3

, 2 3 , .

23.2A

1. 1 2 , . 3 .

3. , 2 .

23.3A

1. 1 .

D

D.1

D.1.1

p1,p2,···,p n n , P ,

P=(p1,p2,···,p n)

P n ( ),P i p i. ,P=(1,2) .

D.1.2 ( )

n

P=(p1,p2,···,p n)

Q=(q1,q2,···,q n)

R=(r1,r2,···,r n)

R=P±Q i r i=p i±q i. , P,Q,S,

P+Q=Q+P( )

(P±Q)±S=P±(Q±S)( )

P+(?P)=0( )

D.1.3

P ( )θ,

Q=θP=(θp1,θp2,···,θp n)

P θ . , P,S θ,γ,

θ(P+S)=θP+θS( )

θ(γP)=(θγ)P( )

D.1.4

P1,P2,···,P n ,

n

θj P j=0?θj=0,j=1,2,···,n

j=1

844 D

n

j=1

θj P j=0, θj=0

. ,

P1=(1,2),P2=(2,4)

, θ1=2 θ2=?1,

θ1P1+θ2P2=0

D.2

D.2.1

. A a ij i j . m n m×n ( ) . , (4×3)

A=?

??

??

a11a12a13

a21a22a23

a31a32a33

a41a42a43

?

??

??= a ij 4×3

D.2.2

(1) , m=n.

(2) , 1, 0.

(3×3)

I3=?

??

100

010

001

?

??

(3) 1 n .

(4) m 1 .

(5) A T A (transpose), i j,A a ij

A T a ji. ,

A=?

??

14

25

36

?

???A T=

123

456

(6) B=0 (zero matrix), B .

(7) A= a ij ,B= b ij , , i,j

a ij=

b ij.

D.2 845

D.2.3

( ) . , ( D.2.6).

( ) A= a ij B= b ij , (m×n) , , D=A+B .

d ij m×n= a ij+b ij m×n

A,B,C ,

A+B=B+A( )

A±(B±C)=(A±B)±C( )

(A±B)T=A T±B T

A= a ij B= b ij , A B , D=AB . A (m×r) ,B (r×n) , D (m×n) , m n . ,D

d ij=

r

k=1

a ik

b kj, i j

,

A=

13

24

,B=

579

680

D=

13

24

579

680

=

1×5+3×61×7+3×81×9+3×0

2×5+4×62×7+4×82×9+4×0

=

23319 344618

,AB=BA, BA .

I m A=AI n=A,I m,I n

(AB)C=A(BC)

C(A±B)=CA±CB

(A±B)C=AC±BC

αAB=(αA)B=A(αB),α

A (m×r) ,

B (r×n) , A B

A= A

11A12A13

A21A22A23

,B=

?

??

B11B12

B21B22

B31B32

?

??

846 D

, i,j,A ij B ij ,

A×B= A

11B11+A12B12+A13B31A11B12+A12B22+A13B32 A21B11+A22B21+A23B31A21B12+A22B22+A23B32

,

???123

105

256

?

??

?

??

4

1

8

?

??=

?

??

??

(1)(4)+(23)

1

8

1

2

(4)+

05

50

1

8

?

??

??=

?

??

??4+2+24

4

8

+

40

53

?

??

??=

?

??

30

44

61

?

??

D.2.4

n

A=?

??

??

?

a11a12 (1)

a21a22 (2)

..

.

..

.

..

.

a n1a n2···a nn

?

??

??

?

,

P j

1j2···j n =a1j

1

a2j

2

···a nj n

A j1,j2,···,j n .

∈j

1j2···j n =

1,j1j2···j n

0,j1j2···j n

ρ n! , A

ρ∈j

1j2···j n

P j

1j2···j n

det A |A|.

A=?

??

a11a12a13

a21a22a23

a31a32a33

?

??

|A|=a11(a22a33?a23a32)?a12(a21a33?a31a23)+a13(a21a32?a22a31) .

(1) , .

(2)|A|=|A T|.

(3) B A , |B|=?|A|.

(4) A ( ) , |A|=0.

(5) α ( ) , |A| .

D.2 847

(6) α,

.

(7) A B n ,

|AB |=|A ||B |

|A | a ij M ij A i j . ,

A =?

?

?a 11

a 12

a 13

a 21a 22a 23a 31a 32a 33

?

??

M 11

= a 22a 23a 32

a 33 ,M 22= a 11a 13a 31a 33

,··· A ij =(?1)i +j M ij B a ij (cofactor), A ||A ij || , adj A = A ij T =?

?

????A 11A 21···A n 1

A 12A 22

···A n 2..

.......A 1n

A 2n ···

A nn

?

?

?

??? ,

A =??

?1232323

34?

??

A 11=(?1)2(3×4?2×3)=6,A 12=(?1)3(2×4?3×2)=?2,···,

adj A =???61?5?2?54?33?1

??

?

D.2.5

r , r . (full-rank) (nonsingular) .

A =???123234357???

A (singular) ,

|A |=1×(21?20)?2×(14?12)+3×(10?9)=0

A r =2,

122

3

=?1=0

相关推荐
相关主题
热门推荐