Engineering Optimization: Theory and Practice, Fourth Edition

800 Answers to Selected Problems

9.10x∗ 1 = 7. 5 , x∗ 2 = 01. 0 9.11x 1 ∗= 06 , x∗ 2 = 07 , x 3 ∗= 08

9.13x∗ 1 = 5 , x 2 ∗= 0 ,x 3 ∗= 5 ,x∗ 4 = 0

CHAPTER 10

10.1 X∗= { 2 , 1 },f∗= 31 10.3 X∗ = { 0 , 9 }, f∗= 72

10.4 X∗ = { 1 , 0 },f∗= 3 1 0.5 X∗= { 0 , 3 }, f∗= 3

1 0.6 X∗= { 3 , 3 },f∗= 93 10.7 X∗= { 4 , 3 }, f∗= 01

10.8 187 =1 0 1 1 1 0 1 1 10.9 X∗= { 1 , 2 , 0 }, f∗= 3

1 0.12 X∗= { 1 , 1 , 1 }, f∗= 81 10.13 X∗= { 1 , 1 , 1 , 1 , 0 }, f∗= 9

1 0.15 X∗= { 4 , 0 },f∗ = 4 1 0.16 X∗ = { 2 , 2. 5 }, f∗= 02. 5

CHAPTER 11

11.2V=

2

√

π h

, σv=

2

h

√

3

8

−

1

π

11.3X= 3. 2 , σX= 0. 8

1 1.4a= 769. 2308 , μX= 1 ,σX= 0. 048038

11.7fX(x)=x+ 1. 5 x^2 , fY(y)=y+ 1. 5 y^2

11.8σX= 0. 006079 cm, rejects= 1 .32% 11.9independent

11.10dependent 11.11(a)0.99904, (b)0.0475,

(c)3616 kgf/ mc^2 11.12 0 .6767

11.13R= 268 .9520 ft, σR= 65 .1941 ft, Rsecond order= 702 .1673 ft

11.15 X∗= { 0 , 0 , 0 , 12 }, f∗= 21

11.17(a) X∗= { 0. 0 , 36. 93 , 174. 40 }, f∗= 1 , 891. 72

(b) X∗= ame as in (a),s σf∗= 245. 50

(c) X∗= ame as in (a),s (f+σf)∗= 2 , 416. 22

CHAPTER 12

12.3x(t)=c 1 et+( 2 −c 1 )e−t− twherec 1 is a constant

1 2.4circle of radiusL/( 2 π )

12.6 X∗=

{

0. 2

0. 2

}

in^2 12.7 X∗=

{

1. 2169

0. 3805

}