Answers to Selected Problems 799(b)φk= 2 x+rk(〈 2 −x〉^2 + 〈 x− 10 〉^2 )
7 .27x 1 ∗= 0. 989637 , x∗ 2 = 1. 979274
7.29^14 x 12 + 161 x 22 − 1 ≤ 0 , x 1 / 5 +x 2 / 3 − 1 ≤ 0 ,r 1 = 1. 5
7 .31x 1 ∗= 4. 1 ,x 2 ∗= 5. 9 7 .34 X∗ ≈ { 0. 8984 , 0 }, f∗≈ 2. 2079
7.36 X∗≈ { 1. 671 , 17. 6 } 7.39x 1 = 0. 4028 , x 2 = 0. 8056
7.42optimum,λ 1 =λ 2 =
1
4
√
2
, λ 3 = 117.45 X∗≈ { 1. 3480 , 0. 7722 , 0. 4299 }, f∗≈ 0. 1154
CHAPTER 8
8.1f≥ 2. 268866 8.2f≥ 3. 464102 8.3f≥ 3
8.5radius= 0 .4174 m, height= 1 .6695 m
8.6radius= 0 .3633 m, height= 2 .9067 m
8.7x 1 ∗= 1. 5 × 106 , x 2 ∗= 1. 0 × 106
8.9x 1 ∗= 5. 7224 , x∗ 2 = 0. 8737 , x 3 ∗= 7. 2813
8.10x 1 ∗= 1. 0845 , x∗ 2 = 1. 1761
8.11x 1 ∗= 8. 6365 , x∗ 2 = 0. 9397 , x 3 ∗= 6. 8219 , x∗ 4 = 0. 9609
8.12x 1 ∗= 1. 1262 , x∗ 2 = 1. 1945 , x 3 ∗= 1. 6575
8.13x 1 ∗= 2. 2629 , x∗ 2 = 7. 1689 , x 3 ∗= 4. 5850
8.14x 1 ∗= 0. 3780 , x∗ 2 = 0. 5345 , x 3 ∗= 0. 5714
8.17d∗= 0. 0 02808 m, D∗= 0. 0 2935 m
8.18V∗= 233 .3201 ft/min, F∗= 0. 0 05 in/rev 8.20 2
8.22R∗= 0. 2118 , L∗= 0. 2907
8.23R∗ = 1. 2821 , L∗= 0. 5266 , f∗= 61. 2056
CHAPTER 9
9.1x 1 ∗ = 2 ,x 2 ∗=x 3 ∗ = 0 ,x 4 ∗= 3 9 .2A-B-F-J-K-L-P
9.3n 1 = 2 , n 2 = 3 , n 3 = 1 9 .424,000 ft atB, C, D, andE
9.5D-H-L-K-J-I-M
9.6stage 1( 0 , n), stage 2( 0 , 2 n/ 3 ), stage 3( 4 n/ 9 , 0 )
9.7A B 1 C 1 D 1 E 9 .9units invested in stations 1, 2, 3: (0, 2, 1)