Tan S.T. Finite Mathematics for the Managerial, Life, and Social Sciences
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43. a. b. 2667 units
45. a.
b. 2000 units
47. (x is measured in units of a thousand)
60,000 units
49. False
Using Technology Exercises 1.3, page 39
1. 2.2875 3. 2.880952381 5. 7.2851648352
7. 2.4680851064
Exercises 1.4, page 46
1. (2, 10) 3. 5. (4, 6)
7. 1000 units; $15,000
9. 600 units; $240
11. a.
b. 8000 units; $112,000
x
y
100
20
102
In units of a thousand
Thousands of dollars
C(x)
R(x)
14,
2
3
2
x
p
80
10
10 20 30 40 50 60
Dollars
In units of a thousand
p
1
2
x 40
x
p
In units of a thousand
20
10
10 20
Dollars
x
p
In units of a thousand
6
5
4
3
2
1
123456
Dollars
c. d. (8000, 0)
13. 9259 units; $83,331
15. a. C
1
(x) 18,000 15x
C
2
(x) 15,000 20x
b.
c. Machine II; machine II; machine I
d. ($1500); $1500; $4750
17. Middle of 2003
19. a.
b. Feb. 2005
21. 8000 units; $9 23. 2000 units; $18
25. a. p 0.08x 725
b. p 0.09x 300
c. 2500 DVD players; $525
27. 300 fax machines; $600
29. a.
b. If c is increased, x gets smaller and p gets larger.
c. If b is decreased, x decreases and p decreases.
31. True
33. a. m
1
m
2
and b
2
b
1
b. m
1
m
2
c. m
1
m
2
and b
1
b
2
Using Technology Exercises 1.4, page 51
1. (0.6, 6.2) 3. (3.8261, 0.1304)
5. (386.9091, 145.3939)
b d
c a
;
bc ad
c a
t
2 4 6 8 10
y
60
50
40
30
20
10
x
y
30
15
1234567
Thousands of dollars
R(x)
C
1
(x)
C
2
(x)
x
P
50
8
In units
of a thousand
Thousands of dollars
–50
P(x)
582 ANSWERS TO CHAPTER 1 ODD-NUMBERED EXERCISES
87533_11_ANS_p579-608 1/31/08 8:52 AM Page 582
7. a.
b. (3548.39, 27,996.77)
c.
x-intercept: 3548
9. a. C
1
(x) 34 0.18x; C
2
(x) 28 0.22 x
b. c. (150, 61)
d. If the distance driven is less than or equal to 150 mi, rent
from Acme Truck Leasing; if the distance driven is more than 150
mi, rent from Ace Truck Leasing.
11. a.
b. (1920, 92)
c. 1920/wk; $92/radio
Exercises 1.5, page 56
1. a. y 2.3x 1.5
b.
3. a. y 0.77x 5.74
b.
x
y
6
5
4
3
2
1
1234567
x
y
12
10
8
6
4
2
1234
p
1
10
x 284; p
1
60
x 60
5. a. y 1.2x 2
b.
7. a. y 0.34x 0.9
b.
c. 1276 applications
9. a. y 2.8x 440
b. c. 420
11. a. y 2.8x 17.6 b. $40,000,000
13. a. y 22.7t 124.2 b. $260.4 billion
15. a. y 25.6x 74 b. 304 million
17. a. y 0.4x 3.6 b. $436 million/yr
19. a. y 0.305x 1.41 b. $0.305 billion/yr c. $3.24 billion
21. a. y 0.4x 5.22 b. $0.4 billion/yr
23. a. y 3.17x 82.1 b. $113,800
25. a. y 0.09x 15.90 b. 19.50 yr c. 18.6 yr
27. y 0.23x 1.16 b. 2.8 billion
29. False 31. True
Using Technology Exercises 1.5, page 62
1. y 2.3596x 3.8639
3. y 1.1948x 3.5525
5. a. y 1.03x 2.33 b. $10.57 billion
x
y
24
440
430
420
Years
x
y
1.0
0.2
123456
In units of a thousand
In units of a thousand
x
y
5
5
ANSWERS TO CHAPTER 1 ODD-NUMBERED EXERCISES 583
87533_11_ANS_p579-608 1/31/08 8:52 AM Page 583
7. a. y 13.321x 72.571 b. 192 million tons
9. a. y 14.43x 212.1 b. 247 trillion cu ft
Chapter 1 Concept Review Questions, page 64
1. Ordered; abscissa (x-coordinate); ordinate (y-coordinate)
2. a. x-; y-; b. third
3.
4. (x a)
2
( y b)
2
r
2
5. a. b. Undefined c. 0 d. Positive
6.
7. a. y y
1
m(x x
1
); point-slope
b. y mx b; slope-intercept
8. a. Ax By C 0 (A, B, not both zero) b.
9. mx b
10. a. Price; demanded; demand
b. Price; supplied; supply
11. Break-even 12. Demand; supply
Chapter 1 Review Exercises, page 65
1. 5 2. 5 3. 5 4. 2
5. x 2 6. y 4
7. x 10y 38 0 8.
9. 5x 2y 18 0 10.
11. 12.
13. 3x 4y 18 0
14. 15. 3x 2y 14 0
16.
17.
18. 60,000 19. a. f (x) x 2.4 b. $5.4 million
21. b. 117 mg 22. a. $200,000/yr b. $4,000,000
23. a. $22,500/yr b. V 22,500t 300,000
24. a. 6x 30,000 b. 10x c. 4x 30,000
x
y
3
– 10
–6
y
x
8
−6
y
3
5
x
12
5
3
5
;
6
5
y
1
2
x 3
y
3
4
x
11
2
y
4
5
x
12
5
a
b
m
1
m
2
; m
1
1
m
2
y
2
y
1
x
2
x
1
21c a2
2
1d b 2
2
d. ($6,000); $2000; $18,000
25. p 0.05x 200
26. 27. (2, 3) 28.
29. (2500, 50,000) 30. 6000; $22
31. a. y 0.25x b. 1600 32. 600; $80
33. a. y 1.9x 27 b. $38.4/hr
34. a. y 0.059x 19.5 b. 21.9 yr c. 21.3 yr
Chapter 1 Before Moving On, page 66
1.
2. y 3x 8 3. Yes
4. a. $15 b. $22,000 c. $18
5. 6. After 5 yr
CHAPTER 2
Exercises 2.1, page 73
1. Unique solution; (2, 1) 3. No solution
5. Unique solution; (3, 2)
7. Infinitely many solutions; ; t, a parameter
9. Unique solution; (1, 2)
11. No solution 13. k 2
15. 42x 30y 18,500 17. 5x y 100
42x 30y 18,600 5x 6y 560
19. x y 1000
0.5x 1.5y 1300
21. .06x .08y .12z 21,600
z 2x
.12z .08y
1t,
2
5
t 2 2
11,
4
3
2
x
5
y
B
A
5
5
16,
21
2
2p
1
36
x
400
9
x
p
200
150
100
50
–50
–1000 1000 50002000 4000 60003000
584 ANSWERS TO CHAPTER 2 ODD-NUMBERED EXERCISES
87533_11_ANS_p579-608 1/31/08 8:52 AM Page 584
23. 18x ⫹ 20y ⫹ 24z ⫽ 26,400
4x ⫹ 4y ⫹ 3z ⫽ 4,900
5x ⫹ 4y ⫹ 6z ⫽ 6,200
25. 12,000x ⫹ 18,000y ⫹ 24,000z ⫽ 1,500,000
x ⫽ 2y
x ⫹ y ⫹ z ⫽ 100
27. 10x ⫹ 6y ⫹ 8z ⫽ 100
10x ⫹ 12y ⫹ 6z ⫽ 100
5x ⫹ 4y ⫹ 12z ⫽ 100
29. True
Exercises 2.2, page 86
1.
3.
5. 3x ⫹ 2y ⫽⫺4 7. x ⫹ 3y ⫹ 2z ⫽ 4
x ⫺ y ⫽ 52x ⫽ 5
3x ⫺ 3y ⫹ 2z ⫽ 6
9. Yes 11. No 13. Ye s 15. No 17. No
19. 21.
23.
25.
27.
—
씮
29.
£
100
010
001
†
⫺1
2
⫺2
§
R
1
⫹ R
3
——
—
씮
⫺R
3
£
10 1
01 0
00⫺1
†
⫺3
2
2
§
R
1
⫺ 3R
2
——
—
씮
R
3
⫹ 9R
2
£
131
010
0 ⫺9 ⫺1
†
3
2
⫺16
§
⫺R
2
—
—
씮
£
131
0 ⫺10
0 ⫺9 ⫺1
†
3
⫺2
⫺16
§
R
2
⫺ 3R
1
——
—
씮
R
3
⫺ 2R
1
£
131
383
2 ⫺31
†
3
7
⫺10
§
c
10
01
`
2
0
d
R
1
⫺ 3R
2
——
—
씮
c
13
01
`
2
0
d
c
13
0 ⫺5
`
2
0
d
R
2
⫺ 2R
1
——
—
씮
c
13
21
`
2
4
dc
39
21
`
6
4
d
£
⫺6 ⫺11 0
241
1 ⫺20
†
⫺5
3
⫺10
§
£
123
0 ⫺1 ⫺5
0 ⫺7 ⫺7
†
6
⫺7
⫺14
§
c
1 ⫺2
016
`
⫺3
20
dc
12
0 ⫺5
`
4
⫺10
d
£
0 ⫺12
22⫺8
034
†
6
7
0
§
c
2 ⫺3
31
`
7
4
d
31. (2, 0) 33.
(⫺1, 2, ⫺2)
35. (4, ⫺2) 37. (⫺1, 2)
39. 41. (19, ⫺7, ⫺15)
43. (3, 0, 2) 45. (1, ⫺2, 1)
47. (⫺20, ⫺28, 13) 49. (4, ⫺1, 3)
51. 300 acres of corn, 200 acres of wheat
53. In 100 lb of blended coffee, use 40 lb of the $5/lb coffee and 60 lb of
the $6/lb coffee.
55. 200 children and 800 adults
57. $40,000 in a savings account, $120,000 in mutual funds, $80,000 in
bonds
59. 400 bags of grade-A fertilizer; 600 bags of grade-B fertilizer;
300 bags of grade-C fertilizer
61. 60 compact, 30 intermediate-size, and 10 full-size cars
63. 4 oz of food I, 2 oz of food II, 6 oz of food III
65. 240 front orchestra seats, 560 rear orchestra seats, 200 front balcony
seats
67. 7 days in London, 4 days in Paris, and 3 days in Rome
69. False
Using Technology Exercises 2.2, page 91
1. x
1
⫽ 3; x
2
⫽ 1; x
3
⫽⫺1; x
4
⫽ 2
3. x
1
⫽ 5; x
2
⫽ 4; x
3
⫽⫺3; x
4
⫽⫺4
5. x
1
⫽ 1; x
2
⫽⫺1; x
3
⫽ 2; x
4
⫽ 0; x
5
⫽ 3
Exercises 2.3, page 97
1. a. One solution b. (3, ⫺1, 2)
3. a. One solution b. (2, 4)
5. a. Infinitely many solutions
b. (4 ⫺ t, ⫺2, t); t, a parameter
7. a. No solution
9. a. Infinitely many solutions
b. (2, ⫺1, 2 ⫺ t, t); t, a parameter
11. a. Infinitely many solutions
b. (2 ⫺ 3s,1 ⫹ s, s, t); s, t, parameters
13. (2, 1) 15. No solution 17. (1, ⫺1)
19. (2 ⫹ 2t, t); t, a parameter
21. ; t, a parameter
23. ; s, t, parameters
25.
27. ; s, t, parameters
29. No solution 31. (2,
⫺1, 4)
11 ⫺
1
4
s ⫹
1
4
t, s, t2
1⫺1,
17
7
,
23
7
2
1⫺2 ⫹
1
2
s ⫺
1
2
t, s, t2
1
4
3
⫺
2
3
t, t2
1
7
9
, ⫺
1
9
, ⫺
2
3
2
ANSWERS TO CHAPTER 2 ODD-NUMBERED EXERCISES 585
—
—
씮
⫺ R
2
1
5
R
1
1
3
87533_11_ANS_p579-608 2/18/08 10:53 AM Page 585
33. x 20 z, y 40 2z; 25 compact cars, 30 mid-sized cars, and
5 full-sized cars; 30 compact cars, 20 mid-sized cars, and 10 full-
sized cars
37. $10,000 in money-market account, $60,000 in stocks, and $30,000 in
bonds; $20,000 in money-market account, $70,000 in stocks, and
$10,000 in bonds
39. a. x
1
x
6
1700
x
1
x
2
x
7
700
x
2
x
3
300
x
3
x
4
400
x
4
x
5
x
7
700
x
5
x
6
1800
b. (1700 s, 1000 s t, 700 s t, 1100 s t, 1800 s,
s, t); (900, 1000, 700, 1100, 1000, 800, 800); (1000, 1100, 800,
1200, 1100, 700, 800)
c. x
6
must have at least 300 cars/hr.
41. k 36; 43. False
Using Technology Exercises 2.3, page 101
1. (1 t,2 t, t); t, a parameter
3. t, a parameter
5. No solution
Exercises 2.4, page 107
1. 4 4; 4 3; 1 5; 4 1 3. 2; 3; 8
5. D; D
T
[1 3 20] 7. 3 2; 3 2; 3 3; 3 3
9. 11.
13. 15.
17.
19.
21. u 3, x , y 7, and z 2
23. x 2, y 2, z , and u 15
31. 33.
35. 37.
39. a.
b. E £
3256 1661 1265
1210 605 539
1353 649 517
§
D £
2960 1510 1150
1100 550 490
1230 590 470
§
B £
350.2 370.8 391.4
422.3 442.9 453.2
638.6 679.8 721
§£
220 215 210 205
220 210 200 195
215 205 195 190
§
£
130
141
220
§≥
3
2
1
5
¥
7
3
5
2
£
7
2
3 1
10
3
19
6
2
3
17
2
23
3
29
3
17
6
1 2
§
c
1.9 3.0 0.6
6.0 9.6 1.2
d
c
3 4 16
17 416
dc
359
41013
d
£
114
1 81
631
§£
16
6 1
22
§
1
17
7
6
7
t, 3 t,
18
7
1
7
t, t2;
14
2
3
y
4
3
z, y, z2
2000 2001 2002
41.
White Black Hispanic
43.
Women Men
45. True 47. False
Using Technology Exercises 2.4, page 113
1.
3.
5.
7.
Exercises 2.5, page 120
1. 2 5; not defined 3. 1 1; 7 7
5. n s; m t 7.
9. 11.
13. 15.
17. 19.
21. 23.
27. ;
31. 33. a.
35. AX B, where , ,
and B c
7
8
d
X c
x
y
dA c
2 3
3 4
d
A
T
c
25
4 6
dA c
2 1
52
d
BA c
58
13 20
dAB c
10 7
22 15
d
c
4 32
715
d£
4 20 4
4120
12 32 20
§
c
513
173
d£
6 30
218
4 49
§
c
0.57 1.93
0.64 1.76
dc
29
516
d
c
4 2
913
dc
9
10
d
c
1
3
d
£
22.2 0.3 12 4.5
21.6 17.7 9 4.2
8.7 4.2 20.7 33.6
§
£
16.44 3.65 3.66 0.63
12.77 10.64 2.58 0.05
5.09 0.28 10.84 17.64
§
£
5 6.3 6.8
3.9
1 0.5 5.4 4.8
0.5 4.2 3.5 5.6
§
£
15 38.75 67.5 33.75
51.25 40
52.5 38.75
21.25 35 65 105
§
White
Black
Hispanic
£
81 76
76.1 69.9
82.2 75.9
§
Women
Men
c
81 76.1 82.2
76 69.9 75.9
d
Mass.
U.S.
c
6.88 7.05 7.18
4.13 4.09 4.06
d
586 ANSWERS TO CHAPTER 2 ODD-NUMBERED EXERCISES
87533_11_ANS_p579-608 1/31/08 8:52 AM Page 586
37. ,
39. ,,
and
41. a.
b. The first entry shows that William’s total stockholdings are
$51,400; the second shows that Michael’s stockholdings are
$54,200.
43. a. NSD R
krones krones krones rubles
b. c. Kaitlin: $81.15; Emma: $91.27
45. ; 2006: $71.412 million, 2007: $74.536 million,
2008: $80.096 million
47. Dem Rep Ind
BA [41,000 35,000 14,000]
49.
51. [277.60]; it represents Cindy’s long-distance bill for phone calls to
London, Tokyo, and Hong Kong.
53. a. b. c.
55. False 57. True
Using Technology Exercises 2.5, page 126
1.
3.
5. £
32.89 13.63 57.17
12.85 8.37 256.92
13.48 14.29 181.64
§
£
20.09 20.61 1.3
44.42 71.6 64.89
20.97 7.17 60.65
§
£
18.66 15.2 12
24.48 41.88 89.82
15.39 7.16 1.25
§
£
17,600
6,760
2,040
§£
8800
3380
1020
§£
8800
3380
1020
§
AB £
1575 1590 1560 975
410 405 415 270
215 205 225 155
§
B £
0.78
0.88
0.80
§
B ≥
0.1651
0.1462
0.1811
0.0387
¥
N
S
D
R
A
Kaitlin
Emma
c
82 68 62 1200
64 74 44 1600
d
AB c
51,400
54,200
d
B £
0
2
4
§
X £
x
1
x
2
x
3
§AX B, where A £
111
2 1 1
324
§
and B £
6
7
4
§
AX B, where A £
2 34
023
1 12
§, X £
x
y
z
§ 7.
9.
11.
Exercises 2.6, page 135
5. 7. Does not exist
9. 11. Does not exist
13.
15.
17. a. ; ;
b. x 1; y 1
19. a. ; ;
b. x 1; y 2; z 3
21. a.
b. x 1; y 1; z 2
23. a. ;
b. x
1
1; x
2
2; x
3
0; x
4
3
25. b. (i) ; (ii) ;
27. b. (i) x 1; y 3; z 2
(ii) x 1; y 8; z 12
y
9
5
x
2
5
y
23
5
x
24
5
B ≥
6
4
7
9
¥X ≥
x
1
x
2
x
3
x
4
¥;A ≥
1111
2110
2101
2 1 13
¥
B £
3
1
7
§A £
141
232
12 3
§; X £
x
y
z
§;
B £
4
3
8
§X £
x
y
z
§A £
2 3 4
001
1 21
§
B c
3
2
dX c
x
y
dA c
25
13
d
≥
3461
2 351
4
471
4 581
¥
£
13
10
7
5
1
2
2
5
1
5
0
7
10
3
5
1
2
§
£
2 11 3
1 6 2
0 1 0
§
c
3 5
12
d
≥
170 18.1 133.1 106.3 341.3
349 226.5 324.1 164 506.4
245.2 157.7 231.5 125.5 312.9
310 245.2 291 274.3 354.2
¥
E
113 117 72 101 90
72 85 36 72 76
81 69 76 87 30
133 157 56 121 146
154 157 94 127 122
U
≥
87 68 110 82
119 176 221 143
51 128 142 94
28 174 174 112
¥
£
128.59 123.08 32.50
246.73 403.12 481.52
125.06 47.01 264.81
§
ANSWERS TO CHAPTER 2 ODD-NUMBERED EXERCISES 587
87533_11_ANS_p579-608 1/31/08 8:52 AM Page 587
29. b. (i) ; ;
(ii) x 1; y 0; z 5
31. b. (i) x
1
1; x
2
4; x
3
5; x
4
1
(ii) x
1
12; x
2
24; x
3
21; x
4
7
33. a.
35. a. ;
37.
39. a. 3214; 3929 b. 4286; 3571 c. 3929; 5357
41. a. 400 acres of soybeans; 300 acres of corn; 300 acres of wheat
b. 500 acres of soybeans; 400 acres of corn; 300 acres of wheat
43. a. $80,000 in high-risk stocks; $20,000 in medium-risk stocks;
$100,000 in low-risk stocks
b. $88,000 in high-risk stocks; $22,000 in medium-risk stocks;
$110,000 in low-risk stocks
c. $56,000 in high-risk stocks; $64,000 in medium-risk stocks;
$120,000 in low-risk stocks
45. All values of k except
47. True 49. True
Using Technology Exercises 2.6, page 141
1.
3.
5.
7. x 1.2; y 3.6; z 2.7
9. x
1
2.50; x
2
0.88; x
3
0.70; x
4
0.51
Exercises 2.7, page 147
1. a. $10 million b. $160 million
c. Agricultural; manufacturing and transportation
3. x 23.75 and y 21.25
5. x 42.85 and y 57.14
9. a. $318.2 million worth of agricultural products and $336.4 million
worth of manufactured goods
b. $198.2 million worth of agricultural products and $196.4 million
worth of manufactured goods
E
0.30 0.85 0.10 0.77 0.11
0.21 0.10 0.01 0.26 0.21
0.03 0.16 0.12 0.01 0.03
0.14 0.46 0.13 0.71 0.05
0.10 0.05 0.10 0.03 0.11
U
≥
0.01 0.09 0.31 0.11
0.25 0.58 0.15 0.02
0.86 0.42 0.07 0.37
0.27 0.01 0.05 0.31
¥
£
0.36 0.04 0.36
0.06 0.05 0.20
0.19 0.10 0.09
§
k
3
2
;
1
3 2k
c
3 2
k 1
d
c
5
7
3
7
3
7
8
7
d
B
1
c
1 3
14
d; C
1
c
1
8
3
8
1
4
1
4
d
A
1
c
3 5
1 2
d;ABC c
410
23
d
A
1
c
5
2
3
2
21
d
z
60
17
y
10
17
x
2
17
11. a. $443.75 million, $381.25 million, and $281.25 million worth of
agricultural products, manufactured goods, and transportation,
respectively
b. $243.75 million, $281.25 million, and $221.25 million worth of
agricultural products, manufactured goods, and transportation,
respectively
13. $45 million and $75 million
15. $34.4 million, $33 million, and $21.6 million
Using Technology Exercises 2.7, page 150
1. The final outputs of the first, second, third, and fourth industries are
602.62, 502.30, 572.57, and 523.46 million dollars, respectively.
3. The final outputs of the first, second, third, and fourth industries are
143.06, 132.98, 188.59, and 125.53 million dollars, respectively.
Chapter 2 Concept Review Questions, page 151
1. a. One; many; no b. One; many; no 2. Equations
3. R
i
씯씮 R
j
; cR
i
; R
i
aR
j
; solution
4. a. Unique b. No; infinitely many; unique
5. Size; entries 6. Size; corresponding
7. m n; n m; a
ji
8. cA; c
9. a. Columns; rows b. m p
10. a. A(BC); AB AC b. n r
11. A
1
A; AA
1
; singular 12. A
1
B
Chapter 2 Review Exercises, page 152
1. 2. 3. [6 2] 4.
5. x 2; y 3; z 1; w 3 6. x 2; y 2
7. a 3; b 4; c 2; d 2; e 3
8. x 1; y 2; z 1
9. 10.
11. 12.
13. 14.
15. 16.
17. x 1; y 1 18. x 1; y 3
19. x 1; y 2; z 3
20. (2, 2t 5, t); t, a parameter 21. No solution
£
3
2
2 5
11
2
111
7
2
30
§£
317 8
256 27
74 78 116
§
£
52019
220 8
26 10 30
§£
11 16 15
4 2 10
614 2
§
£
10 10 18
41426
16 32 4
§£
618 6
12 6 18
24 0 12
§
£
173
2511
10 82
§£
8911
10 13
11 12 10
§
c
17
13
dc
20
26
d£
22
14
33
§
588 ANSWERS TO CHAPTER 2 ODD-NUMBERED EXERCISES
87533_11_ANS_p579-608 1/31/08 8:52 AM Page 588
22. x 1; y 1; z 2; w 2
23. x 1; y 0; z 1 24. x 2; y 1; z 3
25. 26.
27. 28.
29. 30.
31. 32.
33. 34.
35. 36.
37.
38.
39.
40.
41. $9,274, $8,628, and $11,366
42. $2,300,000; $2,450,000; an increase of $150,000
43. a. b.
b. William: $176,641; Michael: $212,738
IBM Google Boeing GM
44. a. ;
IBM Google Boeing GM
IBM Google Boeing GM
b.
45. 30 of each type
46. Houston: 100,000 gallons; Tulsa: 600,000 gallons
47. a. $30 million b. $75 million c. agricultural; manufacturing
C c
100 100 200 300
200 100 100 100
d
Olivia
Max
B c
900 600 1000 1200
700 500 2100 900
d
A c
800 500 1200 1500
500 600 2000 800
d
B ≥
50.26
31.00
103.07
38.67
¥A c
800 1200 400 1500
600 1400 600 2000
d
A
1
£
0
1
7
2
7
1
4
7
6
7
1
2
1
2
1
2
§; x 3; y 1; z 2
A
1
£
1
2
5
4
5
111
1
2
3
5
7
10
§; x 1; y 2; z 4
A
1
c
2
5
3
10
1
5
1
10
d; x 2; y 1
A
1
c
2
7
3
7
1
7
2
7
d; x 1; y 2
c
4
7
3
7
3
7
4
7
dc
2
5
3
5
1
5
1
5
d
c
11
24
7
8
1
12
1
4
dc
3
2
1
7
2
1
d
£
0
1
5
2
5
211
1
1
5
3
5
§£
1
5
2
5
0
2
3
1
3
1
3
1
30
1
15
1
6
§
£
1
4
1
2
1
4
7
8
3
4
5
8
1
8
1
4
3
8
§£
5
4
1
4
7
4
1
4
1
4
3
4
3
4
1
4
5
4
§
c
1
4
1
2
1
8
1
4
dc
12
1
3
2
d
c
3
4
1
2
1
8
1
4
dc
2
5
1
5
1
5
3
5
d
48. $31.18 million, $31.79 million, and $36.31 million worth of the first,
second, and third industry, respectively
49. a. $145.86 million worth of agricultural products; $111.28 million
worth of manufactured goods
b. $45.86 million worth of agricultural products and $31.28 million
worth of manufactured goods
Chapter 2 Before Moving On, page 154
1.
2. a. (2, 3, 1) b. No solution c. (2, 1 3t, t), t, a parameter
d. (0, 0, 0, 0) e. (2 t,3 2t, t), t, a parameter
3. a. (1, 2) b. , t, a parameter
4. a. b. c.
5. 6. (1, 1, 2)
CHAPTER 3
Exercises 3.1, page 161
1. 3.
5. 7.
9.
11. x 1; x 5; y 2; y 4
13. 2x y 2; 5x 7y 35; x 4
15. x y 10; 7x 4y 140; x 3y 30
17. x y 7; x 2; y 3; y 7
x
y
–6
8
x
y
2
4
x
y
x = – 3
x
y
5
–5
x
y
2
£
3 2 5
326
112
§
c
05 3
4 1 11
dc
1437
1451
dc
314
5 26
d
1
4
7
,
5
7
2t, t2
1
2
3
,
2
3
,
5
3
2
ANSWERS TO CHAPTER 3 ODD-NUMBERED EXERCISES 589
Olivia
Max
Olivia
Max
87533_11_ANS_p579-608 1/31/08 8:52 AM Page 589
19.
21.
23.
25.
27.
29.
x
y
3x – 7y = – 24
x + 3y = 8
Unbounded
x
y
4
2
–2
–4
Unbounded
x
y
246
6
4
2
x = 3
Bounded
x
y
3–1
No solutionBounded
x
y
5
Unbounded
x
y
–7
4
8
Unbounded
31.
33.
35.
37. False 39. True
Exercises 3.2, page 168
1. Maximize P 3x 4y
subject to 6x 9y 300
5x 4y 180
x 0, y 0
3. Maximize P 2x 1.5y
subject to 3x 4y 1000
6x 3y 1200
x 0, y 0
5. Maximize P 45x 20y
subject to 40x 16y 3200
3x 4y 520
x 0, y 0
7. Maximize P 0.1x 0.12y
subject to x y 20
x 4y 0
x 0, y 0
9. Maximize P 50x 40y
subject to
x 0, y 0
1
100
x
1
300
y 1
1
200
x
1
200
y 1
x
y
x – y = –6
6
–6
3
x – 2y = –2
Unbounded
x
y
6x + 5y = 30
x + y = 4
3x + y = 6
Bounded
x
y
3
–4
Bounded
590 ANSWERS TO CHAPTER 3 ODD-NUMBERED EXERCISES
87533_11_ANS_p579-608 1/31/08 8:52 AM Page 590
11. Minimize C 14,000x 16,000y
subject to 50x 75y 650
3000x 1000y 18,000
x 0, y 0
13. Minimize C 300x 500y
subject to x y 10
x 5
y 10
y 6
x 0
15. Minimize C 2x 5y
subject to 30x 25y 400
x 0.5y 10
2x 5y 40
x 0, y 0
17. Minimize C 1000x 800y
subject to 70,000x 10,000y 2,000,000
40,000x 20,000y 1,400,000
20,000x 40,000y 1,000,000
x 0, y 0
19. Maximize P 0.1x 0.15y 0.2z
subject to x y z 2,000,000
2x 2y 8z 0
6x 4y 4z 0
10x 6y 6z 0
x 0, y 0, z 0
21. Maximize P 18x 12y 15z
subject to 2x y 2z 900
3x y 2z 1080
2x 2y z 840
x 0, y 0, z 0
23. Maximize P 26x 28y 24z
subject to x y z 310
x y z 205
x y z 190
x 0, y 0, z 0
25. Minimize C 60x
1
60x
2
80x
3
80x
4
70x
5
50x
6
subject to x
1
x
2
x
3
300
x
4
x
5
x
6
250
x
1
x
4
200
x
2
x
5
150
x
3
x
6
200
x
1
0, x
2
0, . . . , x
6
0
27. Maximize P x 0.8y 0.9z
subject to 8x 4z 16,000
8x 12y 8z 24,000
4y 4z 5000
z 800
x 0, y 0, z 0
29. False
Exercises 3.3, page 179
1. Max: 35; min: 5 3. No max. value; min: 27
5. Max: 44; min: 15 7. x 0; y 6; P 18
9. Any point (x, y) lying on the line segment joining and (1, 3);
P 5
11. x 0; y 8; P 64
1
5
2
, 02
1
2
3
4
3
2
3
2
5
4
13. x 0; y 4; P 12
15. x 2; y 1; C 10
17. Any point (x, y) lying on the line segment joining (20, 10) and
(40, 0); C 120
19. x 14; y 3; C 58
21. x 3; y 3; C 75
23. x 15; y 17.5; P 115
25. x 10; y 38; P 134
27. Max: x 6; y ; P 258
Min: x 15; y 3; P 186
29. 20 product A, 20 product B; $140
31. 120 model A, 160 model B; $480
33. 40 tables; 100 chairs; $3800
35. $16 million in homeowner loans, $4 million in auto loans; $2.08
million
37. 50 fully assembled units, 150 kits; $8500
39. Saddle Mine: 4 days; Horseshoe Mine: 6 days; $152,000
41. Reservoir: 4 million gallons; pipeline: 6 million gallons; $4200
43. Infinitely many solutions; 10 oz of food A and 4 oz of food B or
20 oz of food A and 0 oz of food B, etc., with a minimum value of
40 mg of cholesterol
45. 30 in newspaper I, 10 in newspaper II; $38,000
47. 80 from I to A, 20 from I to B, 0 from II to A, 50 from II to B
49. $22,500 in growth stocks and $7500 in speculative stocks; maximum
return; $5250
51. 750 urban, 750 suburban; $10,950
53. False 55. a. True b. True
59. a.
b. No solution
Exercises 3.4, page 195
1. c. $216
3. a. Between 750 and 1425
b. It cannot be decreased by more than 60 units.
5. a. x 3; y 2; P 17 b. c 8
c. 8 b 24 d.
e. Both constraints are binding.
5
4
8
3
x
y
33
2
ANSWERS TO CHAPTER 3 ODD-NUMBERED EXERCISES 591
87533_11_ANS_p579-608 1/31/08 8:52 AM Page 591