22

/ *

22

* /

, .

p.1031122

* /

a, b, ca, b0, axbyc0,axbyc0,axbyc0,axbyc0, .3x 2y 6 , x 2y 4 , 2x + 5y10 , 5x2y 4 . (x, y), .

p.1031122

* /

, , .p.103(1, 4),(0, 2), (1, 0),(2, 2), (3, 4), (2, 1),(3, 1),(4, 1) , (2, 0),(3, 0),(4, 0),(1, 1), (2, 1),(3, 1), (4, 1), 1122

2x + y 2 = 02x + y 2 > 0

* /

p.1032x + y 2=0 .2x + y 2>0 1122

2x + y 2 = 02x + y 2 > 0

* /

.p.104Laxbyc0,a0, LLH1, H2, .L2x+y 2=0, LLH1, H2, .1122

* /

P(x0, y0)H1, PyLP'(x0', y0), p.104P(x0, y0)H1, PyLP'(x0', y0), PP'PP'1122

* /

P(x0 , y0)Laxbyc0 (x0 , y0)axbyc0.

p.104, P(x0 , y0)Laxbyc0 (x0 , y0) axbyc0. , P(x0 , y0)L2xy20 (x0 , y0) 2xy20.1122

* /

a0, axbyc0Laxbyc0. axbyc0Laxbyc0. p.1051122

* /

: (a)(b)p.1051122

* /

, a > 0, a < 0, , x0, .b0, , b > 0. b0, axbyc0Laxbyc0. axbyc0Laxbyc0. p.1051122

* /

::axbyc > 0axbyc < 0, , ,. ax + by +c 0ax + by + c 0, , ,.p.1061122(a)(b)

* /

1L1x2y = 4 , x2y 4L1L1, .

x2y 4. 2xy4 < 0. p.1061122

* /

1L22xy4 = 0, 2xy40L2, .

p.106 x2y 4. 2xy4 < 0. 1122

* /

1L13x + 2y = 6, 3x + 2y 6L1L1, . 3x2y 6. x2y > 2. p.1071122

* /

1L2x 2y = 2, x 2y > 2L2, .

p.107 3x2y 6. x2y > 2. 1122

* /

2

p.1071122

* /

2(a) L1x 2y = 2, x 2y 2L1L1, . (b) L22xy 2=0,p.107

1122

* /

22xy 20L2, .(a)(b), ,.

p.1071122

* /

2

.

p.1071122

* /

2(a) L13x 2y = 6, 3x 2y < 6L1. p.107

1122

* /

2(b) L2 x + 2y + 2 = 0, x + 2y + 2 0L2L2. .

1122p.107

* /

, (x, y)xy, (x, y).p.10833

* /

3

, p.10833

* /

3 x = 0 , x = 7, y = 0, y = 3, x + y = 9, 4x + 5y = 30 , ,.

33p.108

* /

3

y,

, p.10833

* /

3(a)y = 0, , .

(b)y = 1, , x=7.

, p.10833

* /

3(c)y = 2, , x = 5, 6, 7.

(d)y = 3, , x = 4, 5, 6.

, p.10833

* /

3 (7, 1), (5, 2), (6, 2), (7, 2), (4, 3), (5, 3), (6, 3), 7.x. p.108, 33

* /

3, . x, y,, x y,

,

p.10933

* /

3(0, 0), (0, 1), (0, 2), (0, 3), (0, 4), (0, 5), (1, 0), (1, 1), (1, 2), (1, 3), (1, 4), (2, 0), (2, 1), (2, 2), (2, 3), (3, 0), (3, 1), (3, 2), (4, 0)19.

,

33p.109

* /

, , . , , , , . , , , ,, . :p.1094

* /

..., .

..p.1094

* /

476, 3109. , 360, 68, 106. 62000, 103000, p.1104

* /

4 x6, y10, , p.110 4

* /

4

x, y, , p.110p.110 4

* /

43(4, 3), (5, 2), (5, 3), (6, 2), (6, 3), (7, 1), (7, 2)7, 7.

p.110 4

* /

4 k = 2000x3000y,

x, y

p.110 62000, 103000, 4

* /

4(x, y), , (x, y), k = 2000x3000y. , 7, (4, 3), (5, 2), (5, 3), (6, 2), (6, 3), (7, 1), (7, 2). 62000, 103000, 4

* /

4, 7

, 66, 103, 21000.p.111 62000, 103000, 4

* /

4, . , , , 4. p.11155

* /

, .k2000x3000y 4., ., 4, , . , , , .p.11155

* /

5

x, y , 2x+y. 55p.112

* /

5

, . 55p.112

* /

5(x, y), 2xy. 2xy = k, 2xy = k2x(,0).

p.1122.55

* /

5(a)k,2xy = k x. (b)k, 2xy = k x. k, ,,, , k, , 2xyp.11255

* /

5

x, y

3x + 2y. p.11255

* /

5

, .(x, y), 3x + 2y. 3x + 2y = k, 3x + 2y = k x( , 0).p.11255

* /

53x + 2y = k, (a), k.(b), k., k, , , , (2, 2), k, k = 3 2 + 2 2 = 10, 3x + 2y = 10, , 3x + 2y10.55p.112

* /

, axby, , , axby, axby. 5,(0, 0), (3, 0), , (0, 6), 66p.113

* /

2x+y,

: , 2x + y x = 0, y = 0, 2x + y0. 66p.113

(0, 0)(3, 0)(0, 5)2x+y065

* /

6(a) , .

x, y ,

2x + 3y 1. p.11366

* /

6(b) A(1, 1), B(4, 0), C(4, 3), D(1, 6).(c)2x + 3y 1 ,

x, y ,

2x + 3y 1. p.11366

* /

6

: (1)x = 1, y = 1, 2x + 3y 14 (2)x = 1, y = 6, 2x + 3y 119.

x, y ,

2x + 3y 1. p.11366

A(1, 1)B(4, 0)C(4, 3)D(1, 6)2x+3y1471619

* /

6

x, y

2x y+3. p.11466

* /

6(1), .(2)A(4, 3), B(7, 6), C(2, 6), D(2, 5). 2x y + 3,

p.11466

* /

6

, (a)x = 2, y = 6, 2x y + 31(b)x = 7, y = 6, 2x y + 311.

66p.114

A(4, 3)B(7, 6)C(2, 6)D(2, 5)2x y + 381112

* /

, , . , .(a), .(b), ..77p.114

* /

7, 6,5, 3, 3, 400, 18, k.x, y.x, y k., p.11477

* /

7x, y, p.11577

xyx 0, y 0, x + y 400400600x300y600x + 300y 180000 18500x300yk = 500x + 300y

* /

7

k = 500x + 300y. p.11577

* /

7, , (0, 0), (300, 0),(200, 200),(0, 400),77p.115

* /

7k = 500x + 300y, k

, x = 200, y = 200, k160000. 200200, 16.p.11577

(0, 0)(300, 0)(200, 200)(0, 400)k = 500x300y0150000160000120000

* /

7xA, yB, (30 x)A, (40 y)B. ,50, 60, A, B, A30, B40, , A, B, p.11577

/AB500600400550

* /

7(1)

p.11577

* /

7(2)k = 500x + 600y +400(30 x)+ 550(40 y) = 100x + 50y + 34000. (3), , A(10, 0), B(30, 0), C(30, 20), D(10, 40), E(0, 40), F(0, 10),p.11577

* /

7(3) k = 100x + 50y + 34000, k

, 10B, 30A, 30B,34500.p.11577

A(10, 0)B(30, 0)C(30, 20)D(10, 40)E(0, 40)F(0, 10)k=100x+50y +34000350003700038000370003600034500

* /

, , , , ., , .88p.116

* /

8x, y, k. , 20, 50, 10, 30. , 12, 450, , p.11688

* /

8(1)

(2)k = 30x + 20y. p.11688

* /

8(3), ,

k = 30x + 20y, k p.11688

* /

8, , k = 30x + 20y285, , x, y0, .(x, y)30x + 20y 285, 3x + 2y 28.5, x, y0, x, y3x + 2y 28, p.11788

* /

83x + 2y = 28,

(0, 14), (2, 11), (4, 8), (6, 5), (8, 2), (4, 8), (6, 5),(1)x = 4, y = 8, k = 30 4 + 20 8 = 280, (2)x = 6, y = 5, k = 30 6 + 20 5 = 280,4, 8, 6, 5, 280. : 3x + 2y = 28, 3x + 2y = 27, 3x + 2y=26, p.11788

x02468y1411852

* /

8x, y, k. , 60, 9030, 50. , 12, 700, , p.11788

* /

8(1)

(2)k = 30x + 20y. p.11788

* /

8(3), ,

k = 30x + 20y, k

p.11788

* /

8, , k = 30x + 20y265,, x, y0, .(x, y)30x + 20y 265, 3x + 2y 26.5, p.11788

* /

8x, y0, x, y3x + 2y 26, 3x + 2y = 26,

(0, 13), (2, 10), (4, 7), (6, 4), (8, 1), (2, 10), k = 30 2 + 20 10 = 260, 2, 10, 260.p.11788

x02468y1310741

22

* /

, . a > 0, ax + by + c > 0Lax + by + c = 0. b > 0, ax + by + c > 0Lax + by + c = 0. Lax + by = k, a, ba > 0, k, Lx.p.118

* /

ax + by, x, y, . Lax + by = k, a, ba > 0, k, Lx. ax + by, x, y, . p.118

* /

L1 : x + 2y 8 = 0, L2 : x y 2 = 0, L3 : y 4 = 0,

1. p.118

* /

x + 2y 8 0 L1, x y 2 0 L2,y 4 0 L3,

1. p.118

* /

, .

1. p.118

* /

AB2x + y 8 = 0, BCx + y 6 = 0, OCx = 0, OAy = 0, 2.OABC. p.118

* /

OABC p.1182.OABC.

* /

Ex y = k, x, k. p.1193.A, B, C, D, E. (x, y)x y = k, k

* /

A(1, 3), B(2, 1)Lx 3y + k = 0,(1 9 + k)( 2 3 + k) < 0, (k 5)(k 8) < 0, 5 < k < 8. 4.A(1, 3), B(2, 1)Lx 3y + k = 0, k. p.119

* /

(1), .

, 3x 2y + 1. p.119

* /

(2)A(6, 2), B(10, 6), C( 2, 6), (3)3x 2y + 1,k

, (a)x = 2, y = 6, 3x 2y + 117(b)x = 10, y = 6, 3x 2y + 119.p.119

* /

(4, 10) , ,

a = 14, b = 7. 6.ABCD, A(4, 0), B(8, 10), C(6, 14), D(2, 6). k = ax + by + 32a, bABCD(4, 10)18, a, b. p.119

* /

7.1, 2001, 501. 5000, 1000, 30, 160. x, y, k.x, y. x, yk., p.119

* /

p.119

* /

x, y. x, yk., p.119

* /

k = 5000x + 1000y.x, y. x, yk., p.119

* /

, , O(0, 0), A(30, 0), B(30, 80), C(10, 160), D(0, 160)., p.119

* /

k = 5000x + 1000y, k

, 30, 80, 230000. , p.119

* /

y ax = k, y = ax + k, y = ax + ka, yk, , k. 1., y ax. A, a. p.120

* /

AB AC0. , y = ax + kA , 1., y ax. A, a. p.120

* /

xy, k = 90x + 100y, x, y2., , 1000, 500, 90, 1500, 400, 100, 6000, 2000, p.120

* /

, ,p.120

* /

k = 90x + 100y, k

, , , 440. p.120

* /

3., 5040, H1N1, AB2030,

A, B, p.120

* /

xA, yB, k. p.120

* /

(1)

(2) k = 500x + 450y + 400(20 x) + 300(30 y)= 100x + 150y + 17000. p.120

* /

(3), , A(10, 0), B(20, 0), C(20, 30), D(0, 30), E(0, 10), p.120

* /

k = 100x + 150y + 17000, k

, 10A, 10A, 30B, 18000.

Endp.120