|
3
1.
: ) ; ) , .
.
) . OABC . 8.
8
. B (11/2; 21/4).
. OABC , OABC OADEFGKLC, , . (7; 3).
, .
) .
-, . :
(1)
- 53.
53
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| bi
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| di
| x 1
| x 2
| x 3
| x 4
| I
| x 3
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| 16
| x 4
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| F
| =
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| 4
| 3
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| X 1 = (0; 0; 16; 27) ( O (0; 0) . 8), F 0, F 1= 0.
X 1 . II x 1 , x 4 .
-54.
54
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| bi
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| di
| x 1
| x 2
| x 3
| x 4
| II
| x 3
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| 4/3
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| 1/3
| 21/4
| x 1
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| 2/3
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| 1/3
| 27/2
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| F
| =
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| 1/3
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| 4/3
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| X 2 = (9; 0; 7; 0) ( C (9; 0) . 8), F 36, F 2= 36.
X 2 . III , x 2 , x 3 .
- 55.
55
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| bi
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| di
| x 1
| x 2
| x 3
| x 4
| III
| x 2
|
| 21/4
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| 3/4
| 1/4
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| x 1
|
| 11/2
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| 1/2
| 1/2
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| F
| =
| 151/4
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| 1/4
| 5/4
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| X 3 = (11/2; 21/4; 0; 0) ( B (11/2; 21/4) . 8), F 151/4, F 3= 151/4.
X 3 , . , (x 3, x 4) , , X 3 .
, = (11/2; 21/4; 0; 0), = 151/4.
III , .
, . ,
, ,
a.
( , , , , x 1) - 55 :
.
:
,
:
Û
Û Û
Û . (1- )
(2)
- 55, 56.
56
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| bi
|
|
|
|
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| M
| di
| x 1
| x 2
| x 3
| x 4
| x 5
| r 1
| III¢
| x 2
|
| 21/4
|
|
| 3/4
| 1/4
|
|
|
| x 1
|
| 11/2
|
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| 1/2
| 1/2
|
|
| ¥
| r 1
| M
| 1/2
|
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| 1/2
| 1/2
| 1
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| F
| =
| 151/4
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| 1/4
| 5/4
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| M
| =
| 1/2
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| 1/2
| 1/2
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| X 3 = (11/2; 21/4; 0; 0; 0) ( X 3(11/2; 21/4) . 8), F 151/4, F 3= 151/4.
57
|
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| bi
|
|
|
|
|
| M
| di
| x 1
| x 2
| x 3
| x 4
| x 5
| r 1
| IV
| x 2
|
| 9/2
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| 1
| 3/2
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| x 1
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| 1
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| x 3
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| 2
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| F
| =
| 75/2
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| 1/2
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| M
| =
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| X 3 , , x 3, M - (1/2). IV, x 3 , r 1 .
- 57.
X 4 = (6; 9/2; 1; 0; 0) ( X 4(6; 9/2) . 8), F 75/2, F 4= 75/2.
X 4 , r 1, .
, = (6; 9/2; 1; 0; 0) = 75/2.
.
x 2 = 9/2. - 57 :
.
:
,
. (2- )
:
,
- 57, 58.
58
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| bi
|
|
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|
|
|
| M
| di
| x 1
| x 2
| x 3
| x 4
| x 5
| x 6
| r 2
| IV¢
| x 2
|
| 9/2
|
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| 1
| 3/2
|
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| x 1
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| 1
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| ¥
| x 3
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| 2
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| ¥
| r 2
| M
| 1/2
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| 1/2
| 1
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| F
| =
| 75/2
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| 1/2
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| M
| =
| 1/2
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| 1/2
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| X 4¢ = (6; 9/2; 1; 0; 0; 0) ( X 4(6; 9/2) . 8), F 75/2, F 4= 75/2.
X 4¢ , , x 5, M - (1/2). V, x 5 , r 2 .
- 59.
X 5 = (7; 3; 3;0; 1; 0) ( X 5(7; 3) 8), F 37, F 4= 37.
X 5 , r 2, .
, .
59
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| bi
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| M
| di
| x 1
| x 2
| x 3
| x 4
| x 5
| x 6
| r 2
| V
| x 2
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| 1
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| x 1
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| 2
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| x 3
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| 4
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| x 5
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| 2
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| F
| =
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| M
| =
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| ( 8).
= (11/2;21/4), = 151/4.
1- :
Û x 3 + x 4 ³ 1.
x 3 x 4 (1)
x 3 = 16 x 1 2 x 2
x 4 = 27 3 x 1 2 x 2,
,
x 3 + x 4 ³ 1 Û (16 x 1 2 x 2) + (27 3 x 1 2 x 2) ³ 1 Û
Û 4 x 1 4 x 2 ³ 42 Û x 1 + x 2 £ 21/2.
= (6; 9/2), = 75/2.
2- :
Û x 5 ³ 1.
x 5 (2)
x 3 x 4, ,
Û x 3 + x 4 ³ 3 Û (16 x 1 2 x 2) + (27 3 x 1 2 x 2) ³ 3 Û
Û 4 x 1 4 x 2 ³ 40 Û x 1 + x 2 £ 10.
.
8
: .
1. :
) ;
) , .
1.7.
2.
: ) ; ) .
.
) .
9, .
9
( 1, 1). B (16/3; 5), (5; 5).
, .
) .
10
( 1) . Ÿ X 1(16/3; 5), F 1 = 109/3 ( 10).
. , .
, 1 . x 1, , 5 < x 1 < 6 1 x 1, , , . 1 ( 2 3).
1
| 2
| 3
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10
|
10
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X 2(5; 21/4) F 2 = 143/4;
| X 3(6; 3) F 3 = 33.
|
, , , , , .
10 10 2 3. 2, 3, , .
2 , x 2, 2 . 5 < x 1 < 6 1 x 2, 2 ( 4 5), .
2
|
4
| 5
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10
|
10
|
X 4(5; 5) F 4 = 5;
| X 5(4; 6) F 5 = 34.
|
10 10 4 5.
4 5 , .
, :
:
2. :
) ;
) .
2.7.
3. .
.
, (. 11), :
11
t = 0. F = 3 x 1 + 13 x 2 max. 3 x 1 + 13 x 2 = a , X * = A (0; 5), F max = 03 + 513 = 65.
, X * = A (0; 5), F max = 65 t, x 1 + 4 x 2 = 20 (1), :
Þ t = 1/5.
, X * = A (0; 5), F max = 65 5 t.
t = 1/5 AB , X * = a×(0; 5) + (1a)×(4; 4) = (44a; 4+a), aÎ[0; 1], F max = 64.
t > 1/5, X * = B (4; 4), F max = 64 , 2 x 1 + x 2 = 12 (2),
Þ t = 23/3.
, X * = B (4; 4), F max = 64.
t = 23/3 BC , X * = a×(4; 4) + (1a)×(6; 0) = (62a; 4a), aÎ[0; 1], F max = 64.
23/3 < t £ 10, X * = C (6; 0), F max = 18 + 6 t.
:
, X * = (0; 5), F max = 65,
t = 1/5, X * = (44a; 4+a), aÎ[0; 1], F max = 64,
, X * = (4; 4), F max = 64,
t = 23/3, X * = (62a; 4a), aÎ[0; 1], F max = 64,
, X * = (6; 0), F max = 18 + 6 t.
3. .
3.7.
4. .
.
- ( 2, 1). :
- 60.
60
|
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| bi
| 1+ t
|
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| di
|
x 1
| x 2
| x 3
| x 4
|
I
| x 3
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| 8
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x 4
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F
| =
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| 1 t
| 11
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X 1 = (0; 0; 32; 30), F 0, F 1= 0.
X 1 , , x 2, (11). II, x 2 , x 3 .
- 61.
61
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| bi
| 1+ t
|
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| di
|
x 1
| x 2
| x 3
| x 4
|
II
| x 2
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| 3/4
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| 1/4
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| 32/3
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x 4
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| 7/2
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| 1/2
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F
| =
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| 29/4 t
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| 11/4
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X 2 = (0; 8; 0; 14), F 88, F 2= 88.
X 2 :
) 29/4 t > 0 Û t < 29/4, X 2 ;
) 29/4 t = 0 Û t = 29/4, X 2 , , ;
) 29/4 t < 0 Û t > 29/4, X 2 , .
) ) III, x 1 , x 4 .
- 62.
62
|
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| bi
| 1+ t
|
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| di
|
x 1
| x 2
| x 3
| x 4
|
III¢
| x 2
|
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| 5/14
| 3/14
| 14
|
x 1
| 1+ t
|
|
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| 1/7
| 2/7
| ¥
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F
| =
| 59+4 t
|
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X 3 = (4; 5; 0; 0), F (59+4 t), F 3= 59+4 t.
X 3 :
) t = 29/4, X 3 , . :
X * = a×(0; 8; 0; 14) + (1a)×(4; 5; 0; 0) = (44a; 5+3a; 0; 14a), aÎ[0; 1],
F max = 88;
)
,
X 3 ;
) 53/14 1/7 t = 0 Û t = 53/2, X 3 , , ;
) t > 53/2, X 3 , .
) ) IV, x 3 , x 2 .
- 63.
63
|
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| bi
| 1+ t
|
|
|
| di
|
x 1
| x 2
| x 3
| x 4
|
IV²
| x 3
|
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| 14/5
|
| 3/5
|
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x 1
| 1+ t
|
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| 2/5
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| 1/5
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F
| =
| 6+6 t
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X 4 = (6; 0; 14; 0), F (6+6 t), F 4= 6+6 t.
X 4 :
) t = 53/2, X 4 , . :
X * = a×(4; 5; 0; 0) + (1a)×(6; 0; 14; 0) = (62a; 5a; 1414a; 0), aÎ[0; 1],
F max = 165;
)
X 4 .
:
, X * = (0; 8; 0; 14), F max = 88,
t = 29/4, X * = (44a; 5+3a; 0; 14a), aÎ[0; 1], F max = 88,
, X * = (4; 5; 0; 0), F max = 59 + 4 t,
t = 53/2, X * = (62a; 5a; 1414a; 0), aÎ[0; 1], F max = 165,
, X * = (6; 0; 14; 0), F max = 6 + 6 t.
4. .
4.7.
5. .
.
-. :
- 64.
64
|
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| bi
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| di
|
x 1
| x 2
| x 3
| x 4
|
I
| x 3
|
| 35 t
|
|
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|
| 35/3+1/3 t II¢
|
x 4
|
| 14 t
|
| 1
|
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| 71/2 t II²
|
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F
| =
|
| 3
| 2
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X 1 = (0; 0; 35 t; 14 t), F 0, F 1= 0.
X 1 , . II x 1 .
, , :
) Û 34 £ t £ 28/5, x 3 ( II¢);
) Û 28/5 < t £ 13, x 4 ( II²).
- 65 ).
65
|
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| bi
|
|
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|
| di
|
x 1
| x 2
| x 3
| x 4
|
II¢
| x 1
|
| 35/3 + 1/3 t
|
| 5/3
| 1/3
|
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|
x 4
|
| 28/3 5/3 t
|
| 7/3
| 2/3
|
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F
| =
| 35 + t
|
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|
X 2¢ = (35/3 + 1/3 t; 0; 0; 28/3 5/3 t),
F 35 + t, F 2¢= 35 + t.
X 2¢ , . , (x 2, x 3) , , X 2¢ .
- 66 ).
66
|
|
| bi
|
|
|
|
| di
|
x 1
| x 2
| x 3
| x 4
|
II²
| x 3
|
| 14 + 5/2 t
|
| 7/2
|
| 3/2
| 4+5/7 t III¢
|
x 1
|
| 7 1/2 t
|
| 1/2
|
| 1/2
| 14 t III²
|
|
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|
F
| =
| 21 3/2 t
|
| 1/2
|
| 3/2
|
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|
X 2² = (71/2 t; 0; 14 + 5/2 t; 0), F 21 3/2 t, F 2²= 21 3/2 t.
X 2² , . III x 2 .
, , :
)
x 3 ( III¢);
)
x 1 ( III²).
- 67 ).
67
|
|
| bi
|
|
|
|
| di
|
x 1
| x 2
| x 3
| x 4
|
III¢
| x 2
|
| 4 + 5/7 t
|
|
| 2/7
| -3/7
|
|
x 1
|
| 5 6/7 t
|
|
| 1/7
| 5/7
|
|
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F
| =
| 23 8/7 t
|
|
| 1/7
| 9/7
|
|
|
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|
|
|
|
|
|
X 3¢ = (5 6/7 t; 4 + 5/7 t; 0; 0), F 23 8/7 t, F 3¢= 23 8/7 t.
68
|
|
| bi
|
|
|
|
| di
|
x 1
| x 2
| x 3
| x 4
|
III²
| x 3
|
| 35 + 6 t
| 7
|
|
| 5
|
|
x 2
|
| 14 t
|
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|
F
| =
| 28 2 t
|
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|
|
X 3¢ , . , (x 3, x 4) , , X 3¢ .
- 68 ).
X 3² = (0; 14 t; 35 + 6 t; 0), F 28 2 t, F 3²= 28 2 t.
X 3² , . , (x 1, x 4) , , X 3² .
:
, X * = (35/3 + 1/3 t; 0; 0; 28/3 5/3 t), F max = 35 + t,
, X * = (5 6/7 t; 4 + 5/7 t; 0; 0), F max = 23 8/7 t,
, X * = (0; 14 t; 35 + 6 t; 0), F max = 28 2 t.
5. .
5.7.
: 2017-02-25; !; : 339 |
:
:
: , , , , .
==> ...
1476 - | 1359 -
© 2015-2024 lektsii.org - -
: 0.227 .