Івченко І.Ю. Математичне програмування
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171
* * *, + + +, $. % ! 0
*
43
, . 3.2.
' o *, + [,' o*+ …]. min -
h = 1, $>! $ ! $-
h = 1.
+
1–1*0 0 0
0* 1 0 0' 3
0–100
0' 0 0* 3 0
1–1112
+
+
!
h = 1
10*
000
0
*
20
0
'*
3
0
'*
0000
0' 1 0* 3 0
10112
+
+
: 2—3; 1—2—4; 3. ! , «*».
10
*
000
'*
020'0
*
3
0
*
0'000
0' 1 0* 3 0
10
* '
1
12
+
+ + +
+
+
+
10000*
0100*3
0*0000
000*00
10*000
.
h = c
52
= 0. !. ;!
L(,) = 4 + 6 + 2 + 4 + 1 = 17.
2.
54
6
23
1
825
6
1
3
4
6
721
2
8
5354
1
1679
10
1
74357
8
867
9108
max.
321777
042395
400796
014457
70000
7
124430
1 = min,!.
. ; -
!.
min = 3. )
! -
«+»
8 — opt.
172
2
10*6 6 6
0*42395
4 0796
014457
7000*0'7
124430*
+++
+
+
–1 –2 –3* 3 3 3
–3* 1 –1 0 6 2
1–3*–3 4 63
–3 –2 1 1 2 4
7000*0'7
–2 –1 1 1 0 –3*
+
210*336
0
*
420
*'
65
40*0 4 6 6
0
*
14127
10 3 3
0
*
0
'*
+
+++ +
210*333
0* 4 2 0* 6 5
40*0 4 6 6
0*14124
10 3 3 0 0* 10
124100*
+
+
++++++
+
+
+
+
+
+
opt.
L = 6 + 6 + 6 + 8 + 10 + 8 = 44
3.
23354
42462
2
2243
434
35
01
0
20
43465
a
20111
01003
21222
00030
42445
1
2
20*1 1 1
0* 1 0 0' 3
10111
0' 0 0* 3 0
20223
+
+
+
+
+
' «0» $. = 0' = «0*».
'$! $ min = 1 = h.
173
'! $ ! $ -
h = 1.
1–1*0 0 0
0* 1 0 0' 3
0–10 0 0
0' 0 0* 3 0
1–11 1 2
+
+
+
10*0
00
0
*
20
0
'*
3
0
'*
0000
0' 1 0* 3 0
10112
1
0
*
00
0
'*
0' 2 0 0
*
3
0
*
0' 0 0 0
010*30
10112
+
+
+
+
+
+
+
10*0 0 0'
0' 2 0 0* 3
0* 0' 0 0 0
0' 1 0* 3 0
10'112
.
a
10000*
0 2 00*3
0*0000
010*30
10*112
min = 0
+
+
+
+
+
+
+
+
L = 4 + 6 + 2 + 4 + 1 = 17.
4.
54623
1
82561
3
46721
2
85354
1
167910
1
743578
8679108
210*66
6
0*4239
5
40*079
6
01445
7
7000*0'
7
124
430*
+++
+
+
min = 3
174
–1 –2 –3* 3 3 3
–3* 1 –1 0 6 2
1–3*–3463
–3 –2 1 1 3 4
7000*0'7
–2 –1 1 1 0 –3*
210*336
0
*
420
*'
65
40*0466
0
*'
14 1 37
10 3 3
0
*
0
*
10
124100*
210*33
6
0* 4 2 0' 6
5
40*0 4 6
6
0'1412
7
10 3 3 0* 0'
10
124100*
+
+
+
++ +
+
+
+
210*66
6
0*4239
5
40*079
6
01445
7
7000*0'
7
1244
30*
+++
+
+
+
min = 3
L
max
= 44
210*33
6
0420*
6
5
40*
046
6
0*
1412
7
10 3 3 0 0*
10
1. H ’
.
2. ’
.
1.
<, > -
# "
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175
%#'&:
1. 11.
2315847
65341715
532918
7671143
5101678
6347151
41565317
91853211
1137674
6851017
71163145
8723154
2. 12.
6347151
5101678
7671143
532918
65341718
2315847
445683771561
717510568788
574746118483
928543895148
937685641758
157253486427
3. 13.
3416958
76451816
6431029
8781254
6112789
7458162
138416594538
274656151816
626453105219
584778127764
561152372819
477445481642
4. 14.
769842
653417
532938
267543
573655
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767542
653417
532352
678543
575472
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5. 15.
634756
551678
767149
532913
653718
417297
161314212521
151411232218
171627211423
252312292119
262523142718
121315181417
176
6. 16.
161314212521
151411232218
171627211423
252312292119
262523142718
121315181417
3152874
53641517
325981
6771134
1015687
3467115
7. 17.
3416958
912765
6112789
8781254
687534
6431029
613715124
51067410
7611437
5391482
657953
2384715
8. 18.
176981412
65134117
153129318
1267151413
1571211157
735198
131416958
17161451816
6141310229
87812154
61122789
74581612
9. 19.
634756
471236
767149
579431
653718
937845
476659485425
463513443117
15331292318
221627252413
154733262515
33334224421
10. 20.
151112141510
172723162114
121517131814
151118142322
161421132125
251219232921
231539
157586
764791
435667
351687
719472
177
×àñòèíà 4
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19
3(8 3 25
1.
43 (. 3(8 3 25
@
$ , $ , ’ "-
! = = . C-
, = ( " (n!),
( ),
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= ! $ -
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$. O" , # ’ =
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// " $ : @ 1960 .,
= " ’ -
$ :, , ) 1963 .,
=.
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& :
$
min o Z = f (8) (19.1)
, #
8 G, (19.2)
G — =, f(8) =
G .
178
' = $, # > -
" $ . ? -
G
0
= G. C $-
[(G
0
), = >, # -
!
f (x) t [(G
0
), x G
0
, (19.3)
$ $ x G
0
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),
$ [(G
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) ! => > Z. [(G
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) =
G
0
, # !, $ ! 8* ,
# f(8*) = [(G
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), $ 8* — ’ (f(x)
= $ > [(G
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=
)1(
i
G
, #$
)1()1()1(
1
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jii
n
i
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@ =
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min
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(4) =
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(19.5) . ., , $ -
. % , # "
=> > =,
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179
2. 8( 3 48
@ = (. . 7).
1
4
5
6
7
1
3
4
6
3
4
4
24
3
1
6
1
2
3
&. 7. % =
;$ " " " 1 7, # -
" 4 5.
; ! ", # " 1 "
4 5 " 7.
1. &$! = ", # "-
1 2 =: G
1
— = ",
# > " 1 " 2 " 7;G
2
—
= ", # > " 1 " 3 -
" 7 (. . 8).
J [ = $ [1,2] [1,3], #
", = " = t [i.
[1,3,2] [1,3,4] [1,3,5][1,2,4] [1,2,6] [1,2,7]
[
1
= 3
[
2
=1
[
1
= 9
[
2
=5 [
3
=5 [
4
= 3
[
1
=11
[
2
=11 [
3
=6 [
4
=6 [
5
= 7
4 5
[1,3,5,4] [1,3,5,7][1,3,4,6] [1,3,4,7][1,3,2,7] [1,3,2,4]
[1,3,2,6]
4 5
1)
2)
3)
4)
[
1,2
]
[
1,3
]
G
&. 8. @ ’
180
C " [1, 3, 5, 7], # ! ,
$ # < " 1 — 7 ! -
" 5, " " = "-
: ([1, 3, 2] = ([1, 3, 4] = 5 < f ([1, 3, 5, 7]) = 7, -
=! = " [1, 3, 2] [1, 3, 4].
C [1, 3, 4, 7] f(X) = 6. %
((G ( ) = 6
! f (X) = 6, ’ .
P " " = $", -
# " # ! .
// ! ’ $ -
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# $ $ = = -
= $ , # = -
< .
1. $ -
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2. N *
3. K
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(. 9).
7
5
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7
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6
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3
4
5
6
7
2
1
&. 9. % =