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: . : 01.12.2012. : 2012. : 23. antiplagiat.ru: < 30%

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1. , 1, , , :
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c1 c2 c3 c4
11 12 13 14 b1
a21 a22 a23 a24 b2
a31 a32 a33 a34 b3 .
, , , , , ? ? (. 4).
Q-1, .
, .
- , , , . ( 12).
2. , , , , ( ). , , (. 5).
.
3. " " (. 6). , . ? ? , ( , ); , . .
1, 2, 3 [. . 31]. .
4. 2, (a1,..., am), - (b1,..., bn) ꠠ =(ij), i =; j =



b1 b2 . . . bn
a1 c11 c12 . . . c1n
a2 c21 c22 . . . c2n
. . . . . . . . . . . . . . . . . . . .
am cm1 cm2 . . . cmn
, (. 7). ( 12).
5. (. 8), 700 . ., , 3 ( 100 .).
16. (. 12) , 7.
17. (. 13): - m0, - m1, m2 c s1, s2. 8.







































35
41
22
12

2
2
3
4
151
3
1
0
2
156
1
4
4
0
162


, 4 , 3 . , :
2 2 3 4 151
= 3 1 0 2 = 156 =(35,41,22,12)
1 4 4 0 162

, .
:

X = (x1, x2, x3, x4)

z=35x1+41x2+22x3+124?max (1)
z(x1, x2, x3, x4) = c1x1 + c2x2 + c3x3 + c4x4 ? max (z- );
:

2x1 + 2x2 + 3x3 + 4x4 ? 151
3x1 + x2 + + 2x4 ? 156 (2)
x1 +4x2 + 4x3 ? 162

a11x1+a12x2+a13x3+a14x4 < 1
211+222+233+344 < 2;
311+322+333+344 < 3

:
x1?0, x2?0, x3?0, x4?0 (3)


. (2) 5, 6, 7 :

2x1 + 2x2 + 3x3 + 4x4 + x5 = 151
3x1 + x2 + + 2x4 + x6 = 156 (4)
x1 + 4x2 + 4x3 + x7 = 162

x5, x6, x7 .

x1?0, x2?0, x3?0, x4?0, x5?0, x6?0, x7?0. (5)
(4), (5), , (1) .
, (4) , . 1, 2, 3, 4, :
x1=0, x2=0, x3=0, x4=0, x5=151, x6=156, x7=162 (6)
,
x1=0, x2=0, x3=0, x4=0 (7)
(1) , 2- , . , . , . (4) .
x5=151- 2x1 - 2x2 - 3x3 - 4x4
x6=156- 3x1 - x2 - - 2x4 (8)
x7=162- x1 - 4x2 - 4x3

2=3=4=0 2. ,

151- 2x2 ? 0 x2? 75,5
156- x2 ? 0 x2? 156 .. 0? x2?40,5 (9)
162 - 4x2 ? 0 x2? 40,5

2 2 = 40,5, , (8). (4)
x1=0, x2=40,5, x3=0, x4=0, x5=61, x6=115,5, x7=0 (10)

, (4), (4) 2 , , ,

min (bi/ai2>0) = min (151/2,156/1,162/4) = 162/4,



32=4 젠 3
x2
-, , (4) :
2




3/2x1 +x3 + 4x4 + x5 - 1/2x7 = 70
11/4x1 - x3 + 2x4 + x6 - 1/4x7 = 231/2 (11)
1/4x1+ x2 + x3 + 1/4x7 = 162/4

2, 3, 4, 7, , (10),
x1=38, x2=0, x3=0, x4=0 (12)

, , .. . (1) 2, 3, 4, 7.
(11) 1 (1). :
z = 48*(38-5/6x2 - 1/6x3 -1/6x7) +30x2+29x3+104 =
= 1824 - 40x2 -8x3 -8x7 +30x2 +29x3 +10x4 = 1824-10 x2+21 x3+10 x4-8 x7 (13)
, (12) , , , , z 3. 3 (11) ,
min (24,30,228) = 24 - - 1

, . (1)
-48x1-30x2-29x3-104 =0- z (14)
(4).

3x1 + 2x2 + 4x3 + 3x4 + x5 = 198
2x1 + 3x2 + x3 + 2x4 + x6 = 96 (15)
6x1 + 5x2 + x3 + x7 = 228
-48x1-30x2-29x3-104 =0- z

, (15), (15) 8 ,
48 x1+40 x2+8 x3+8 x7=1824
10 x2-21 x3-10 x4+8 x7=1824 - z (16)
, (11) (16), :

-0,5x2 + 3,5x3 + 3x4 + x5 - 0,5 x7 = 84
4/3x2 +2/3 x3 +2x4 + x6 - 1/3x7 = 20 (17)
x1+ 5/6x2 + 1/6x3 +1/6x7 = 38
10 x2-21 x3-10 x4+8 x7=1824 - z

, ?j - xj (17), . (13) , , .. (17)
min(?j<0) = min(-21,-10) = -21 = ?3
3 , , 13=4.
, (11), (17), :

ij = rj/ rs , r = i
2



11= 0
12 = -1/7
13 =1
14 =6/7
15 =2/7
16 = 0
17 = -1/7
2



ij = ij is/ rs * rj , i?r
2



21= 0
22 =30/21
23 =0
24 =10/7
25 = -4/7
26 =1
27 = -5/21
2




2



31 =1
32 = 6/7
33=0
34 = -1/7
35 = -1/21
36 =0
37 = 4/21
2



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