Математика. Жулева Л.Д - 82 стр.

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82 3. ëÏÎÔÒÏÌØÎÁÑ ÒÁÂÏÔÁ ½6
óÏÓÔÁ×ÌÑÅÍ ÉÓÈÏÄÎÙÊ ÐÌÁÎ ÚÁÄÁÞÉ.
éÓÈÏÄÎÙÊ ÐÌÁÎ X
1
i âÁÚÉÓ c
i
X
1
4 2 0 0 0 0
P
1
P
2
P
3
P
4
P
5
P
6
1 P
3
0 5 1 0 1 0 0 0
2 P
4
0 14 2 1 0 1 0 0
3 P
5
0 10 1 1 0 0 1 0
4 P
6
0 8 0 1 0 0 0 1
5 z
j
− c
j
z
0
= 0 − 4 −2 0 0 0 0
éÓÈÏÄÎÙÊ ÂÁÚÉÓ ÓÏÓÔÏÉÔ ÉÚ ×ÅËÔÏÒÏ× P
3
, P
4
, P
5
, P
6
; ÅÍÕ ÓÏÏÔ×ÅÔÓÔ×Õ-
ÅÔ ÐÌÁÎ X
1
= (x
1
, x
2
, x
3
, x
4
, x
5
, x
6
) = (0, 0, 5, 14, 10, 8). ðÏÓËÏÌØËÕ c
3
, c
4
, c
5
, c
6
ÒÁ×ÎÏ ÎÕÌÀ, ÚÎÁÞÅÎÉÅ ÌÉÎÅÊÎÏÊ ÆÏÒÍÙ Z
0
= 0.
÷ ÂÁÚÉÓ ××ÏÄÉÔÓÑ ×ÅËÔÏÒ, ËÏÔÏÒÙÊ ÓÏÏÔ×ÅÔÓÔ×ÕÅÔ min(Z
j
− C
j
). ôÁËÏÊ
ÒÁÚÎÏÓÔØÀ Ñ×ÌÑÅÔÓÑ Z
1
− c
1
= −4; ÅÊ ÓÏÏÔ×ÅÔÓÔ×ÕÅÔ ×ÅËÔÏÒ
P
1
, ÓÌÅÄÏ×Á-
ÔÅÌØÎÏ, ×ÅËÔÏÒ P
1
ÎÕÖÎÏ ××ÅÓÔÉ × ÂÁÚÉÓ. þÔÏÂÙ ÏÐÒÅÄÅÌÉÔØ, ËÁËÏÊ ×ÅËÔÏÒ
ÎÅÏÂÈÏÄÉÍÏ ×Ù×ÅÓÔÉ ÉÚ ÂÁÚÉÓÁ, ×ÙÞÉÓÌÉÍ:
θ
0
= min
i
x
i
x
i1
= min
5
1
,
14
2
,
10
1
= 5.
÷ÅËÔÏÒ P
3
ÎÕÖÎÏ ×Ù×ÅÓÔÉ ÉÚ ÂÁÚÉÓÁ. ðÏÌÕÞÁÅÍ ÒÁÚÒÅÛÁÀÝÕÀ ÓÔÒÏËÕ É
ÒÁÚÒÅÛÁÀÝÉÊ ÓÔÏÌÂÅÃ (× ÔÁÂÌÉÃÅ ×ÙÄÅÌÅÎÏ ÒÁÍËÏÊ).
ðÒÅÏÂÒÁÚÏ×Á× ÐÌÁÎ X
1
ÐÏ ÆÏÒÍÕÌÁÍ (2), ÐÏÌÕÞÉÍ ÎÏ×ÙÊ ÐÌÁÎ:
X
2
= (x
1
, x
2
, x
3
, x
4
, x
5
, x
6
) = (5, 0, 0, 4, 5, 8).
ðÌÁÎ X
2
4 2 0 0 0 0
i âÁÚÉÓ c
i
X
2
P
1
P
2
P
3
P
4
P
5
P
6
1 P
1
4 5 1 0 1 0 0 0
2 P
4
0 4 0 1 −2 1 0 0
3 P
5
0 5 0 1 −1 0 1 0
4 P
6
0 8 0 1 0 0 0 1
5 Z
0
j
− c
j
Z
0
0
= 20 0 − 2 4 0 0 0
82                                                           3. ëÏÎÔÒÏÌØÎÁÑ ÒÁÂÏÔÁ ½6

     óÏÓÔÁ×ÌÑÅÍ ÉÓÈÏÄÎÙÊ ÐÌÁÎ ÚÁÄÁÞÉ.
                                      éÓÈÏÄÎÙÊ ÐÌÁÎ X 1
                      i âÁÚÉÓ ci X 1          4 2 0 0 0 0
                                              P1 P2 P3 P4 P5 P6
                      1     P3     0    5      1    0   1    0    0    0
                      2     P4     0 14        2    1   0    1    0    0
                      3     P5     0 10        1    1   0    0    1    0
                      4   P6    0 8 0 1                 0    0    0    1
                      5 zj − cj z0 = 0 − 4 −2           0    0    0    0

   éÓÈÏÄÎÙÊ ÂÁÚÉÓ ÓÏÓÔÏÉÔ ÉÚ ×ÅËÔÏÒÏ× P 3, P 4, P 5, P 6 ; ÅÍÕ ÓÏÏÔ×ÅÔÓÔ×Õ-
ÅÔ ÐÌÁÎ X 1 = (x1, x2, x3, x4, x5, x6) = (0, 0, 5, 14, 10, 8). ðÏÓËÏÌØËÕ c3 , c4, c5, c6
ÒÁ×ÎÏ ÎÕÌÀ, ÚÎÁÞÅÎÉÅ ÌÉÎÅÊÎÏÊ ÆÏÒÍÙ Z0 = 0.
   ÷ ÂÁÚÉÓ ××ÏÄÉÔÓÑ ×ÅËÔÏÒ, ËÏÔÏÒÙÊ ÓÏÏÔ×ÅÔÓÔ×ÕÅÔ min(Zj − Cj ). ôÁËÏÊ
ÒÁÚÎÏÓÔØÀ Ñ×ÌÑÅÔÓÑ Z1 − c1 = −4; ÅÊ ÓÏÏÔ×ÅÔÓÔ×ÕÅÔ ×ÅËÔÏÒ P 1, ÓÌÅÄÏ×Á-
ÔÅÌØÎÏ, ×ÅËÔÏÒ P 1 ÎÕÖÎÏ ××ÅÓÔÉ × ÂÁÚÉÓ. þÔÏÂÙ ÏÐÒÅÄÅÌÉÔØ, ËÁËÏÊ ×ÅËÔÏÒ
ÎÅÏÂÈÏÄÉÍÏ ×Ù×ÅÓÔÉ ÉÚ ÂÁÚÉÓÁ, ×ÙÞÉÓÌÉÍ:
                                                     
                                   xi         5 14 10
                          θ0 = min    = min    , ,      = 5.
                                i xi1         1 2 1

   ÷ÅËÔÏÒ P 3 ÎÕÖÎÏ ×Ù×ÅÓÔÉ ÉÚ ÂÁÚÉÓÁ. ðÏÌÕÞÁÅÍ ÒÁÚÒÅÛÁÀÝÕÀ ÓÔÒÏËÕ É
ÒÁÚÒÅÛÁÀÝÉÊ ÓÔÏÌÂÅÃ (× ÔÁÂÌÉÃÅ ×ÙÄÅÌÅÎÏ ÒÁÍËÏÊ).
   ðÒÅÏÂÒÁÚÏ×Á× ÐÌÁÎ X 1 ÐÏ ÆÏÒÍÕÌÁÍ (2), ÐÏÌÕÞÉÍ ÎÏ×ÙÊ ÐÌÁÎ:

                      X 2 = (x1, x2, x3, x4, x5, x6) = (5, 0, 0, 4, 5, 8).

                                             ðÌÁÎ X 2
                                               4 2 0 0 0 0
                  i       âÁÚÉÓ ci      X2     P1 P2 P3 P4 P5 P6
                  1        P1     4      5      1   0    1    0    0     0
                  2        P4     0      4      0   1   −2    1    0     0
                  3        P5     0      5      0   1   −1    0    1     0
                  4    P6   0   8               0 1 0         0    0     1
                     0        0
                  5 Zj − cj Z0 = 20             0 −2 4        0    0     0

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