Математика. Жулева Л.Д - 81 стр.

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3.2. ìÉÎÅÊÎÏÅ ÐÒÏÇÒÁÍÍÉÒÏ×ÁÎÉÅ 81
z
j
−c
j
É ×ÙÂÉÒÁÅÔÓÑ ÎÏ×ÙÊ ×ÅËÔÏÒ, ÓÏÏÔ×ÅÔÓÔ×ÕÀÝÉÊ min(z
j
−c
j
); ÏÐÔÉÍÁÌØ-
ÎÙÊ ÐÌÁÎ × ÜÔÏÍ ÓÌÕÞÁÅ ÂÕÄÅÔ ÄÏÓÔÉÇÎÕÔ, ËÏÇÄÁ ×ÓÅ ÒÁÚÎÏÓÔÉ (z
j
− c
j
) > 0.
ðÒÉÍÅÒ 4. îÁÊÔÉ ÍÁËÓÉÍÕÍ ÌÉÎÅÊÎÏÊ ÆÏÒÍÙ z = 4x
1
+ 2x
2
ÐÒÉ ÓÌÅÄÕ-
ÀÝÉÈ ÏÇÒÁÎÉÞÅÎÉÑÈ:
x
1
6 5,
2x
1
+ x
2
6 14,
x
1
+ x
2
6 10,
x
2
6 8,
x
1
> 0, x
2
> 0.
òÅÛÅÎÉÅ. ðÒÉ×ÅÄÅÍ ÚÁÄÁÞÕ Ë ËÁÎÏÎÉÞÅÓËÏÍÕ ×ÉÄÕ:
x
1
+ x
3
= 5,
2x
1
+ x
2
+ x
4
= 14,
x
1
+ x
2
+x
5
= 10,
x
2
+ x
6
= 8,
x
j
> 0 (j = 1, 2, 3, 4, 5, 6),
z = 4x
1
+ 2x
2
+ 0x
3
+ 0x
4
+ 0x
5
+ 0x
6
.
óÉÓÔÅÍÕ ÏÇÒÁÎÉÞÅÎÉÊ × ×ÅËÔÏÒÎÏÊ ÆÏÒÍÅ ÍÏÖÎÏ ÚÁÐÉÓÁÔØ ÔÁË:
P
1
x
1
+ P
2
x
2
+ P
3
x
3
+ P
4
x
4
+ P
5
x
5
+ P
6
x
6
= P
0
ÉÌÉ
P x = P
0
, ÇÄÅ
X =
x
1
x
2
x
3
x
4
x
5
x
6
P
0
=
5
14
10
8
P
1
=
1
2
1
0
P
2
=
0
1
1
1
P
3
=
1
0
0
0
P
4
=
0
1
0
0
P
5
=
0
0
0
0
P
6
=
0
0
0
1
ðÏÓËÏÌØËÕ ÉÝÅÔÓÑ ÍÁËÓÉÍÕÍ ÚÁÄÁÞÉ, ÏÐÔÉÍÁÌØÎÙÊ ÐÌÁÎ ÂÕÄÅÔ ÄÏÓÔÉÇ-
ÎÕÔ, ËÏÇÄÁ ×ÓÅ ÒÁÚÎÏÓÔÉ (z
j
− c
j
) > 0.
3.2. ìÉÎÅÊÎÏÅ ÐÒÏÇÒÁÍÍÉÒÏ×ÁÎÉÅ                                            81

zj −cj É ×ÙÂÉÒÁÅÔÓÑ ÎÏ×ÙÊ ×ÅËÔÏÒ, ÓÏÏÔ×ÅÔÓÔ×ÕÀÝÉÊ min(zj −cj ); ÏÐÔÉÍÁÌØ-
ÎÙÊ ÐÌÁÎ × ÜÔÏÍ ÓÌÕÞÁÅ ÂÕÄÅÔ ÄÏÓÔÉÇÎÕÔ, ËÏÇÄÁ ×ÓÅ ÒÁÚÎÏÓÔÉ (zj − cj ) > 0.
   ðÒÉÍÅÒ 4. îÁÊÔÉ ÍÁËÓÉÍÕÍ ÌÉÎÅÊÎÏÊ ÆÏÒÍÙ z = 4x1 + 2x2 ÐÒÉ ÓÌÅÄÕ-
ÀÝÉÈ ÏÇÒÁÎÉÞÅÎÉÑÈ:
                             
                               x       6 5,
                              1
                             
                               2x1 + x2 6 14,
                             
                               x1 + x2 6 10,
                             
                                     x2 6 8,
                             x1 > 0, x2 > 0.
  òÅÛÅÎÉÅ. ðÒÉ×ÅÄÅÍ ÚÁÄÁÞÕ Ë ËÁÎÏÎÉÞÅÓËÏÍÕ ×ÉÄÕ:
                 
                   x        + x3                   = 5,
                  1
                 
                   2x1 + x2       + x4              = 14,
                 
                   x1 + x 2           +x5          = 10,
                 
                         x2                  + x6 = 8,
                    xj > 0      (j = 1, 2, 3, 4, 5, 6),
               z = 4x1 + 2x2 + 0x3 + 0x4 + 0x5 + 0x6.
  óÉÓÔÅÍÕ ÏÇÒÁÎÉÞÅÎÉÊ × ×ÅËÔÏÒÎÏÊ ÆÏÒÍÅ ÍÏÖÎÏ ÚÁÐÉÓÁÔØ ÔÁË:
              P 1 x1 + P 2 x2 + P 3 x3 + P 4 x4 + P 5 x5 + P 6 x6 = P 0
ÉÌÉ P x = P 0, ÇÄÅ
                       
                     x1                                       
                   x2                   5                    1
                       
                   x3                  14                2
                X=
                   x4 
                                  P0 =     
                                         10           P1 = 
                                                             1
                                                                 
                       
                   x5                   8                    0
                     x6
                                                          
                        0              1                     0
                      1                                 1
                 P2 =        P3 =  0  P4 =                
                      1             0                   0
                        1              0                     0
                                          
                                  0          0
                                0        0
                           P5 =           
                                 0  P6 =  0 
                                  0          1
  ðÏÓËÏÌØËÕ ÉÝÅÔÓÑ ÍÁËÓÉÍÕÍ ÚÁÄÁÞÉ, ÏÐÔÉÍÁÌØÎÙÊ ÐÌÁÎ ÂÕÄÅÔ ÄÏÓÔÉÇ-
ÎÕÔ, ËÏÇÄÁ ×ÓÅ ÒÁÚÎÏÓÔÉ (zj − cj ) > 0.

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