, .
õ
1. (I, II, III) 90, 70, 50 , (1, 2, 3, 4) 80, 60, 40, 30 . , 1 1, 2, 3, 4 I 2, 1, 3, 2 ., II 2, 3, 3, 1 ., III 3, 3, 2, 1 . .
.
, .
1
³ | |||||
I | x11 2 | x12 1 | x13 3 | x14 2 | |
II | X21 2 | X22 1 | X23 3 | X24 2 | |
III | X31 2 | X32 1 | X33 3 | X34 2 | |
xij , i- j- . , x23 , II 3- , x12 I 2- .. ʳ , I ,
x11 + x12 + x13+ x14 .
90, I
x11 + x12 + x13+ x14 = 90.
II III
x21 + x22 + x23+ x24 = 70,
x31 + x32 + x33+ x34 = 50.
, I, II, III,
x11 + x12 + x13 = 80,
x12 + x22 + x32 = 60,
x13 + x23 + x33 = 40,
x14 + x24 + x34 = 30.
, xij, i = 1, 2, 3 j = 1, 2, 3, 4 (1) ( ).
F , (2).
(1)
F = 2x11 + x12 + 3x13 + 2x14 + 2x21 + 3x22 + 3x23 + x24 +
+ 3x31 + 3x32 + + 2x33 + x34. (2)
(1) ( ). , F. .
2 3, . ¢ .
2. , -, , , -, : . 2. 3 .., 8 . . , , .
|
|
2
1 | ||||
() | ||||
() | ||||
() | ||||
() | ||||
( . .) |
. x , y . (10x + 70y) (20x + 70y) . 320 , 420 ,
(300x + 400y) . ,
, ,
200x + 100y = 3400.
, (3):
(3)
(4):
F = 3x + 8y. (4)
y x 200x + 100y = 3400 y (3) (4)
(5)
F = 3x + 8(34 2x) = -13x + 272. (6)
(5)
(6)
, F = 272 13x , x = 16
Fmax = 272 - 1316 = 64 (. .).
.
(3),
¢
F = 3x + 8y. (7)
( ), (3) (. 14). , . OACKL ( ). г 2x + y = 34 OACKL . EN. , F . 3x + 8y = ( F), C (, 120, 240 .). .
dz 3x + 8y = C (. 14). EN, 3x + 8y = C, E. . ¢
(8)
E 2x + y =34 2x + 5y = 42. (8) (16; 2). .
Fmax = 316 + 82 = 64.
. 14.
õ
1. .
, . .
|
|
, 1- 18- , 2- 12- , 3- 12- , 4- 9- .
3 , . , .
I 4 ., II 6 . .
.
3
1- | 2- | 3- | 4- | |
I | 0,5 | |||
II | ||||
() |
2. Fmax = 4x1 + 6x2
2. ³, , 6- , 12- , 4- . . 4 , 1 :
4
I | II | |
A | ||
B | ||
C |
ֳ I 5 . , II 6 . . , ?
õ
1. 84 . 4 , 3 . , 6 ., 3 .? ³, 15, 20.
2. .
1.1. 1.2. 1.3.
3. , , , . ³, 6- , 8- , 12- . , , I, II, III , 5:
5
ճ | |||
I | |||
II | |||
III | 1,5 |
I, II, III : I 3 ., II 3 ., III 2,5 . , .
4. .
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1
6