. :
- , . .
- , . , ( , , ).
- . z, , -. . + z, - z. , , , . , .
- 1 .
1,2,3 1,2,3 . i ci .. 1,2,3,4 b1,b2,b3,b4 . cij .. i j .
, 1,2,3 1,2,3,4.
1) .
. | ||||||
b1 | b2 | b3 | b4 | |||
1 | ||||||
2 | ||||||
3 |
xij i- j- .
xij.
i i, :
11 + 12 + 13 + 14 < 600,
21 + 22 + 23 + 24 < 400, (1)
31 + 32 + 33 + 34 < 700.
, , :
11 + 21 + 31 > 500,
12 + 22 + 32 > 300, (2)
13 + 23 + 33 > 800,
14 + 24 + 34 > 200.
, , , xij > 0; i=1,2,3; j=1,2,3,4.
F :
F = 411 + 212 + 613 + 814 + 421 + 322 + 523 + 724 + 531 + 832 + 1033 + 434 (3)
2*600+4*400+3*700=4900, : f = F + 4900.
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: (1) (2) X = (x11, x12,, x33, x34), (3) .
2) , (500 + 300 + 800 + 200 = 1800 > 600 + 400 + 700 = 1700), .
, " " . 100 = 1800 - 1700. .
(1) (2) :
11 + 12 + 13 + 14 = 600,
21 + 22 + 23 + 24 = 400,
31 + 32 + 33 + 34 = 700,
41 + 42 + 43 + 44 = 100.
11 + 21 + 31 + 41 = 500,
12 + 22 + 32 + 42 = 300,
13 + 23 + 33 + 43 = 800,
14 + 24 + 34 + 44 = 200.
(3) . .
- . x11 11 = 500; , ( ; , , ).
"- " (1,2) . , 1 500 , 100 = 600 - 500 , , 12 = 100. . "- " .. :
, "- " :
f (Xc-) = 4*500 + 2*100 + 3*200 + 5*200 + 10*600 + 4*100 + 0*100 + 4900 = 15100 . .
" ".
(1,2). 300. , . (1,1) 11 = 300. , . (2,1) 21 = 200 .. :
, " "
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f () = 4*300 + 2*300 + 4*200 + 5*200 + 10*500 + 4*200 + 0*100 + 4900 = 14300 . .
800 .., .
3) . " " , , , .
, .
, , (), . .
. -4. ( ).
(1,1) (2,1) ; , 0; (2;1) 0 ..
0(2) | ||||
0(3) | ||||
-5(6) | ||||
+5(8) |
-4(1) 2(4) 5(5) +1(7)
.
, , .
, .
4) .
(3,1).
(2,1) (2,3)
(3,1) (3,3)
, , x31 = min{500, 200} = 200. , 200 , :
-4(2) | ||||
0(6) | ||||
-5(4) | ||||
+5(8) |
0(1) +2(3) 5(5) +1(7)
, .
(1,3).
(1,1) (1,3)
(3,1) (3,3)
, , x13 = min{300, 300} = 300. , 300 , :
+1 | ||||
-4 | ||||
+6 |
1 2 6 0
:
, . (3,3) , .
5) , 1 300 2 300 3; 2 400 3; 3 500 1 200 4.
, 1, 2, 3 .
3 100 .
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f () = 4900 + 300*2 + 300*6 + 400*5 + 500*5 + 200*4 = 12600 ..