Å„Å‚
ôÅ‚
ôÅ‚cx min
ôÅ‚
òÅ‚
x " Rn x1, x2
ôÅ‚Ax = b,
ôÅ‚
ôÅ‚
ół
x e" 0,
x1, x2
1 1
x1 + x2
2 3
Å„Å‚
ôÅ‚
ôÅ‚cx max
ôÅ‚
ôÅ‚
ôÅ‚
ôÅ‚
òÅ‚
Ax = b, x " Rn
ôÅ‚
ôÅ‚x e" 0,
ôÅ‚
ôÅ‚
ôÅ‚
ôÅ‚
ółx " Z j = 1, . . . , n
j
G f : G R max f(x) Õ
x"G
Õ(G) = max f(x)
x"G
" x " G Õ({x}) = f(x)
x " G1 ‚" G f(x) e" Õ(G1)
G Z4 f : G R max f(x) Õ
x"G
G = Q1 *" Q2 *" Q3 Q1, Q2, Q3
Õ(Q1) = f(1, 0, 1, 0) = 29, 5 Õ(Q2) = 29 Õ(Q3) = 30
max f(x)
x"G
max f(x)
x"G
Å„Å‚
ôÅ‚10x11 + 12x12 + 24x21 + 20x22 + 8x31 + 5x32 + 100y1 + 200y2 + 158y3 min
ôÅ‚
ôÅ‚
ôÅ‚
ôÅ‚
ôÅ‚
ôÅ‚
ôÅ‚
ôÅ‚
ôÅ‚x11 + x12 d" 6y1, x21 + x22 d" 8y2, x31 + x32 d" 6y3,
ôÅ‚
òÅ‚
x11 + x21 + x31 = 4, x12 + x22 + x32 = 8, (Plok)
ôÅ‚
ôÅ‚x , x12, x21, x22, x31, x32 e" 0,
ôÅ‚
ôÅ‚
11
ôÅ‚
ôÅ‚
ôÅ‚0 d" y1, y2, y3 d" 1,
ôÅ‚
ôÅ‚
ôÅ‚
ôÅ‚
óły , y2, y3 " Z.
1
(Plok)
Å„Å‚
n
ôÅ‚
cjxj max
ôÅ‚
j=1
ôÅ‚
ôÅ‚
ôÅ‚
ôÅ‚
òÅ‚
n
aj, cj > 0 j = 1, . . . , n b > 0 ajxj d" b, (Pzal)
j=1
ôÅ‚
ôÅ‚0 d" xj d" 1, j = 1, . . . , n,
ôÅ‚
ôÅ‚
ôÅ‚
ôÅ‚
ółx " Z, j = 1, . . . , n,
j
n
aj < b (Pzal)
j=1
n
aj = b (Pzal)
j=1
n
aj > b (Pzal)
j=1
îÅ‚ Å‚Å‚
" 15 10 10 15 18
ïÅ‚ śł
12 " 10 13 8 7
ïÅ‚ śł
ïÅ‚ śł
4 0 " 4 5 6
ïÅ‚ śł
.
ïÅ‚ śł
8 8 9 " 10 2
ïÅ‚ śł
ðÅ‚ ûÅ‚
10 13 10 9 " 7
8 7 6 7 8 "
(4, 6)
Õ((3, 2)) = 35 Õ
Z = f(S) = K((0, 0), 2)