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14x1 + 8x2 + 6x3 + 4x4 d" 20,
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cjxj max
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z = (z1, . . . , zn) z1 = min{a1, b}
a1 e" b z1 = b z2 = . . . =
zn = 0 (b, 0, . . . , 0) " Rn
n cj
z f(z) > f(b, 0, . . . , 0) f(z) := zj
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a1 < b z1 = a1 z1 = a1
n - 1 z2 =
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ôÅ‚20x + 10x2 + 6x3 + 3x4 max
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14x1 + 8x2 + 6x3 + 4x4 d" 20
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14 8 6 4
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0 d" x1, x2, x3, x4 d" 1
z1 = min{a1, b} = min{14, 20} = 14 x 1 =
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= 1
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ôÅ‚20 + 10x2 + 6x3 + 3x4 max
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ôÅ‚8x2 + 6x3 + 4x4 d" 6
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0 d" x2, x3, x4 d" 1
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z2 = min{a2, b - a1} = min{8, 6} = 6 x 2 = = x 3 = x 4 = 0
8 4
3
[1, , 0, 0]
4
271
2
G
Õ Õ(G) = 271
2
G Q
xr = 0 xr = 1
G Q1 = {x " G : x2 = 0} Q2 = {x " G : x2 = 1}
Õ(Qi) i = 1, 2
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ôÅ‚20x1 + 6x3 + 3x4 max
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Q1 - lin
ôÅ‚14x1 + 6x3 + 4x4 d" 20
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0 d" x1, x3, x4 d" 1
z1 = min{14, 20} = 14 x 1 = 1 z3 = min{6, 6} = 6 x 3 = 1 x 4 = 0
Õ(Q1) = f(1, 0, 1, 0) = 26 f(x1, x2, x3, x4) = 20x1 + 10x2 + 6x3 + 3x4
Q2
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ôÅ‚20x1 + 6x3 + 3x4 + 10 max
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Q2 - lin
ôÅ‚14x1 + 6x3 + 4x4 d" 12
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0 d" x1, x3, x4 d" 1
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z1 = min{14, 12} = 12 x 1 = z3 = z4 = 0 x 3 = 0 x 4 = 0
14
Õ(Q2) = f(6, 1, 0, 0) = 271
7 7
Q2 Õ(Q1) < Õ(Q2)
G Q1, Q3, Q4
Q2 - lin Q2
Q3 = {x " G : x2 = 1, x1 = 0} Q4 = {x " G : x2 = 1, x1 = 1}
Õ(Qi) i = 3, 4
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ôÅ‚6x3 + 3x4 + 10 max
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Q3 - lin
ôÅ‚6x3 + 4x4 d" 12
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0 d" x3, x4 d" 1
z3 = min{6, 12} = 6 x 3 = 1 z4 = min{4, 6} = 4 x 4 = 1
Õ(Q3) = f(0, 1, 1, 1) = 19 Q4
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ôÅ‚6x3 + 3x4 + 30 max
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Q4 - lin
ôÅ‚6x3 + 4x4 d" -2
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0 d" x3, x4 d" 1
Q4 - lin Õ(Q4) = -"
Q Õ(Q) = maxi"{1,3,4} Õ(Qi) = Õ(Q1) = f(1, 0, 1, 0) =
26 Õ(Q1) = f(1, 0, 1, 0) x = [1, 0, 1, 0]