deber_4_io
TRANSCRIPT
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x1 = 0 x2 = 6 x2 = 6 x1+ x2 = 8 x1+ x2 = 8 x1 = 5 x1 = 5 x2 = 0 x2 = 0 x1 = 0
x1 x2
(x1, x2) = (0, 6) (x1, x2) = (6, 2) (x1, x2) = (5, 3) (x1, x2) = (5, 0) (x1, x2) = (0, 0)
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x2 = 6 x1+ x2= 8 x1 = 5 x2 = 0 x1 = 0
P= 4500x1+ 4500x2
x1 1
x2 1
5000x1+ 4000x2 6000
400x1+ 500x2 600
x1, x2 0
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7/25/2019 Deber_4_IO
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(P= 4500x1+ 4500x2)
(0, 1.5) (0, 1.2)
(0, 1)
(0.25, 1) (0.4, 1)
(1, 1) (0.67, 0.67)
(1, 0.4) (1, 0.25)
(1, 0) (1.2, 0)
(1.5, 0) (0, 0)
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7/25/2019 Deber_4_IO
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M = (0, 0) C = (1, 0) J = (0, 1)
x1+ 2x2
x1+ 3x2+ x3 = 8
x1+ x2+ x4 = 4
x1, x2, x3, x4 0
(0, 0) (0, 0, 8, 4) x1, x2 x3, x4
0, 8
3
0, 8
3, 0, 4
3
x1, x3 x2, x4
(2, 2) (2, 2, 0, 0) x3, x4 x1, x2 (4, 0) (4, 0, 4, 0) x2, x4 x3, x4
x1 = x2 = 0
x3 = 8
x4 = 4
x1 = x3 = 0
3x2 = 8
x2 = 8
3
x2+ x4 = 4
x4 = 4
3
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x3 = x4 = 0
x1+ 3x2 = 8
x1+ x2 = 4
x1 = x2 = 2 x2 = x4 = 0
x1+ x3 = 8
x3 = 4
x1 = 4
(0, 4) (0, 4,4, 0) x1, x4 x2, x3 (8, 0) (8, 0, 0,4) x2, x3 x1, x4
x1 = x4 = 0
3x2+ x3 = 8
x3 = 4
x2 = 4
x2 = x3 = 0
x1 = 8
x1+ x4 = 4
x4 = 4
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7/25/2019 Deber_4_IO
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Z = x1+ 2x2
x1+ 3x2+ x3 = 8
x1+ x2+ x4 = 4
x1, x2, x3, x4 0
x1 = x2= 0 = x3 = 8 x4 = 4 z= x1 + 2x2 = 0 x2
x1 = 0 x2
x3 = 8 3x2 0
x2 8
3
x4 = 4 x2 0
x2 4
8
3 x2 x3 = 0
Z = 1
3x1
2
3x3+
16
31
3x1+ x2+
1
3x3 =
8
32
3x1
1
3x3+ x4 =
4
3x1, x2, x3, x4 0
0, 8
3, 0, 4
3
x1
1
3>0 x1
x4
Z = 1
2x3
1
2x4+ 6
x2+1
2x3+
1
2x4 = 2
x1 1
2x3+
3
2x4 = 2
x1, x2, x3, x4 0
x3 x4 x =
(2, 2, 0, 0) Z = 6
x = (2, 2, 0, 0) Z = 6
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Z = 2x1+ 4x2+ 3x3
x1+ 3x2+ 2x3 30
x1+ x2+ x3 24
3x1+ 5x2+ 3x3 60
x1, x2, x3 0
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x1 >0 x2 = 0 x3 > 0
x2 = 0
Z = 2x1+ 3x3
x1+ 2x3 30
x1+ x3 24
3x1+ 3x3 60
x1, x3 0
Z = 2x1+ 3x3
x1+ 2x3 30
x1+ x3 20
x1, x3 0
x1 >0 x3 >0
(x1, x
2, x
3) = (10, 0, 10) Z = 50
x1 x3 x4 x5
z
x4
x5
x1 x3 x4 x5
z
x3
x5
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x1 x3 x4 x5
z
x3
x1
(x1, x
2) = (2, 2) Z = 6
x1 x3 x4 x5
z
x3
x4
x1 x3 x4 x5
z
x2
x4
x1 x3 x4 x5
z
x2
x1
Z = 5x1+ 9x2+ 7x3
x1+ 3x2+ 2x3 10
3x1+ 4x2+ 2x3 12
2x1+ x2+ 2x3 8
x1, x2, x3 0
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x1 = x2= x3 = 0
Z 5x1 9x2 7x3 = 0
x1+ 3x2+ 2x3+ x4 = 10 = x4 = 10
3x1+ 4x2+ 2x3+ x5 = 12 = x5 = 12
2x1+ x2+ 2x3+ x6 = 8 = x6 = 8
(0, 0, 0, 10, 12, 8) x2
x1+ 3x2+ 2x3+ x4 = 10
x4 = 10 3x2
x2 10
3
3x1+ 4x2+ 2x3+ x5 = 12
x5 = 12 4x2
x2 3....mn.
2x1+ x2+ 2x3+ x6 = 8
x6 = 8 x2
x2 8
x5 x1 = x5 = x3 = 0
Z+ 1.75x1 2.5x3+ 2.25x5 = 27
1.25x1+ 0.5x3+ x4 0.75x5 = 1 = x4 = 1
0.75x1+ x2+ 0.5x3+ 0.25x5 = 3 = x2 = 3
1.25x1+ 1.5x3 0.25x5+ x6 = 5 = x6 = 5
x3 (0, 3, 0, 1, 0, 5) x3
1.25x1+ 0.5x3+ x4 0.75x5 = 1 = x4= 1 0.5x3 2...mn.
0.75x1+ x2+ 0.5x3+ 0.25x5 = 3 = x2= 3 0.5x3 6
1.25x1+ 1.5x3 0.25x5+ x6 = 5 = x6= 5 1.5x3 10
3
x4 x1 = x5 = x4 = 0
Z 4.5x1+ 5x4 1.5x5 = 32
2.5x1+ x3+ 2x4 1.5x5 = 2 = x3 = 2
2x1+ x2 x4+ x5 = 2 = x2 = 2
5x1 3x4+ 2x5+ x6 = 2 = x6 = 2
x1 (0, 2, 2, 0, 0, 2) x1
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2.5x1+ x3+ 2x4 1.5x5 = 2 = x3 = 2 + 2.5x1
2x1+ x2 x4+ x5 = 2 = x2 = 2 2x1 = x1 1
5x1 3x4+ 2x5+ x6 = 2 = x6 = 2 5x1 = x1 0.4...mn.
x6 x6 = x5 = x4 = 0
Z+ 2.3x4+ 0.3x5+ 0.9x6 = 33.8
x3+ 0.5x4 0.5x5+ 0.5x6 = 3 = x3 = 3
x2+ 0.2x4+ 0.2x5 0.4x5 = 1.2 = x2 = 1.2
x1 0.6x4+ 0.4x5+ 0.2x6 = 0.4 = x1 = 0.4
(0.4, 1.2, 3, 0, 0, 0)
(x1.x
2, x
3) = (0.4, 1.2, 3) Z = 33.8
x1 x2 x3 x4 x5 x6
z
x4
x5
x6
x1 x2 x3 x4 x5 x6
z
x4
x2
x6
x1 x2 x3 x3 x4 x5
z
x4
x2
x6
x1 x2 x3 x3 x4 x5
z
x3
x2
x1
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