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Transcript of ` À ^ « Y ` À Y z ¤ ° ¿ v « Y ` ¿ z W Y | l « Y ` ¿ y º ...Ü · ÷.(:():: ...
:
:
:)Programmation linéaire(
:)Transport(
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.
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X 10.X,Y 0.X + Y = 30.
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:Max Z = 8X + 6Y
4X + 2Y 602X+ 4Y 48
X, Y 0
)(.:-) :1 ...(4X + 2Y = 60
)2 ...(2X + 4 Y = 48-XY)X ()Y (:
X = 0 Y = 30Y = 0 X = 15X = 0 Y = 12Y = 0 X = 24
)X ()Y (:
)1 ()2 ()A B C D (
C)1 ()2.(:
-A)00:(Z = 00 < 60(A)0 < 48
(0, 0) = (0, 0)-B)012:(Z = 72
24 < 6048 = 48
(0, 12) (0, 0).-D)150:(120 =Z
60<2448 =48
(1)
(2)
)0,0 ()15,0(-C): (
C)1 ()2 ()126 (:132 =Z
60 =6048 =48
)0,0 (>)12,6()Z ( )0 (
132=Z)C ( . :126
132.
: )MaxMin.(
-)Min:(:X =12
Min Z = 18X + 10Y)1(Y =6)1(484X + 8YX =10)2( 12X + 10Y 12)2(Y =12)3(10X + 15Y 150X =15
X,Y 0)3(Y =10
A = (1) (2) = (8.57, 1.71) Z = 171.36.B = (2) (3) = (3.75, 7.5) Z = 142.5.D (12, 0) Z = 216.C (15, 0) Z = 270.
B.
-:1-):(
)Z (.
:Max Z = 2X + 4Y)1 (X = 8
X 8 (1))2 (Y = 3Y 3 (2))3(X=10
3X + 6Y 30 (3) Y = 5 X,Y 0
A(0, 0) Z = 0 B(0. 3) Z = 12 E(8, 0) Z =16 0 < 8 0 < 8 8 = 8 0 < 3 3 = 3 0 < 3 0 < 30 18 < 30 24< 30 (0, 0) = (0, 0) (0, 3) (0, 0) (8,0) (0,0)
C(?, ?) = (2) (3) D (?, ?) = (1) (3) = (4, 3) = (8, 1)Z = 20 Z = 204 < 8 8 = 83 = 3 1 < 330 = 30 30 = 30(4, 3) > (0, 0) (8, 1) > (0, 0)
CDZ.
2-):(.
: MaxZ=6X + 4Y X = 10 (1) X 10 (1) Y = 12 (2) Y 12 (2) X, Y 0
) ( .
3-) (:) (
.: Max Z = 12X + 8YX = 4(1)
Y = 6 6X + 4Y 24 (1) (2) X = 8 2X + 4Y 16 (2) Y = 4 Y 7 (3) (3) Y = 7 (X, Y) (0, 0)
)1 ()2 ( )3()3 ( .
)1 ()2 (.
4-:.
: X1 = 10 MaxZ=2X1 + 5X2
X2 = 10 (1) X1 + X2 10 (1) X1 = 24 2X1 + 3X2 48 (2) X2 =16 (2) X1, X2 0X1
X2
20
10
16
10 20 24
.
5- (=):)(
.(=) ) (.
: 10 = X Max Z = 6X + 8Y 15 = Y (1) 30X + 20Y 300 (1) 22 = X 5X + 10Y 110 (2) 11 = Y (2) 4X – Y = 0 (3) 4X = Y (3) X = 2 (4) X = 2 (4) X,Y 0
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2X + 3Y = 40 (1) Max Z = 4X + 5Y 3X + Y = 50 (2) 2X + 3Y 40 (1)
: 3X + Y 50 (2) X = 15.71 X, Y 0Y = 2.85 Z = 77.09 .
:-.- :
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5-3-):(
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:
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)aij(
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Max Z = 8X + 6Y 4X + 2Y 60 2X + 4Y 48 X, Y 0
:1-)(::
:-) ()ei(
).(:4X + 2Y + e1 = 604X + 2Y 60
2X + 4Y +e2 = 482X + 4Y 48-)Ai(
M . .:Max -MAiMin +MAi
:MaxZ = 8X + 6Y + 0 e1 + 0 e2
4X + 2Y + e1 = 602X + 4Y + e2 = 48
X, Y, e1, e2 0
:8 6 0 0X Y e1 e2bjVCk
4 2 1 02 4 0 1
6048
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e2
00
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j
ab
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1 21
41 0
1 3 21 1
1518
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80
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61
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31
126
XY
86
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C0126132
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35
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Max.:
Min Z = X1 + 3X2 + 0e1 + 0e2 + MA1 + MA2. X1 + X2 – e1 +A1 = 4 (1) 2X1 + X2 + e2 = 6 (2) X2 + A2 = 3 (3) X1, X2, e1, e2, A1, A2 0
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+ ei =Z.- ei =.
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1 3 0 0 M MX1 X2 e1 e2 A1 A2bjVCk
1 1 -1 0 1 02 1 0 1 0 0
0 1 0 0 0 1
463
A1
e2
A2
M0M
M-1 2M-3 -M 0 0 0Z = 7M1 0 -1 0 1 -1
2 0 0 1 0 -1 0 1 0 0 0 1
133
A1
e2
X2
M03
M-1 0 -M 0 0 3-2MZ = M+91 0 -1 0 1 -1
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113
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:) ( )(
.
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3x+4y 205x+6y 30x+y 10x,y 0
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)- (: - (5x+6y) -30-5x -6y -30
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3A-5B+1C 14A-6B+1C 2A,B,C 0
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6-2-1-:
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: Min Z=40Y1+90Y2 Max Z=X1+3X2
2Y1+Y2 1 2X1+X2 40 Y1+4Y2 3 X1+4X2 90 Y1, Y2 0 X1, X2 0Min Z=40Y1+90Y2+0e1+0e2+MA1+MA2 Max Z=X1+3X2+0e1+0e2
2Y1+Y2-e1+A1=1 2X1+X2+e1=40 Y1+4Y2-e2+A2=3 X1+4X1+e2=90
X1, X2, e1, e2 0Y1, Y2, e1, e2, A1, A2 0 )(
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A2
1 0 - 74 + 7
1
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75
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y2
4090
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6-1-3-:
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5Y1+8Y2+11Y3 2 5X1+6X2+7X3 20 (1) 6Y1+9Y2+12Y3 3 8X1+9X2+10X3 30 (2) 7Y1+10Y2+13Y3 4 11X1+12X2+13X3 40 (3) Y1, Y2, Y3 0 X1, X2, X3 0
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72
1020
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) (:2 4 3 0 0 0A B C e1 e2 e3bjVCk
31 1 0 3
1 - 31 0
65 0 1 - 6
13
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35 0 0 + 3
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320
350
380
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430
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13
633
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31 +
65 0
31
65
65 .
13
25
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32 0
31
32 2
- 633 - 2
5 0 2
+++++++++++++++++++---------------------------------------------------
[0, 2]B [0+4,2+4]B
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Z 611 0 0
65
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65 +
611 0
511
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61 +
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32 +
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------------------------------------- +++++++++++++++++++
[0, 5]C[0+3,5+3] .
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[-20, 40][-20+60,40+60][40,100]
.
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320
31
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350
32
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380
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Y3Y2Y1Yi
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56X1
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6616
16X2
77 41 024
4116
368
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21541 0102 36 072 16 0
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::
:-:-.-:-.
-.
2-) (:
) (
..
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Y3Y2Y1Yi
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56 0884
56X1
82 41 25 016
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16X2
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.
Y3Y2Y1Yi
Xi
56 088456X1
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4124
4116
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.:
- :.- :.
4-::
Y3Y2Y1Yi
Xi
56 0884
56X1
82 41 016
4124
4116
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Z
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X1Y2 + X2Y2 = 10X1Y3 + X2Y3 = 10
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