Bài Toán Đơn Hình

GiI BI TON N HNHCho bi ton n hnh sauZ= 4x1 + 6x2 +8x3 -> MAX

x1 + 2x2 3x3 123x1 + x2 +x3 42x1 + 2x2 +5x3 5xj 0 , j = 1,3

B1- chuyn v bi ton phZ= 4x1 + 6x2 +8x3 -> MAX

x1 + 2x2 3x3 + x4 = 123x1 + x2 + x3 + + x5 = 42x1 + 2x2 + 5x3 + + x6 = 5xj 0 , j = 1,6

B2- Nhn xt vi cu nh bn di:Trong x4, x5, x6 l 3 bin ph.NX: BT ph c dng chun, c 3 bin c s l x4, x5, x6Lp bng n hnh

20/4/2012 1

GiI BI TON N HNHZ= 4x1 + 6x2 +8x3 + 0x4 + 0x5 +0x6 -> MAX

x1 + 2x2 3x3 + x4 = 123x1 + x2 + x3 + + x5 = 42x1 + 2x2 + 5x3 + + x6 = 5xj 0 , j = 1,6

i C s Ci BiP/a

x1 x2 x3 x4 x5 x6 4 6 8 0 0 0

1 x4 0 12 1 2 -3 1 0 0

2 x5 0 4 3 1 1 0 1 0

3 x6 0 5 2 2 5 0 0 1

20/4/2012 2

GiI BI TON N HNHi C s Ci Bi

P/ax1 x2 x3 x4 x5 x6 4 6 8 0 0 0

1 x4 0 12 1 2 -3 1 0 0

2 x5 0 4 3 1 1 0 1 0

3 x6 0 5 2 2 5 0 0 1

j

= 000

X1245

-> 0

0 * 12 + 0 * 4 + 0 *5 = 020/4/2012 3


P/ax1 x2 x3 x4 x5 x6 4 6 8 0 0 0

1 x4 0 12 1 2 -3 1 0 0

2 x5 0 4 3 1 1 0 1 0

3 x6 0 5 2 2 5 0 0 1

j 0

= 000

X134

4- -> -4

0 * 1 + 0 * 3 + 0 *4 = 020/4/2012 4


P/ax1 x2 x3 x4 x5 x6 4 6 8 0 0 0

1 x4 0 12 1 2 -3 1 0 0

2 x5 0 4 3 1 1 0 1 0

3 x6 0 5 2 2 5 0 0 1

j 0 -4

= 000

X212

6- -> -6

0 * 2 + 0 * 1 + 0 * 2 = 020/4/2012 5


P/ax1 x2 x3 x4 x5 x6 4 6 8 0 0 0

1 x4 0 12 1 2 -3 1 0 0

2 x5 0 4 3 1 1 0 1 0

3 x6 0 5 2 2 5 0 0 1

j 0 -4 -6

= 000

X-315

8- -> -8

0 * (-3) + 0 * 1 + 0 *5 = 020/4/2012 6


P/ax1 x2 x3 x4 x5 x6 4 6 8 0 0 0

1 x4 0 12 1 2 -3 1 0 0

2 x5 0 4 3 1 1 0 1 0

3 x6 0 5 2 2 5 0 0 1

j 0 -4 -6 -8 0 0 0

Tng t lm chox4, x5, x6, s chora kt qu l 0 0 0

20/4/2012 7

GiI BI TON N HNH

i C s Ci BiP/a

x1 x2 x3 x4 x5 x6 4 6 8 0 0 0

1 x4 0 12 1 2 -3 1 0 0

2 x5 0 4 3 1 1 0 1 0

3 x6 0 5 2 2 5 0 0 1

j 0 -4 -6 -8 0 0 0

Bi ton Max nn Vi mi denta j 0 th bi ton mi ti u, bi ton cha tha iukin-> xc nh ct xoay

BT Max -> ct xoayl s m nh nht(hoc s m c trtuyt i ln nht)

20/4/2012 8

GiI BI TON N HNH

i C s Ci BiP/a

x1 x2 x3 x4 x5 x6 4 6 8 0 0 0

1 x4 0 12 1 2 -3 1 0 0

2 x5 0 4 3 1 1 0 1 0

3 x6 0 5 2 2 5 0 0 1

j 0 -4 -6 (-8) 0 0 0

c ct xoay -> tm lamda xc nh dng xoay

= 12 / -3 -> -4 V l s -4 (sm) nn s ghivo du -

20/4/2012 9

GiI BI TON N HNH

i C s Ci BiP/a

x1 x2 x3 x4 x5 x6 4 6 8 0 0 0

1 x4 0 12 1 2 -3 1 0 0 -

2 x5 0 4 3 1 1 0 1 0

3 x6 0 5 2 2 5 0 0 1

j 0 -4 -6 (-8) 0 0 0

Tm lamda xc nh dng xoay

= 4 / 1 -> 4

20/4/2012 10

GiI BI TON N HNH

i C s Ci BiP/a

x1 x2 x3 x4 x5 x6 4 6 8 0 0 0

1 x4 0 12 1 2 -3 1 0 0 -

2 x5 0 4 3 1 1 0 1 0 4

3 x6 0 5 2 2 5 0 0 1

j 0 -4 -6 (-8) 0 0 0

Tm lamda xc nh dng xoay

= 5 / 5 -> 1

20/4/2012 11

GiI BI TON N HNH

i C s Ci BiP/a

x1 x2 x3 x4 x5 x6 4 6 8 0 0 0

1 x4 0 12 1 2 -3 1 0 0 -

2 x5 0 4 3 1 1 0 1 0 4

3 x6 0 5 2 2 5 0 0 1 1

j 0 -4 -6 (-8) 0 0 0

Dn xoay s l dng c lamda dng nh nht

s 1 l lamdadng nh nht

20/4/2012 12

GiI BI TON N HNH

i C s Ci BiP/a

x1 x2 x3 x4 x5 x6 4 6 8 0 0 0

1 x4 0 12 1 2 -3 1 0 0 -

2 x5 0 4 3 1 1 0 1 0 4

3 x6 0 5 2 2 (5) 0 0 1 (1)

j 0 -4 -6 (-8) 0 0 0

xc nh c dng xoay -> ti sao phi xc nh dng xoay vo ct xoay ?Tht ra xc nh bit c bin vo v bin ra c s y bin vo l ct xoay (x3) v bin ra l dng xoay (x6)

Ra khi c s

20/4/2012 13

GiI BI TON N HNH

i C s Ci BiP/a

x1 x2 x3 x4 x5 x6 4 6 8 0 0 0

1 x4 0 12 1 2 -3 1 0 0 -2 x5 0 4 3 1 1 0 1 0 43 x6 0 5 2 2 (5) 0 0 1 (1)

j 0 -4 -6 (-8) 0 0 01 x4 02 x5 03 x3 8

j

= -> 15 / 5

20/4/2012 14

GiI BI TON N HNH

i C s Ci BiP/a

x1 x2 x3 x4 x5 x6 4 6 8 0 0 0

1 x4 0 12 1 2 -3 1 0 0 -2 x5 0 4 3 1 1 0 1 0 43 x6 0 5 2 2 (5) 0 0 1 (1)

j 0 -4 -6 (-8) 0 0 01 x4 02 x5 03 x3 8 1

j

= -> 2/52 / 5

20/4/2012 15

GiI BI TON N HNH

i C s Ci BiP/a

x1 x2 x3 x4 x5 x6 4 6 8 0 0 0

1 x4 0 12 1 2 -3 1 0 0 -2 x5 0 4 3 1 1 0 1 0 43 x6 0 5 2 2 (5) 0 0 1 (1)

j 0 -4 -6 (-8) 0 0 01 x4 02 x5 03 x3 8 2/5 1

j

= -> 2/52 / 5

20/4/2012 16

GiI BI TON N HNH

i C s Ci BiP/a

x1 x2 x3 x4 x5 x6 4 6 8 0 0 0

1 x4 0 12 1 2 -3 1 0 0 -2 x5 0 4 3 1 1 0 1 0 43 x6 0 5 2 2 (5) 0 0 1 (1)

j 0 -4 -6 (-8) 0 0 01 x4 02 x5 03 x3 8 2/5 2/5 1

j

= -> 15 / 5

20/4/2012 17

GiI BI TON N HNH

i C s Ci BiP/a

x1 x2 x3 x4 x5 x6 4 6 8 0 0 0

1 x4 0 12 1 2 -3 1 0 0 -2 x5 0 4 3 1 1 0 1 0 43 x6 0 5 2 2 (5) 0 0 1 (1)

j 0 -4 -6 (-8) 0 0 01 x4 02 x5 03 x3 8 1 2/5 2/5 1 0 0 1/5

j

lm tng t c kt qu nh

bng20/4/2012 18

GiI BI TON N HNH

i C s Ci BiP/a

x1 x2 x3 x4 x5 x6 4 6 8 0 0 0

1 x4 0 12 1 2 -3 1 0 0 -2 x5 0 4 3 1 1 0 1 0 43 x6 0 5 2 2 (5) 0 0 1 (1)

j 0 -4 -6 (-8) 0 0 01 x4 02 x5 03 x3 8 1 2/5 2/5 1 0 0 1/5

j0 = ->1-1 ? *

S y btbuc l s 0, vyta phi tm h s.c h s s tmc gi tr dng

ny

1 hehe, h s l 1,khe ri.

20/4/2012 19

GiI BI TON N HNH

i C s Ci BiP/a

x1 x2 x3 x4 x5 x6 4 6 8 0 0 0

1 x4 0 12 1 2 -3 1 0 0 -2 x5 0 4 3 1 1 0 1 0 43 x6 0 5 2 2 (5) 0 0 1 (1)

j 0 -4 -6 (-8) 0 0 01 x4 02 x5 0 03 x3 8 1 2/5 2/5 1 0 0 1/5

j= ->2/5-1 1 * nu l h s 1, khng

cn phi nhn cho2/5. c th tr trc

tip cho 2/5

3/5

20/4/2012 20

GiI BI TON N HNH

i C s Ci BiP/a

x1 x2 x3 x4 x5 x6 4 6 8 0 0 0

1 x4 0 12 1 2 -3 1 0 0 -2 x5 0 4 3 1 1 0 1 0 43 x6 0 5 2 2 (5) 0 0 1 (1)

j 0 -4 -6 (-8) 0 0 01 x4 02 x5 0 3/5 03 x3 8 1 2/5 2/5 1 0 0 1/5

j= ->2/5-3 13/5

20/4/2012 21

GiI BI TON N HNH

i C s Ci BiP/a

x1 x2 x3 x4 x5 x6 4 6 8 0 0 0

1 x4 0 12 1 2 -3 1 0 0 -2 x5 0 4 3 1 1 0 1 0 43 x6 0 5 2 2 (5) 0 0 1 (1)

j 0 -4 -6 (-8) 0 0 01 x4 02 x5 0 13/5 3/5 03 x3 8 1 2/5 2/5 1 0 0 1/5

j= ->1-4 3

20/4/2012 22

GiI BI TON N HNH

i C s Ci BiP/a

x1 x2 x3 x4 x5 x6 4 6 8 0 0 0

1 x4 0 12 1 2 -3 1 0 0 -2 x5 0 4 3 1 1 0 1 0 43 x6 0 5 2 2 (5) 0 0 1 (1)

j 0 -4 -6 (-8) 0 0 01 x4 02 x5 0 3 13/5 3/5 0 0 0 -1/53 x3 8 1 2/5 2/5 1 0 0 1/5

j

Tng t lm s ckt qu nh bng

20/4/2012 23

GiI BI TON N HNH

i C s Ci BiP/a

x1 x2 x3 x4 x5 x6 4 6 8 0 0 0

1 x4 0 12 1 2 -3 1 0 0 -2 x5 0 4 3 1 1 0 1 0 43 x6 0 5 2 2 (5) 0 0 1 (1)

j 0 -4 -6 (-8) 0 0 01 x4 0 02 x5 0 3 13/5 3/5 0 0 0 -1/53 x3 8 1 2/5 2/5 1 0 0 1/5

j0 = ->1--3 ? *


ny

-3 hehe, h s l -3,khng khe cht

no20/4/2012 24

GiI BI TON N HNH

i C s Ci BiP/a

x1 x2 x3 x4 x5 x6 4 6 8 0 0 0

1 x4 0 12 1 2 -3 1 0 0 -2 x5 0 4 3 1 1 0 1 0 43 x6 0 5 2 2 (5) 0 0 1 (1)

j 0 -4 -6 (-8) 0 0 01 x4 0 02 x5 0 3 13/5 3/5 0 0 0 -1/53 x3 8 1 2/5 2/5 1 0 0 1/5

j= ->2/5-2 -3 * 16/5 2 + 6/5 =16/5

ci ny cng trphn s thi

20/4/2012 25

GiI BI TON N HNH

i C s Ci BiP/a

x1 x2 x3 x4 x5 x6 4 6 8 0 0 0

1 x4 0 12 1 2 -3 1 0 0 -2 x5 0 4 3 1 1 0 1 0 43 x6 0 5 2 2 (5) 0 0 1 (1)

j 0 -4 -6 (-8) 0 0 01 x4 0 16/5 02 x5 0 3 13/5 3/5 0 0 0 -1/53 x3 8 1 2/5 2/5 1 0 0 1/5

j= ->2/5-1 -3 * 11/5 1 + 6/5 =11/5

hehe

20/4/2012 26

GiI BI TON N HNH

i C s Ci BiP/a

x1 x2 x3 x4 x5 x6 4 6 8 0 0 0

1 x4 0 12 1 2 -3 1 0 0 -2 x5 0 4 3 1 1 0 1 0 43 x6 0 5 2 2 (5) 0 0 1 (1)

j 0 -4 -6 (-8) 0 0 01 x4 0 11/5 16/5 02 x5 0 3 13/5 3/5 0 0 0 -1/53 x3 8 1 2/5 2/5 1 0 0 1/5

j= ->1-12 -3 * 15 12 + 3=15

hehe

20/4/2012 27

GiI BI TON N HNH

i C s Ci BiP/a

x1 x2 x3 x4 x5 x6 4 6 8 0 0 0

1 x4 0 12 1 2 -3 1 0 0 -2 x5 0 4 3 1 1 0 1 0 43 x6 0 5 2 2 (5) 0 0 1 (1)

j 0 -4 -6 (-8) 0 0 01 x4 0 15 11/5 16/5 0 1 0 3/52 x5 0 3 13/5 3/5 0 0 0 -1/53 x3 8 1 2/5 2/5 1 0 0 1/5

jLm tng t tac nh bng trn

20/4/2012 28

GiI BI TON N HNH

i C s Ci BiP/a

x1 x2 x3 x4 x5 x6 4 6 8 0 0 0

1 x4 0 12 1 2 -3 1 0 0 -2 x5 0 4 3 1 1 0 1 0 43 x6 0 5 2 2 (5) 0 0 1 (1)

j 0 -4 -6 (-8) 0 0 01 x4 0 15 11/5 16/5 0 1 0 3/52 x5 0 3 13/5 3/5 0 0 0 -1/53 x3 8 1 2/5 2/5 1 0 0 1/5

j

= 008

X1531 -> 8

0 * 15 + 0 * 3 + 8 * 1 = 820/4/2012 29


P/ax1 x2 x3 x4 x5 x6 4 6 8 0 0 0

1 x4 0 12 1 2 -3 1 0 0 -2 x5 0 4 3 1 1 0 1 0 43 x6 0 5 2 2 (5) 0 0 1 (1)

j 0 -4 -6 (-8) 0 0 01 x4 0 15 11/5 16/5 0 1 0 3/52 x5 0 3 13/5 3/5 0 0 0 -1/53 x3 8 1 2/5 2/5 1 0 0 1/5

j 8

= 008

X44/531 ->

4

0 * 44/5 + 0 * 3 + 8 * 1 = 8

- 4

20/4/2012 30


P/ax1 x2 x3 x4 x5 x6 4 6 8 0 0 0

1 x4 0 12 1 2 -3 1 0 0 -2 x5 0 4 3 1 1 0 1 0 43 x6 0 5 2 2 (5) 0 0 1 (1)

j 0 -4 -6 (-8) 0 0 01 x4 0 15 11/5 16/5 0 1 0 3/52 x5 0 3 13/5 3/5 0 0 0 -1/53 x3 8 1 2/5 2/5 1 0 0 1/5

j 8 4

= 008

X16/53/52/5 ->

-14/5

0 * 16/5 + 0 * 3/5 + 8 * 2/5 = 16/5

- 6

20/4/2012 31


P/ax1 x2 x3 x4 x5 x6 4 6 8 0 0 0

1 x4 0 12 1 2 -3 1 0 0 -2 x5 0 4 3 1 1 0 1 0 43 x6 0 5 2 2 (5) 0 0 1 (1)

j 0 -4 -6 (-8) 0 0 01 x4 0 15 11/5 16/5 0 1 0 3/52 x5 0 3 13/5 3/5 0 0 0 -1/53 x3 8 1 2/5 2/5 1 0 0 1/5

j 8 4 -14/5

= 008

X001 ->

0

0 * 0 + 0 * 0 + 8 * 1 = 8

- 8

20/4/2012 32


P/ax1 x2 x3 x4 x5 x6 4 6 8 0 0 0

1 x4 0 12 1 2 -3 1 0 0 -2 x5 0 4 3 1 1 0 1 0 43 x6 0 5 2 2 (5) 0 0 1 (1)

j 0 -4 -6 (-8) 0 0 01 x4 0 15 11/5 16/5 0 1 0 3/52 x5 0 3 13/5 3/5 0 0 0 -1/53 x3 8 1 2/5 2/5 1 0 0 1/5

j 8 4 -14/5 0 0 0 8/5

Lm tng t tac nh bng trn

20/4/2012 33


P/ax1 x2 x3 x4 x5 x6 4 6 8 0 0 0

1 x4 0 12 1 2 -3 1 0 0 -2 x5 0 4 3 1 1 0 1 0 43 x6 0 5 2 2 (5) 0 0 1 (1)

j 0 -4 -6 (-8) 0 0 01 x4 0 15 11/5 16/5 0 1 0 3/5 75/162 x5 0 3 13/5 3/5 0 0 0 -1/5 53 x3 8 1 2/5 2/5 1 0 0 1/5 5/2

j 8 4 (-14/5) 0 0 0 8/5

ly phng nchia cho ct xoay

-> lamda

= /

20/4/2012 34


P/ax1 x2 x3 x4 x5 x6 4 6 8 0 0 0

1 x4 0 12 1 2 -3 1 0 0 -2 x5 0 4 3 1 1 0 1 0 43 x6 0 5 2 2 (5) 0 0 1 (1)

j 0 -4 -6 (-8) 0 0 01 x4 0 15 11/5 16/5 0 1 0 3/5 75/162 x5 0 3 13/5 3/5 0 0 0 -1/5 53 x3 8 1 2/5 (2/5) 1 0 0 1/5 (5/2)

j 8 4 (-14/5) 0 0 0 8/5

lamda dng bnht lm dng

xoayta c x3 ra v x2vo c s

20/4/2012 35

i C s Ci BiP/a

x1 x2 x3 x4 x5 x6 4 6 8 0 0 0

1 x4 0 12 1 2 -3 1 0 0 -2 x5 0 4 3 1 1 0 1 0 43 x6 0 5 2 2 (5) 0 0 1 (1)

j 0 -4 -6 (-8) 0 0 01 x4 0 15 11/5 16/5 0 1 0 3/5 75/162 x5 0 3 13/5 3/5 0 0 0 -1/5 53 x3 8 1 2/5 (2/5) 1 0 0 1/5 (5/2)

j 8 4 (-14/5) 0 0 0 8/51 x4 02 x5 03 x2 6

= -> 12/5 / 2/5

20/4/2012 36

i C s Ci BiP/a

x1 x2 x3 x4 x5 x6 4 6 8 0 0 0

1 x4 0 12 1 2 -3 1 0 0 -2 x5 0 4 3 1 1 0 1 0 43 x6 0 5 2 2 (5) 0 0 1 (1)

j 0 -4 -6 (-8) 0 0 01 x4 0 15 11/5 16/5 0 1 0 3/5 75/162 x5 0 3 13/5 3/5 0 0 0 -1/5 53 x3 8 1 2/5 (2/5) 1 0 0 1/5 (5/2)

j 8 4 (-14/5) 0 0 0 8/51 x4 02 x5 03 x2 6 1

= -> 12/5 / 2/5

20/4/2012 37

i C s Ci BiP/a

x1 x2 x3 x4 x5 x6 4 6 8 0 0 0

1 x4 0 12 1 2 -3 1 0 0 -2 x5 0 4 3 1 1 0 1 0 43 x6 0 5 2 2 (5) 0 0 1 (1)

j 0 -4 -6 (-8) 0 0 01 x4 0 15 11/5 16/5 0 1 0 3/5 75/162 x5 0 3 13/5 3/5 0 0 0 -1/5 53 x3 8 1 2/5 (2/5) 1 0 0 1/5 (5/2)

j 8 4 (-14/5) 0 0 0 8/51 x4 02 x5 03 x2 6 1 1

= -> 5/21 / 2/5

20/4/2012 38

i C s Ci BiP/a

x1 x2 x3 x4 x5 x6 4 6 8 0 0 0

1 x4 0 12 1 2 -3 1 0 0 -2 x5 0 4 3 1 1 0 1 0 43 x6 0 5 2 2 (5) 0 0 1 (1)

j 0 -4 -6 (-8) 0 0 01 x4 0 15 11/5 16/5 0 1 0 3/5 75/162 x5 0 3 13/5 3/5 0 0 0 -1/5 53 x3 8 1 2/5 (2/5) 1 0 0 1/5 (5/2)

j 8 4 (-14/5) 0 0 0 8/51 x4 02 x5 03 x2 6 5/2 1 1 5/2 0 0 1/2

= ->/ 2/5

20/4/2012 39

i C s Ci BiP/a

x1 x2 x3 x4 x5 x6 4 6 8 0 0 0

1 x4 0 12 1 2 -3 1 0 0 -2 x5 0 4 3 1 1 0 1 0 43 x6 0 5 2 2 (5) 0 0 1 (1)

j 0 -4 -6 (-8) 0 0 01 x4 0 15 11/5 16/5 0 1 0 3/5 75/162 x5 0 3 13/5 3/5 0 0 0 -1/5 53 x3 8 1 2/5 (2/5) 1 0 0 1/5 (5/2)

j 8 4 (-14/5) 0 0 0 8/51 x4 02 x5 03 x2 6 5/2 1 1 5/2 0 0 1/2

= ->/ 2/5 Lm tng t sc kt qu nh

bng20/4/2012 40

i C s Ci BiP/a

x1 x2 x3 x4 x5 x6 4 6 8 0 0 0

1 x4 0 12 1 2 -3 1 0 0 -2 x5 0 4 3 1 1 0 1 0 43 x6 0 5 2 2 (5) 0 0 1 (1)

j 0 -4 -6 (-8) 0 0 01 x4 0 15 11/5 16/5 0 1 0 3/5 75/162 x5 0 3 13/5 3/5 0 0 0 -1/5 53 x3 8 1 2/5 (2/5) 1 0 0 1/5 (5/2)

j 8 4 (-14/5) 0 0 0 8/51 x4 02 x5 0 03 x2 6 5/2 1 1 5/2 0 0 1/2

0 = ->1-3/5 ? *


ny

3/5

20/4/2012 41

i C s Ci BiP/a

x1 x2 x3 x4 x5 x6 4 6 8 0 0 0

1 x4 0 12 1 2 -3 1 0 0 -2 x5 0 4 3 1 1 0 1 0 43 x6 0 5 2 2 (5) 0 0 1 (1)

j 0 -4 -6 (-8) 0 0 01 x4 0 15 11/5 16/5 0 1 0 3/5 75/162 x5 0 3 13/5 3/5 0 0 0 -1/5 53 x3 8 1 2/5 (2/5) 1 0 0 1/5 (5/2)

j 8 4 (-14/5) 0 0 0 8/51 x4 02 x5 0 03 x2 6 5/2 1 1 5/2 0 0 1/2

= ->1-13/5 3/5 * 2 13/5-3/5=10/5=2

20/4/2012 42

i C s Ci BiP/a

x1 x2 x3 x4 x5 x6 4 6 8 0 0 0

1 x4 0 12 1 2 -3 1 0 0 -2 x5 0 4 3 1 1 0 1 0 43 x6 0 5 2 2 (5) 0 0 1 (1)

j 0 -4 -6 (-8) 0 0 01 x4 0 15 11/5 16/5 0 1 0 3/5 75/162 x5 0 3 13/5 3/5 0 0 0 -1/5 53 x3 8 1 2/5 (2/5) 1 0 0 1/5 (5/2)

j 8 4 (-14/5) 0 0 0 8/51 x4 02 x5 0 2 03 x2 6 5/2 1 1 5/2 0 0 1/2

= ->5/2-3 3/5 * 3/2 3-3/5*5/2= 3-3/2= 3/2

20/4/2012 43

i C s Ci BiP/a

x1 x2 x3 x4 x5 x6 4 6 8 0 0 0

1 x4 0 12 1 2 -3 1 0 0 -2 x5 0 4 3 1 1 0 1 0 43 x6 0 5 2 2 (5) 0 0 1 (1)

j 0 -4 -6 (-8) 0 0 01 x4 0 15 11/5 16/5 0 1 0 3/5 75/162 x5 0 3 13/5 3/5 0 0 0 -1/5 53 x3 8 1 2/5 (2/5) 1 0 0 1/5 (5/2)

j 8 4 (-14/5) 0 0 0 8/51 x4 02 x5 0 3/2 2 0 3/2 0 0 1/23 x2 6 5/2 1 1 5/2 0 0 1/2

Lm tng t c kt qu nh

bng20/4/2012 44

i C s Ci BiP/a

x1 x2 x3 x4 x5 x6 4 6 8 0 0 0

1 x4 0 12 1 2 -3 1 0 0 -2 x5 0 4 3 1 1 0 1 0 43 x6 0 5 2 2 (5) 0 0 1 (1)

j 0 -4 -6 (-8) 0 0 01 x4 0 15 11/5 16/5 0 1 0 3/5 75/162 x5 0 3 13/5 3/5 0 0 0 -1/5 53 x3 8 1 2/5 (2/5) 1 0 0 1/5 (5/2)

j 8 4 (-14/5) 0 0 0 8/51 x4 0 02 x5 0 3/2 2 0 3/2 0 0 1/23 x2 6 5/2 1 1 5/2 0 0 1/2

0 = ->1-16/5 ? *


ny

16/5

20/4/2012 45

i C s Ci BiP/a

x1 x2 x3 x4 x5 x6 4 6 8 0 0 0

1 x4 0 12 1 2 -3 1 0 0 -2 x5 0 4 3 1 1 0 1 0 43 x6 0 5 2 2 (5) 0 0 1 (1)

j 0 -4 -6 (-8) 0 0 01 x4 0 15 11/5 16/5 0 1 0 3/5 75/162 x5 0 3 13/5 3/5 0 0 0 -1/5 53 x3 8 1 2/5 (2/5) 1 0 0 1/5 (5/2)

j 8 4 (-14/5) 0 0 0 8/51 x4 0 02 x5 0 3/2 2 0 3/2 0 0 1/23 x2 6 5/2 1 1 5/2 0 0 1/2

= ->1-11/5 16/5 * -1 11/5-16/5 = -5/5=-1 hehe

20/4/2012 46

i C s Ci BiP/a

x1 x2 x3 x4 x5 x6 4 6 8 0 0 0

1 x4 0 12 1 2 -3 1 0 0 -2 x5 0 4 3 1 1 0 1 0 43 x6 0 5 2 2 (5) 0 0 1 (1)

j 0 -4 -6 (-8) 0 0 01 x4 0 15 44/5 16/5 0 1 0 3/5 75/162 x5 0 3 13/5 3/5 0 0 0 -1/5 53 x3 8 1 2/5 (2/5) 1 0 0 1/5 (5/2)

j 8 4 (-14/5) 0 0 0 8/51 x4 0 -1 02 x5 0 3/2 2 0 3/2 0 0 1/23 x2 6 5/2 1 1 5/2 0 0 1/2

= ->5/2-15 16/5 * 7 15 16/5*5/2 =7

20/4/2012 47

i C s Ci BiP/a

x1 x2 x3 x4 x5 x6 4 6 8 0 0 0

1 x4 0 12 1 2 -3 1 0 0 -2 x5 0 4 3 1 1 0 1 0 43 x6 0 5 2 2 (5) 0 0 1 (1)

j 0 -4 -6 (-8) 0 0 01 x4 0 15 44/5 16/5 0 1 0 3/5 75/162 x5 0 3 13/5 3/5 0 0 0 -1/5 53 x3 8 1 2/5 (2/5) 1 0 0 1/5 (5/2)

j 8 4 (-14/5) 0 0 0 8/51 x4 0 7 28/5 0 -8 1 0 -12 x5 0 3/2 2 0 3/2 0 0 1/23 x2 6 5/2 1 1 5/2 0 0 1/2

Tnh tng t tas c kt qu

20/4/2012 48

i C s Ci BiP/a

x1 x2 x3 x4 x5 x6 4 6 8 0 0 0

1 x4 0 12 1 2 -3 1 0 0 -2 x5 0 4 3 1 1 0 1 0 43 x6 0 5 2 2 (5) 0 0 1 (1)

j 0 -4 -6 (-8) 0 0 01 x4 0 15 44/5 16/5 0 1 0 3/5 75/162 x5 0 3 13/5 3/5 0 0 0 -1/5 53 x3 8 1 2/5 (2/5) 1 0 0 1/5 (5/2)

j 8 4 (-14/5) 0 0 0 8/51 x4 0 7 28/5 0 -8 1 0 -12 x5 0 3/2 2 0 3/2 0 0 1/23 x2 6 5/2 1 1 5/2 0 0 1/2

j

= 006

X73/25/2 ->

15

0 * 7 + 0 * 3/2 + 6 * 5/2 = 820/4/2012 49

i C s Ci BiP/a

x1 x2 x3 x4 x5 x6 4 6 8 0 0 0

1 x4 0 12 1 2 -3 1 0 0 -2 x5 0 4 3 1 1 0 1 0 43 x6 0 5 2 2 (5) 0 0 1 (1)

j 0 -4 -6 (-8) 0 0 01 x4 0 15 44/5 16/5 0 1 0 3/5 75/162 x5 0 3 13/5 3/5 0 0 0 -1/5 53 x3 8 1 2/5 (2/5) 1 0 0 1/5 (5/2)

j 8 4 (-14/5) 0 0 0 8/51 x4 0 7 28/5 0 -8 1 0 -12 x5 0 3/2 2 0 3/2 0 0 1/23 x2 6 5/2 1 1 5/2 0 0 1/2

j 15

= 006

X28/521 -> 2

0 *28/5 + 0 * 2 + 6 * 1 = 6- 4

20/4/2012 50

i C s Ci BiP/a

x1 x2 x3 x4 x5 x6 4 6 8 0 0 0

1 x4 0 12 1 2 -3 1 0 0 -2 x5 0 4 3 1 1 0 1 0 43 x6 0 5 2 2 (5) 0 0 1 (1)

j 0 -4 -6 (-8) 0 0 01 x4 0 15 44/5 16/5 0 1 0 3/5 75/162 x5 0 3 13/5 3/5 0 0 0 -1/5 53 x3 8 1 2/5 (2/5) 1 0 0 1/5 (5/2)

j 8 4 (-14/5) 0 0 0 8/51 x4 0 7 28/5 0 -8 1 0 -12 x5 0 3/2 2 0 3/2 0 0 1/23 x2 6 5/2 1 1 5/2 0 0 1/2

j 15 2

= 006

X001 -> 0

0 *0 + 0 * 0 + 6 * 1 = 6- 6

20/4/2012 51

i C s Ci BiP/a

x1 x2 x3 x4 x5 x6 4 6 8 0 0 0

1 x4 0 12 1 2 -3 1 0 0 -2 x5 0 4 3 1 1 0 1 0 43 x6 0 5 2 2 (5) 0 0 1 (1)

j 0 -4 -6 (-8) 0 0 01 x4 0 15 44/5 16/5 0 1 0 3/5 75/162 x5 0 3 13/5 3/5 0 0 0 -1/5 53 x3 8 1 2/5 (2/5) 1 0 0 1/5 (5/2)

j 8 4 (-14/5) 0 0 0 8/51 x4 0 7 28/5 0 -8 1 0 -12 x5 0 3/2 2 0 3/2 0 0 1/23 x2 6 5/2 1 1 5/2 0 0 1/2

j 15 2 0 7 0 0 3

Tnh tng t tas c kt qu

20/4/2012 52

i C s Ci BiP/a

x1 x2 x3 x4 x5 x6 4 6 8 0 0 0

1 x4 0 12 1 2 -3 1 0 0 -2 x5 0 4 3 1 1 0 1 0 43 x6 0 5 2 2 (5) 0 0 1 (1)

j 0 -4 -6 (-8) 0 0 01 x4 0 15 44/5 16/5 0 1 0 3/5 75/162 x5 0 3 13/5 3/5 0 0 0 -1/5 53 x3 8 1 2/5 (2/5) 1 0 0 1/5 (5/2)

j 8 4 (-14/5) 0 0 0 8/51 x4 0 7 28/5 0 -8 1 0 -12 x5 0 3/2 2 0 3/2 0 0 1/23 x2 6 5/2 1 1 5/2 0 0 1/2

j 15 2 0 7 0 0 3V j 0 vi mi j nn phng n c bn bng 3 l phng n ti uphng n ti u l X* = (0 , 5/2, 0)Zmax = 15

20/4/2012 53

Bài Toán Đơn Hình

Documents

Transcript of Bài Toán Đơn Hình