Optimización222

7/21/2019 Optimizacin222

1/8


2/8

Co+ #& 3,o.o .# G-* ,"-+@o"-o#& ,#- #+ *+- -,"5

R T W X Y Z

F1 1 0 3 0 4 00F2201200=0F3101002=0F42

Ponemos como primera ecuacin aquella con coeficiente ! en este caso es " # $espu%s&acemos ' los $em(s elementos $e la primera columna! # continuamos con las si)uientescolumnas*

R

T W X Y Z F1 1 0 3 0 4 0 0 F22 0 1 2 0 0 0 F3 1 0 1 0 0

0F42210000F50

-F1 -F4+F2

R

T W X Y Z F1 1 0 3 0 4 0 0 F20 2 0 2 0 0 0 F3 1 0 1 0 0

0

F4

2

2

1

0

0

0

0

F5

0

-F1+F3 -2F1+F4

R

T W X Y Z F1 1 0 3 0 4 0 0 F20 2 0 2 0 0 0 F3 0 0 2 0 4

0F40270800F50

F5F2

Intercambiamos las filas 5 y 2 para mantener el orden ecalonado

RT W X Y Z F1 1 0 3 0 4 0 0 F20 1 0 1 3 1 2 F3 0 0 2 0 4

0F4 0270800F5

-1/2F3 -2F2+F4 2F2+F5 -2F2+F6

Se!imos "ol"iendo # las si!ientes col!mnas

ELIMINACIN GAUSSIANA(?0 P*+,o)

5

6Y 7 89 7 R 0

2; 7 9 < 2 R 0

2Z < 9 < R 0

2T 7 9 < 2R 0

=; 7 8Y < Z < T 2

2; 7Y < Z < 2T 6


3/8

R

T W X Y Z F1 1 0 3 0 4 0 0 F20 1 0 1 3 1 2 F3 0 0 1 0 2

10F400721424

$F3+F4

R

T W X Y Z F1 1 0 3 0 4 0 0 F20 1 0 1 3 1 2 F3 0 0 1 0 2

10F40002094F

1/2F4

R

T W X Y Z F1 1 0 3 0 4 0 0 F20 1 0 1 3 1 2 F3 0 0 1 0 2

10F4000109/22

-4F4+F6

R

T W X Y Z F1 1 0 3 0 4 0 0 F20 1 0 1 3 1 2 F3 0 0 1 0 2

10F4000109/22

F6+F5

R

T W X Y Z F1 1 0 3 0 4 0 0 F20 1 0 1 3 1 2 F3 0 0 1 0 2

10F4000109/22

5F5+F6

R

T W X Y Z F1 1 0 3 0 4 0 0 F20 1 0 1 3 1 2 F3 0 0 1 0 2

10F4000109/22

-F5 1/112F6

RT W X Y Z F1 1 0 3 0 4 0 0 F20 1 0 1 3 1 2 F3 0 0 1 0 2

10F4000109/22

-3F3+F1 F4+F2


4/8

R

T W X Y Z F1 1 0 0 0 2 3 0 F20 1 0 0 3 7/2 0 F3 0 0 1 0 2

10F4000109/22F

-2F5+F1 3F5+F2 2F5+F3

R

T W X Y Z F1 1 0 0 0 0 41 20 F20 1 0 0 0 121/2 30 F3 0 0 1 0 0

3920F4 000109

-41F6+F1 121/2F6+F2 3%F6+F3 %/2F6+F4 1%F6+F5

R

T W X Y Z F1 1 0 0 0 0 0 69/56 F20 1 0 0 0 0 149/112 F3 0 0 1 0 0

11/56F400010

&l res!ltado indica '!e(

)* -6%/56 *14%/112 ,*11/56 * 3$/112 .*-%/56 * 2%/56

0omprobando

4.-3,-)*#

4-%/56-311/56--6%/56 10)789

-36/56-33/56+6%/56

-36-33+6%/56

#/56*#

2-,+2)*#

23$/112-11/56+2-6%/56 2 :

3$/56-11/56+-13;/56

3$-11-13;/56

3$-14%/56

-112/56

-14/$* -2

2+,+)*#

22%/56+11/56+-6%/56 3 0)789

5;+11-6%/56

#/56*#

2-,+2)*#

214%/112-11/56+2-6%/56 4 0)789


5/8

14%-11-13;/56

#/56*#

--3.++*2

-3$/112-3-%/56+2%/56+14%/112 5 0)789

-3$+14%/112+2$/56+2%/56

112/112+2$+2%/561+1*2

2-.++2*4

23$/112--%/56+2%/56+214%/112 6 0)789

$4/112+%+2%/56+2%;/112

$4+2%;/112+3;/56

1;6/56+1%/2;

%3/2;+1%/2;

%3+1%/2;

112/2;*4

;= 6Y = Z= T 0 2 2

Y= 6; < Z7 YT 0 2

=; 7 Y 0

=; 7 Y2< 2 0

9espeamos las mismas inc=nitas en 2 ec!aciones

-*.

*-.

-* Y2

-2

* - Y2

+2

S!stit!imos !na en el otro

-.* - Y2

+2

IGUALACIN(> P*+,o)5


6/8

Y2

-.-2*#

tili?amos la f=rm!la de se!ndo rado

8*1 7* -1 0* -2

y=b b

24 ac2a

y=(1)(1)

24 ( 1 )(2)2(1)

y=19

2(1)

y=

1+32(1) * 2

y=132(1) * -1

S!stit!imos

Y2

-.-2*.-2@.+1

8; < >Y < 8Z >

6; < 6Y < 2Z ?

2; < 8Y < Z 8

-"- #+,#+.#" #Bo" #+*#"-"# &- #/*-/o+#

#/*-/+ ?

8; < >Y < 8Z >

REDUCCIN(6 P*+,o)5


7/8

#/*-/+ 2

6; < 6Y < 2Z ?

#/*-/+ 8

2; < 8Y < Z 8

-&/-o #& 3,o.o .# "#.*//+ #+,"# &- #/*-/+ ? 8

(=2) (8; < >Y < 8Z >)(8) (2; < 8Y < Z 8)

$$$$$$$$$$$$$$$$$$$$$$=>; = ?2Y < >Z =?2>; < Y < 8Z

$$$$$$$$$$$$$$$$$$$$= 8Y = 8Z =8 L- &&--"#o #/*-/+ +*#"o 6

-&/-o #& 3,o.o .# "#.*//+ #+,"# &- #/*-/+ 2 8

6; < 6Y < 2Z ?(=2) (2; < 8Y < Z 8)

$$$$$$$$$$$$$$$$$$$$$$$$$$6; < 6Y < 2Z ?=6; = >Y = 2Z =>

$$$$$$$$$$$$$$$$$$$$$$$$$$=2Y =

Ao"- 4*# ,"-!-B-o o!"# *+- o&- '-"-! o.#o .##B-" Y * @H/+,#5

=2Y =Y ==2

Y 21

Ao"- *,,*o #& '-&o" .# Y #+ &- #/*-/+ +#"o 6 -"- o!,#+#" #& '-&o" .# Z

= 8Y = 8Z =8=8(21) = 8Z =8

=K1 = 8Z = 8=8Z =8 < K1

=8Z 61Z 61=8

Z =?1


8/8

Ao"- *,,*o #& '-&o" .# Y .# Z #+ /*-&4*#"- .# &- #/*-/o+# ?1 2 o 85 E+ #,#/-o *-"# &- #/*-/+ +*#"o 85

2; < 8Y < Z 82; < 8(21) < ?(=?1) 8

2; < K1 = ?1 82; 8 = >2; =8; =82

; =?1

R#*&,-.o:

; =?5 Y 25 Z =?5

Po.#o /o"o!-"&o *,,*#+.o &o "#*&,-.o .# ;1Y1Z #+ /*-&4*#"- .# &-

#/*-/o+# ?1218 o &o /o"o!-"# /o+ &- #/*-/+ +*#"o 8

2; < 8Y < Z 82(=?1) < 8(25) ?(=?1) 8

=8 < K1 = ?1 8

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Optimización222