Aplicación de La Programación Lineal en La Industria Textil (2) (4)

UNIVERSIDAD NACIONAL DE INGENIERÍA FACULTAD DE INGENIERIA QUMICA Y TEXTIL

INDICE

Pag. INTRODUCCIÓN………………………………………………………………………… ……………… 2 ANTECEDENTES………………………………………………………………………… …………….… 2 MODELO DE PROGRAMACION………………………………………………………………….. PROGRAMACION………………………………………………………………….. 4 PLANTEAMIENTO DEL PROBLEMA……………………………………………………………. 6 FUNCIÓN OBJETIO………………………………………………………………………………….. 6 ARIABLES DE DECISIÓN…………………………………………………………………………… 6 RESTRICCIONES………………………………………………………………………… ………………. ! CONCLUSIONES ……………………………………………………………………………………….. " BIBLIOGRAFIA…………………………………………………………………………… ……………… "

1


APLICACIÓN DE LA PROGRAMACIÓN LINEAL EN LA INDUSTRIA TEXTIL I.- INTRODUCCION La P$%g$a&a'()* L(*+a, +- *a /+$$a&(+*0a & 0(, 'a*3% -+ (+$+ 0%&a$ 3+'(-(%*+- +* +, 5&(0% 3+ ,a ,%g7-0('a 3+ ,a +&8$+-a9 3+-3+ /a'+ &'/% 0(+&8% +, /%&$+ /a :+*(3% 8%*(+*3% +* 8$5'0('a ,a P$%g$a&a'()* L(*+a,. ;% +* 37a +<(-0+* &'/%- 8$%g$a&a- + *%- 8+$&(0+* %0+*+$ +, $+*3(&(+*0% &5<(&% +* *a 8$%3''()*9 &a0(=a'()* 3+ '%-0%- 3+ 8$%3''()*9 %80(&(=a$ ,a 8$%3''()*9 +0'. P+$% 0%3%- +-0%- 8$%g$a&a- >*'(%*a* a?% * &(-&% 8$(*'(8(% +, 'a, +- ,a P$%g$a&a'()* L(*+a,9 8a$a 8%3+$ +?+'0a$ +-0a /+$$a&(+*0a /a'+ >a,0a '%*%'+$ ,a- :a$(a,+- 3+ 3+'(-()* ,a- 'a,+- *%- 8+$&(0+* >%$&a* * 8a$5&+0$%  * -(-0+&a 3+ +'a'()*. E* +-0+ 0$aa?% -+ :+$5 * 8$%,+&a + -+ 8+3+ +*'%*0$a$ +* 'a,(+$ +&8$+-a9 +, 'a, +- +, a?% $+*3(&(+*0% 3+ ,a 8$%3''()* +-8+$a3a9 8a$a $+-%,:+$ +-0+ 8$%,+&a 0+*3$+&%+ '%*%'+$ ,a- '(+$0%- 8a$5&+0$%- @a$(a,+- 3+ 3+'(-()* 8a$a +,,% '%*-,0a&%- '%* ,a +&8$+-a 8a$a + *%- $(*3+* ,a (*>%$&a'()* *+'+-a$(a  a-7 8%3+$ /a'+$ -% 3+ ,a P$%g$a&a'()* L(*+a,.

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Mantel de 2.50  !.20 Se"#$lleta% de 0.&5  0.&5 Mantel de S'$tt$n( S)*ana +a,e"a G"" t$ a/el

Ca,$%a A l1nea de #e%t$" ata %an$ta"$a +n +ell %"t l%a A l1nea de #e%t$" G"" t$ 3e4 A Pantaln anade" l1nea de t"a*a6

L%- -(g(+*0+- 3a0%- + &%-0$a$+&%- >+$%* -&(*(-0$a3%- 8%$ +, E'%*%&7a 3+ ,a +*0(3a3.

3+8a$0a&+*0% 3+

P"d+t Mantel de Ind$+ad" 2.50 !.20

Se"#$ll eta% de 0.&50. &5

Mant el de S'$tt$ n(

Sa*a na +a,e "a

G"" t$ a/ el

Ca,$% a 7A8 l1nea de #e%t$"

ata %an$ta"$ a +n +ell %"t

l%a 7A8 l1nea de #e%t$"

G"" t$ 3e 4 7A8

P"e+$ de 6.6 #enta  n$dad

H.6H

#.!

1.11

H.6!

#.#4

#.1#

2.

H.!H

Pantal n anad e" l1nea de t"a*a6  4.6H

Ta*la N9!: P"e+$% de l% P"d+t% ;e %n #end$d%

CON
Te6$d% =,et"% de tela " n$dad de "d++$n> Te6$d de ?anta%1a Te6$d Te6$d D"$ll %'$tt$n( Da+"n lan+ 2.5@00 0.!&00

Mantel de %'$tt$n(

!.5000

Sa*ana Ca,e"a

!.000

G"" t$ a/el Ca,$%a A l1nea de #e%t$"

0.&000 !.5000

ata %an$ta"$a +n +ell

!.B500

l%a A l1nea de #e%t$" G"" t$ e4 A Pantaln anade" l1nea de t"a*a6 D$%n$*$l$dad

!.&000 0.2000 !.B500 !20

22@0

!0!5

Ta*la N92: Cant$dad de Tela ;e %e e,lea en la "d++$n

#


CON
Ot"a% ,ate"$a% "$,a% $l=,et" %> @

Se"#$lleta% 0.&5 0.&5

tn =n.>

F$e" =n.>

!.2

Mantel de %'$tt$n(

2

Sa*ana Ca,e"a G"" t$ a/el Ca,$%a A l1nea de #e%t$" ata %an$ta"$a +n +ell l%a A l1nea de #e%t$" G"" t$ e4 A Pantaln anade" l1nea de t"a*a6

@  &0 20 20 & @0

 @ @ !

!

Ta*la N9&: Cant$dad de t"a% ,ate"$a% "$,a% ;e %e e,lea en la "d++$n

La 3(-8%*((,(3a3 3+ +-0a- &a0+$(a- 8$(&a- +-

!5 +n% de $l de 5000 ,et"% !5@B0 *tne% 5B0 H$e". CON
Etaa% de +n?e++$n="a% ,*"e>

Mantel de 2.50!.20 Se"#$lleta% 0.&5 0.&5

0.0 0.0&

Cn?e++$ n de la $eHa 0.2 0.0&

Mantel de %'$tt$n(

0.0&

0.!0

Sa*ana Ca,e"a

0.!0

0.&&

G"" t$ a/el

0.0&

0.@5

Ca,$%a A l1nea de #e%t$"

0.0

!.

0.0

0.!

0.!5

ata %an$ta"$a +n +ell

0.05&

!.&&

0.0

0.0@2

0.0@!

0.0

!.

0.0B2

0.0@2

0.0@!

0.02

0.2

0.0

0.05

!.

0.!0

0.0!

0.02

500

200

200

200

200

l%a A l1nea de #e%t$" G"" t$ e4 A Pantaln anade" l1nea de t"a*a6 D$%n$*$l$dad

C"te de la $eHa

Candel $lla

Cl+a+$n del 6al

A++e%" $%

Ta*la N9@: P"+e%% 4 el t$e, de d"a+$n del ,$%, %e(Jn +ada $eHa de "d++$n

La 3+&a*3a &5<(&a 3+ 8a*0a,%*+- 3+ 8a*a3+$% +- 3+ 2H  ,a &7*(&a +- 3+ 1HH 8a*0a,%*+-. #


III.- MODELO DE PROGRAMACION La- $a7'+- 3+ ,a (*:+-0(ga'()* 3+ %8+$a'(%*+- -+ $+&%*0a* a 'a*3% -+ /('(+$%* ,%8$(&+$%- (*0+*0%- 8a$a +&8,+a$ +, &0%3% '(+*07'% +* ,a a3&(*(-0$a'()* 3+ *a +&8$+-a. S(* +&a$g%9 +, (*('(% 3+ +-0a 3(-'(8,(*a -+ a0$(+ a ,%- -+$:('(%- &(,(0a$+- 8$+-0a3%- a 8$(*'(8(%- 3+ ,a -+g*3a g+$$a &*3(a,. D+-3+ +*0%*'+- +<(-07a ,a 8$+%'8a'()* 8%$ +, a,0% &a*3% &(,(0a$ 3+ I*g,a0+$$a  ,+g% EE.UU. ,a *+'+-(3a3 3+ /a'+$ * -% $a'(%*a, 3+ ,%$+'$-%- &5- 3+'(0a$(%- a ,a /%$a 3+ 3+-a$$%,,a$ ,a- %8+$a'(%*+- &(,(0a$+-  ,a- a'0(:(3a3+3+*0$% 3+ +-0a-. @R+'$-%- + +* 0(+&8% 3+ g+$$a $+-,0a* -+$ &5- +-'a-%-. La a3&(*(-0$a'()* &(,(0a$ $(05*('a  ,a 3+ EE.UU. ,,a&a$%* a * g$a* *&+$% 3+ '(+*07'%'%* +, * 3+ (*:+-0(ga$ ,a- %8+$a'(%*+- &(,(0a$+-  a8,('a$ 8$%'+3(&(+*0%- '(+*07'%- +* ,a -%,'()* 3+ 8$%,+&a- 05'0('%-  +-0$a0g('%-. E-0%- +(8%- '(+*07'%- >+$%* ,%- 8$(&+$%3+ (*:+-0(ga'()* 3+ %8+$a'(%*+-. La- -%,'(%*+- 3a3a- 8%$ +-0%- +(8%- 8+$&(0(+$%* + -+ ga*a$a* a0a,,a- (&8%$0a*0+- 8a$a +-0%- 8a7-+-. E<(-0+* 3%- a-8+'0%- (&8%$0a*0+- + (*+$%* +* +, 3+-a$$%,,% 3+ ,a I*:+-0(ga'()* 3+ O8+$a'(%*+- '%&% '(+*'(a9 +-0%- -%* E, 8$%g$+-% --0a*'(a, + -+ ,,+:) a 'a% 8a$a &+?%$a$ ,a- 0'*('a- 3(-8%*(,+- 8a$a ,a I*:+-0(ga'()* 3+ O8+$a'(%*+-. La $+:%,'()* 3+ ,a- '%&80a3%$a- @+, &+?%$ $+ga,% 8a$a ,a I*:+-0(ga'()* 3+ O8+$a'(%*+- La (*:+-0(ga'()* 3+ %8+$a'(%*+- (*0+*0a +*'%*0$a$ *a &+?%$ -%,'()*9 @,,a&a3a -%,'()* )80(&a 8a$a +, 8$%,+&a a?% '%*-(3+$a'()*. La I*:+-0(ga'()* 3+ O8+$a'(%*+- +- * 8$%'+3(&(+*0% '(+*07'% 8a$a 0%&a$ 3+'(-(%*+-%$+ ,a- %8+$a'(%*+- 3+ -(-0+&a- %$ga*(=a'(%*a,+- @+?+&8,% *a +&8$+-a9 +- 3+'($9 ,a I*:+-0(ga'()* 3+ O8+$a'(%*+- 8$+-8%*+ +, +&8,+% 3+ &%3+,%-  &0%3%- 'a*0(0a0(:%8a$a ,a 0%&a 3+ 3+'(-(%*+-9 +*0$+ ,%- + -+ +*'+*0$a ,a P$%g$a&a'()* L(*+a,. M'/a- 8+$-%*a- ',a-('a* +, 3+-a$$%,,% 3+ ,a P$%g$a&a'()* L(*+a, +*0$+ ,%- a:a*'+'(+*07'%- &5- (&8%$0a*0+- 3+ &+3(a3%- 3+, -(g,% XX. E* ,a a'0a,(3a3 +- *a /+$$a&(+*0a '%&* + /a a/%$$a3% &(,+- % &(,,%*+- 3+ 3),a$+- a &'/a- '%&8a7a-  *+g%'(%-9 (*',+*3% (*3-0$(a- &+3(a*a- +* 3(-0(*0%- 8a7-+- 3+, &*3%. KC5, +- ,a *a0$a,+=a 3+ +-0a *%0a,+ /+$$a&(+*0a   0(8% 3+ 8$%,+&a- 8+3+ &a*+?a$ E<8$+-a3% $+:+&+*0+9 +, 0(8% &5- '%&* 3+ a8,('a'()* aa$'a +, 8$%,+&a g+*+$a, 3+ a-(g*a$ $+'$-%- ,(&(0a3%- +*0$+ a'0(:(3a3+- '%&8+0(0(:a- 3+ ,a &+?%$ &a*+$a 8%-(,+ @+- 3+'($9 +* >%$&a )80(&a. E-0+ 8$%,+&a 3+ a-(g*a'()* 8+3+ -$g($ 'a*3% 3+a +,+g($-+ +, *(:+, 3+ '(+$0a- a'0(:(3a3+- + '%&8(0+* 8%$ $+'$-%- +-'a-%- 8a$a $+a,(=a$,a-. La :a$(+3a3 3+ -(0a'(%*+- a ,a- + -+ 8+3+ a8,('a$ +-0a 3+-'$(8'()* +- -(* 33a & g$a*3+9  :a 3+-3+ ,a a-(g*a'()* 3+ (*-0a,a'(%*+- 8$%3'0(:a- a ,%- 8$%3'0%-9 /a-0a ,a a-(g*a'()* 3+ ,%- $+'$-%- *a'(%*a,+- a ,a- *+'+-(3a3+- 3+ * 8a7- 3+-3+ ,a 8,a*+a'()* ag$7'%,a9 /a-0a +, 3(-+% 3+ *a 0+$a8(a 3+ $a3(a'()* +0'. N% %-0a*0+9 +, (*g$+3(+*0+ '%&* 3+ 0%3a- +-0a- -(0a'(%*+- +- ,a *+'+-(3a3 3+ a-(g*a$ $+'$-%- a ,a- a'0(:(3a3+-. La P$%g$a&a'()* L(*+a, +- *a 0'*('a 3+0+$&(*(-0a9 *% (*',+ 8$%a(,(3a3+-  0(,(=a * &%3+,% &a0+&50('% 8a$a 3+-'$(($ +, 8$%,+&a. E, a3?+0(:% ,(*+a, -(g*('a + 0%3a- ,a>*'(%*+- &a0+&50('a- 3+, &%3+,% 3++* -+$ >*'(%*+- ,(*+a,+-. E* +-0+ 'a-%9 ,a 8a,a$a 8$%g$a&a'()* *% -+ $++$+ a 8$%g$a&a'()* +* '%&80a3%$a- +* +-+*'(a +- * -(*)*(&% 3+ 8,a*+a'()*. A-79 ,a P$%g$a&a'()* L(*+a, 0$a0a ,a 8,a*+a'()* 3+ ,a- a'0(:(3a3+- 8a$a %0+*+$ * $+-,0a3% )80(&%9 +-0% +-9 +, $+-,0a3% + &+?%$ a,'a*'+ ,a &+0a +-8+'('a3a @-+g* +, &%3+,% +*0$+ 0%3a- ,a- %8'(%*+- 3+ -%,'()*. A*+ ,a a-(g*a'()* 3+ $+'$-%- a ,aa'0(:(3a3+- +- ,a a8,('a'()* &5- >$+'+*0+9 ,a P$%g$a&a'()* L(*+a, 0(+*+ &'/a- %0$a#


8%-((,(3a3+-. D+ /+'/%9 'a,(+$ 8$%,+&a '% &%3+,% &a0+&50('% -+ a?-0+ a, >%$&a0% g+*+$a, 3+, &%3+,% 3+ P$%g$a&a'()* L(*+a, +- * 8$%,+&a 3+ P$%g$a&a'()* L(*+a,. E, 8$%,+&a g+*+$a, 3+ ,a 8$%g$a&a'()* ,(*+a, 8+3+ -+$ 3+-'$(0% 3+ ,a -(g(+*0+ >%$&a Da3a *a >*'()* ,(*+a, 3+ :a$(a- :a$(a,+-9 -+ (+$+* 3+0+$&(*a$ :a,%$+- *% *+ga0(:%8a$a 3('/a- :a$(a,+- + &a<(&('+* % &(*(&('+* +, :a,%$ 3+ ,a >*'()* ,(*+a,9 -?+0a a * '(+$0% *&+$% 3+ ,(&(0a'(%*+- + a-&+* ,a >%$&a 3+ * -(-0+&a 3+ +'a'(%*+-  % (*+'a'(%*+- ,(*+a,+-. C%*-(3+$a*3% a * '%&% +, *&+$% 3+ :a$(a,+-  a & '%&% +, *&+$% 3+ +'a'(%*+- + (*+'a'(%*+-  -( -+ '&8,+ + & < * +*0%*'+- +, &%3+,% &a0+&50('% -+$7a +, -(g(+*0+ Min o Max Z = C 1 X 1 + C 2 X 2 + C n X n

(1)

Sujeto a : ai1 X 1 + ai 2 X 2 + ........ + a1n X n{ ≤ = ≥}bi X j ≥ 0 j =1, ..., n

i =1, ...m (2)

(3)

La- +<8$+-(%*+- @1 @2  @# '%&8%*+* +, &%3+,% +'%*)&('%&a0+&50('% 3+ 8$%g$a&a'()* ,(*+a,. La +<8$+-()* @1 $+8$+-+*0a ,a >*'()* + :a a -+$ %80(&(=a3a9 ,a 'a, -+ 3+*%&(*a FUNCIÓN OBJETIO  -+ $+8$+-+*0a 8%$ . L%- '$(0+$(%- 3+ %80(&(=a'()* 3+8+*3+$5* 3+ ,%%?+0(:%- % &+0a- + -+ (+$a* a,'a*=a$ +* ,a +&8$+-a  ,a 8$(%$(3a3 3+ ,%- &(-&%-. C j L%-%* ,%- '%+'(+*0+- 3+ ,a >*'()* %?+0(:%. E-0a- '%*-0a*0+- 8+3+* 0+*+$ 3(>+$+*0+- -(g*('a3%-9 8%$ +?+&8,%9 '%-0%- 3+ 8$%3''()*9 ga*a*'(a-9 *%$&a- 3+ 0(+&8% % 3+ $+'$-%-9 8$+'(%-9 +0'. X j

La-%* ,a- :a$(a,+- +-+*'(a,+- % 3+ 3+'(-()* 3+, &%3+,% + -+ 8$+0+*3a 3(-+a$. Ca3a *a $+8$+-+*0a *a a'0(:(3a3 +'%*)&('a  -- :a,%$+- $+8$+-+*0a* ,%- *(:+,+- 3+ +-aa'0(:(3a3+-. La +<8$+-()* @2 +- +, -(-0+&a 3+ +'a'(%*+- % (*+'a'(%*+- ,(*+a,+- + -+ :a 3+*%&(*a$ bi

'%&% -(-0+&a 3+ $+-0$(''(%*+- ,(*+a,+-9 3%*3+ ,%- 9 +- 3+'($9 ,%- 0$&(*%- (*3+8+*3(+*0+8+3+* 0+*+$ 3(>+$+*0+- -(g*('a3%- '%&% -%*9 3+&a*3a- &5<(&a- % &7*(&a- 3+ 8$%3''()*9 3(-8%*((,(3a3 3+ $+'$-%-9 $++$(&(+*0%- &7*(&%- 3+ 0(,(=a'()* 3+ ai

3+0+$&(*a3%- $+'$-%-9 +*0$+ %0$%-. L%- '%+'(+*0+-%* ,a- '%*-0a*0+- a-%'(a3a- a 'a3a *a 3+ ,a- :a$(a,+- +* 'a3a *a 3+ ,a- $+-0$(''(%*+-9 >$+'+*0+&+*0+ +<8$+-a* *%$&a- 0'*('a- 3+ '%*-&% 3+ &a0+$(a,+-9 3+ 0(+&8%9 +0'. La +<8$+-()* @# +-0a,+'+ + ,a- :a$(a,+- 3+, &%3+,% -%,% 8+3+* 0%&a$ :a,%$+- *% *+ga0(:%-9 A +-0a +<8$+-()* -+ ,+ '%*%'+ '%&% '%*3('()* 3+ *% *+ga0(:(3a3. E, '%*?*0% 3+ -%,'(%*+- + -a0(->aga ,a- +<8$+-(%*+- @19 @2  @# -+ ,+ '%*%'+ '%&% -%,'()* 8%-(,+ )80(&a.

IV.- PLANTEAMIENTO DEL PROLEMA ,0(&a&+*0+ ,%- (*g$+-%- +-0(&a3%- '%&% 8a$0+ 3+ - +-0$a0+g(a >*3a&+*0a, 3+ 8$%3''()*9 *% -+ '%$$+-8%*3+* '%* ,%- (*g$+-%- %0+*(3%-9 8%$ ,% + -+ /a'+ *+'+-a$(% +, #


-% 3+ ,a 8$%g$a&a'()* ,(*+a, '%&% 0'*('a9 8a$a 3+0+$&(*a$ -( ,a +-0$a0+g(a 0(,(=a3a 8%$ ,a +&8$+-a +- ,a )80(&a % *%.

V.- +''(%*+-9 ,a- 'a,+- 0(+*+* ,a &5- a,0a 3+&a*3a 3+*0$% 3+, '%*-&% 0%0a,. La >*'()* %?+0(:% 3+ &a<(&(=a$ ,a 8$%3''()* 0(+*+ ,a -(g(+*0+ >%$&a MAXZ = 6.65 X 1

+ 0.60 X 2 + 3.97 X 3 + 1.11 X 4 + 0.67 X 5 + 3.34 X 6 + 3.13 X 7 + 2.90 X 8 + 0.70 X 9 + 4.60 X 10

VI.- VARIALES DE DECISION La- :a$(a,+- 3+ 3+'(-()* + 0(,(=a$+&%- -+$5*

X 1 :

Un$dade% de ,antele% de 2.50  !.20 a "d+$" en el %e,e%t"e.

X 2 :

Un$dade% de %e"#$lleta% de 0.&5  0.&5 a "d+$" en el %e,e%t"e. X 3 :

Un$dade% de ,antele% de %'$tt$n( a "d+$" en el %e,e%t"e. X 4 :

Un$dade% de %a*ana% +a,e"a% a "d+$" en el %e,e%t"e. X 5 :

Un$dade% de (""% t$ a/el a "d+$" en el %e,e%t"e. X 6 :

Un$dade% de +a,$%a% A de la l1nea de #e%t$" a "d+$" en el %e,e%t"e. X 7 : Un$dade% de *ata% %an$ta"$a% +n +ell %"t a "d+$" en el %e,e%t"e. X 8

: Un$dade% de *l%a% A de la l1nea de #e%t$" a "d+$" en el %e,e%t"e. X 9

: Un$dade% de (""% de t$ e4 a "d+$" en el %e,e%t"e. X 10

: Un$dade% de antalne% de anade" de la l1nea de t"a*a6 a "d+$" en el %e,e%t"e.

X ij

≥0

K: !!0

VII.- RESTRICCIONES S+g* ,%- 3a0%- 3+ ,a- Ta,a- 8%3+&%- 8,a*0+a$ ,a- -(g(+*0+- $+-0$(''(%*+- #


Te6$d de ?anta%1a %'$tt$n( 2.54 X 1 + 0.13 X 2 + 1.5 X 3 + 1.9 X 4 ≤ 6120

Te6$d da+"n 0.3 X 5 + 1.5 X 6 + 1.75 X 7 + 1.3 X 8 ≤ 2240

Te6$d d"$ll 0.2 X 9 + 1.75 X 10 ≤ 1015

D$%n$*$l$dad de *tne% 6X6  4X!  4X"  X1H

≤

14!H

D$%n$*$l$dad de H$e" X 10

≤ 570

D$%n$*$l$dad de $l 4 X 1 + 1.2 X 2 + 2 X 3 + 4 X 4 + 6 X 5 + 30 X 6 + 20 X 7 + 20 X 8 + 3 X 9 + 40 X 10 ≤ 75000

D$%n$*$l$dad de "a% ,*"e en +"te

H.H6X1  H.H#X2  H.H#X#  H.1X4  H.H"#X  H.H66X6  H.H#X!  H.H6X"  H.H26X  H.HX1H

≤

HH

D$%n$*$l$dad de "a% ,*"e en +n?e++$n

H.26X1  H.H"#X2  H.1X#  H.##X4  H.4X  1.6X6  1.##X!  1.6X"  H.26X  1.6X1H

≤

62HH

D$%n$*$l$dad de "a% ,*"e en +andel$lla 0.06 X 6 + 0.08 X 7 + 0.072 X 8 + 0.088 X 9 + 0.1X 10 ≤ 200

D$%n$*$l$dad de "a% ,*"e en +l+a+$n de 6al 0.16 X 6 + 0.042 X 7 + 0.0042 X 8 + 0.01X 10 ≤ 200

D$%n$*$l$dad de "a% ,*"e en +l+a+$n de a++e%"$% 0.15 X 6 + 0.041 X 7 + 0.041 X 8 + 0.02 X 10 ≤ 200

De,anda ,)$,a de antalne% X 10

#

≤ 290


De,anda ,1n$,a de antalne% X 10

≥ 100

VIII.- CONCLUSIONES La P$%g$a&a'()* L(*+a, +- *a /+$$a&(+*0a & -+*'(,,a9 8+$% 0(+*+ * g$a* -%9 8%$ ,a- +&8$+-a- Na'(%*a,+- + (*0+$*a'(%*a,+-9 +* +, 5&(0% a3&(*(-0$a0(:%  ,%g7-0('%. Pa$a 8%3+$ /a'+$ -% 3+ ,a P$%g$a&a'()* L(*+a, +- *+'+-a$(% 0+*+$ ,a- $+-0$(''(%*+*+'+-a$(a-  ,a- :a$(a,+- a3+'a3a- 8a$a 8%3+$ 0%&a$ *a 3+'(-()* %80(&a* '%* $+>+$+*0+ a, 8$%,+&a +*'%*0$a3%.

IX.- ILIOGRA<ÍA Anderson, D.R.et al. Introducción a los Modelos Cuantitativos para la Administración. Editorial Iberoamericana S.A. 6 ta Edición. México, !!". #ueno, E. Econom$a de la Empresa. An%lisis de las decisiones empresariales. &omo I ' II. Editorial (ir%mide S.A., Madrid, !)!. Dor*man, R.+(ro-ramación lineal ' an%lisis económico. Editorial Revolucionaria. a /abana, !66. 0elipe, (. ' otros. +(ro-ramación Matem%tica I. Ciudad de la /abana, !)". Documentos de la Empresa CAC120

#

Aplicación de La Programación Lineal en La Industria Textil (2) (4)

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