p20203 linear programming - E, r _..__. , MM, 2E Prova de...

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Unformatted text preview: E, r _..__. , MM, 2E Prova de P.Linear UERJ 09/02/2004 lé Questéo (<3 pentes) Escreva 0 Dual (10 Inedele abaixo: :— 3331 ‘— 7502 + 7334 ‘— 6235 —' 836 3.21. 232 + 3533 — 824 — 536 S 331 + 832 — 734 + 835 + 41116 2 —5 $1+5$2—$3+3$4 *3235 S —12:z:1 -— 51:2 + 33:3 —- 51:6 2 8 121:1 + 30:; — 40:3 —— 60:4 + 10:03 2 18 $29 €133, €134, 5135 Z 0 1:1, 1:3 2:» Irrestritas em sinal 2fl Questéo pentes) Uma empresa preduz detenninade produte em 3 fabric-as (I, II 0 III ) 9 es envia para 4 centres (10 distribnigfie A’ B, C e D). Carla llma clas 3 fabricas pede preduzir, per m'és, 300 teneladas do predute. Per sua vez e centre de distribuigae A querS mensalmente, 100 teneladas do predute, e B quer 500 teneladas enquante que 0 C e D querem, cada 11m, 200 teneladas. O custe de transportar 1 tenelada de predute entre cada fabrica e cada centre de distri- buiqzio esté dado na tabela abaixe: Fébrica Centre Dist. A Centre Dist. B Centre Dist. C Centre Dist. D Nada pede ser transportade (1a fabrica II para 0 Centre C. Censiderande que 0 ebjetive é minimizar e custe total de transporte, come 0 predute deve ser enviade de cada fabrica para cada Centre de Distribuigée e qua] seré. o Gusto total? 3g Questéio ('3 pentes) E necessarie se determinar come 4 tarefas (I, II, III 0 IV) serie feitas. Existem ‘5 mziqui— mas (A, B, C, D e que pedem fazer as tarefas. Cada tarefa so pede SQI‘ feita per uma Ill-Aquina. e cada maiquina so pede fazer ulna tarefa. O custe de cada, Inaquina fazer cada tarefa esté dado 11a tabela abaixe: Tarefa I Méquina A Méquina B Méquina C Méquina D Méquina E ! A méqnina D 11510 pede fazer tarefns [I 9 IV. Qual seré e custe total minime para se fazer as tarefas e qual méquina ficaré sem tarefa para fazer ? Prof. Mauricio Pereira {f Qvam (MA¥)%: 3Z4—?’I4+ 9‘1”! ~5IJ— ~yl’é [4.4. iy¢+313—371y~i75 5M M3511 3X4 4—sz ~}Xy+YKr+V/Ié 2—: ~>ye. [Q if +rKl~ 3 13"”(14 '1lX{~3)(L+Y/(3 +615; v/Olé fi’z/P—agr M. 13,)V,!lr>/o 7(1, 75 ———~>I.o('ua,6 bad (MM/)y: 4634-271-wffg3 “fay—{fyr ijz+y3+4lgq-4ljy: W911 £34+KU;+FJ3+5—JV'Bjr >/—? ->>re 3U4”213'33L{+Y35 3’0 W9¥3 yQA~SU3 '>/-—é~ “>14, u h 2 1 IE 4 0 1/ 2 0 - 12!, l. ‘3 x t 1 5 a 1: 1!- i » E z: r W a v I w P _ m 0 9 S _ 1 m 1 fl m 9 I1 0 0 0 0 1 * P 0 0 0. 0 9 D1 0. 0 0 0_ * S 0 0 0 0 . 1 3, 3 3_ 1 * I 3 3 3_ 1 9 M _ * D m _ . 9 ‘ r: -T‘Ezgi I 11 * all! .......................... L1- ,,,,,,,,,,, i} 9 M , fl 1 _ = 4_ . m n # 4 , _ I D_ _ _ 0 l wa_ 0 0 M. M . 0 e 0_ m 0 18 .6 4 0 2 m. 2 0 i15l2. \ f_,lz§ier .1 4ft: 1! E1|!l|L v X 1 ET, x sfl t z 2 it? I x ‘ 5 ‘15. 2 _ 1 w u l. I _ # . 2 3 _ 1 _ , 3 _ _ 0 D“ 0 C D 0 I 0 0 mu m n 1 m. 0 m m 0 7 M 1 0 C W 1 ( m i: 1 iiiii: ‘ z} 1 £31 I Izléilsiiaiii 0 m _ m . 2 2 a m D 0 Q awD_ 0 0 0 n 0 3 w w I m m1 m M w r : 5 2 3 0 m I . P . , k a M m 2 m «m. m I a T ., o 1 o m o I m I I _ I o 0 1A 1 om , mm m R W ‘4 .8 M9 0 w 1M L M 1 1W M , W B 0 Tail I T m T .ZL, J r x , O z w I w _ , .m w W W I W I o I W 1 w 2 m 3“ F C1 * w . 1 2 I 3 I F «m. m F , F F w H , M W H 1 1 F w F 1 F w mT... I 1 . , m 1 a 1 mm 1 3 H fig/£11m” } 2' Questéo NAo BASICAS ***** q- a I ‘ -2 4 _1 -999995 : §BASICA i ***** A ULTIMA SOLUCAD E OTIMA ***** E ! IEM n- c : EBASICA :5 :2 VALORES DOS V‘is / W‘js - COEFICIENTES DAS VAR. : gAsICA fBASICA *‘k‘k‘k‘k‘k 1 PEG . 11:24 07/02/04 (09/02/2004) Prova 28 i 3‘ Questéo 999.999 M: . MINIMEZAR COM 1.ARTIFICIAL 10 MATRIZ ORIGINAL Ix ¢ I 71in?! SUBTRAINDO MENOR GUSTO DE CADA LINHA #####v : ¥ i i (F | i 1 ##4##}:1 0M1 , 7 2 _ ##### f): ,J\l:ill«l:xlii}ll;)[:14 SUBTRAINDO O MENOR,CUSTO DE CADA COLUNA 2 z RAG. :24 (09/02/2004) 07/02/04 11 Prova 2a E 3a Questao rm __ \t I 1 I | a 4 TRACANDO RETAS PARA COBRIR TODOS OS ZEROS S m ,K;i;:%-:xg‘-:s,l- m. 1511:: E H m w A# _# S i O _ HM m Cp_ 0 H 4 0 3 3 0 1 S #u S m w _ .A ,1. n 3 3 ~m 3 M 0 M 0 m . 9 ‘11?! v J 54 Si i4 31 ' V \ kl {11:51, 31:5,} 1 q! E S # _ B a.“ a m m m cm W “# 0 2 5 0 1_ ~m #”5_ o W m an m Ms M # _ O , # , T w m _ 1. 3 0 0. 0 O ,0 7 I 11! 5T; x if 2!: i: , l O _ \ liltwl m M _ _ .m 1 _ 1 at" U A _,. W w m M # L an O _ . S , 3 1 2 31 0. S 3 9 71 50 24 <<---~ #####§ -——«>> 2 ...
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p20203 linear programming - E, r _..__. , MM, 2E Prova de...

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