156:@0.054582:0.966558:0.078778:0.966558:0.078778:0.950778:0.054582:0.950778:0.000000:0.000000:0.000000
M.5.2.27. Resolver y plantear aplicaciones (un modelo simple de línea de producción, un modelo en la industria química, un problema de transporte simplificado), :@0.148948:0.943402:0.888430:0.943402:0.888430:0.933360:0.148948:0.933360:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
interpretando y juzgando la validez de las soluciones obtenidas dentro del contexto del problema.:@0.148948:0.952203:0.572051:0.952203:0.572051:0.942161:0.148948:0.942161:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Modelización de problemas :@0.404235:0.117192:0.746084:0.117192:0.746084:0.072532:0.404235:0.072532:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de programación lineal:@0.404235:0.154911:0.692309:0.154911:0.692309:0.110251:0.404235:0.110251:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Saberes previos:@0.199646:0.115710:0.307805:0.115710:0.307805:0.100238:0.199646:0.100238:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿Qué es un modelo :@0.199884:0.144338:0.330630:0.144338:0.330630:0.129274:0.199884:0.129274:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
matemático?:@0.153341:0.160180:0.236946:0.160180:0.236946:0.145116:0.153341:0.145116:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Desequilibrio cognitivo:@0.199646:0.207331:0.363493:0.207331:0.363493:0.191858:0.199646:0.191858:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
En la práctica, ¿para qué :@0.199884:0.235958:0.359334:0.235958:0.359334:0.220895:0.199884:0.220895:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
te sirve maximizar o minimizar :@0.153341:0.251800:0.356451:0.251800:0.356451:0.236737:0.153341:0.236737:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
recursos?:@0.153341:0.267642:0.212337:0.267642:0.212337:0.252579:0.153341:0.252579:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Modelo simple de línea de producción:@0.404236:0.185805:0.711340:0.185805:0.711340:0.168123:0.404236:0.168123:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Una planta industrial de plástico produce dos tipos de accesorios :@0.404236:0.202512:0.895978:0.202512:0.895978:0.186014:0.404236:0.186014:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
para refrigeradoras: tipo 1 y tipo 2. Para su producción, el tipo 1 re-:@0.404236:0.219862:0.891778:0.219862:0.891778:0.203365:0.404236:0.203365:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
quiere 3 horas/máquina por cada 100 unidades. Mientras que para su :@0.404236:0.237213:0.895995:0.237213:0.895995:0.220715:0.404236:0.220715:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
producción, el tipo 2 requiere 1 hora/máquina por cada 100 unida-:@0.404236:0.254564:0.891772:0.254564:0.891772:0.238066:0.404236:0.238066:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
des. La planta dispone al mes de 120 horas/máquina.:@0.404236:0.271915:0.778365:0.271915:0.778365:0.255417:0.404236:0.255417:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
El próximo mes se deben producir 3 500 refrigeradoras que utilizan el :@0.404236:0.303594:0.895901:0.303594:0.895901:0.287097:0.404236:0.287097:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
accesorio tipo 1 y 4 500 refrigeradoras que utilizan el accesorio tipo 2. :@0.404236:0.320945:0.895920:0.320945:0.895920:0.304447:0.404236:0.304447:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
La utilidad neta en la producción de una unidad del tipo 1 es $ 3,5 y del :@0.404236:0.338296:0.895805:0.338296:0.895805:0.321798:0.404236:0.321798:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
tipo 2 es $ 2,5. Determina la cantidad de unidades del tipo 1 y del tipo :@0.404236:0.355646:0.895980:0.355646:0.895980:0.339149:0.404236:0.339149:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2 que deben producirse mensualmente para maximizar la utilidad.:@0.404236:0.372997:0.867951:0.372997:0.867951:0.356500:0.404236:0.356500:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a):@0.404236:0.407916:0.418781:0.407916:0.418781:0.391201:0.404236:0.391201:0.000000:0.000000
 :@0.418781:0.407699:0.422923:0.407699:0.422923:0.391201:0.418781:0.391201:0.000000
Restricciones:@0.427971:0.407916:0.524567:0.407916:0.524567:0.391201:0.427971:0.391201:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.404236:0.425049:0.408378:0.425049:0.408378:0.408552:0.404236:0.408552:0.000000
Designamos con   al número de unidades del tipo 1, y con   al :@0.427971:0.425049:0.895914:0.425049:0.895914:0.408552:0.427971:0.408552:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.552829:0.425165:0.561807:0.425165:0.561807:0.408696:0.552829:0.408696:0.000000
b:@0.865369:0.425165:0.874636:0.425165:0.874636:0.408696:0.865369:0.408696:0.000000
número de unidades del tipo 2, producidas mensualmente.:@0.427990:0.442400:0.847584:0.442400:0.847584:0.425903:0.427990:0.425903:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.404255:0.466879:0.408397:0.466879:0.408397:0.450382:0.404255:0.450382:0.000000
Producción de una unidad de  : 0,03 :@0.427990:0.466879:0.692211:0.466879:0.692211:0.450382:0.427990:0.450382:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.643952:0.466995:0.652929:0.466995:0.652929:0.450526:0.643952:0.450526:0.000000
h/máquina:@0.692211:0.466995:0.771411:0.466995:0.771411:0.450526:0.692211:0.450526:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
.:@0.771413:0.466879:0.774168:0.466879:0.774168:0.450382:0.771413:0.450382:0.000000
 :@0.404255:0.484230:0.408397:0.484230:0.408397:0.467732:0.404255:0.467732:0.000000
Producción de una unidad de  : 0,01 :@0.427990:0.484230:0.692498:0.484230:0.692498:0.467732:0.427990:0.467732:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
b:@0.643950:0.484346:0.653217:0.484346:0.653217:0.467877:0.643950:0.467877:0.000000
h/máquina:@0.692498:0.484346:0.771698:0.484346:0.771698:0.467877:0.692498:0.467877:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
.:@0.771702:0.484230:0.774457:0.484230:0.774457:0.467732:0.771702:0.467732:0.000000
   Balance de horas/máquina: 0,03  + 0,01  ≤ 120. :@0.404255:0.508709:0.769024:0.508709:0.769024:0.492211:0.404255:0.492211:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.651968:0.508825:0.660946:0.508825:0.660946:0.492356:0.651968:0.492356:0.000000
b:@0.708280:0.508825:0.717547:0.508825:0.717547:0.492356:0.708280:0.492356:0.000000
 :@0.404255:0.526060:0.408397:0.526060:0.408397:0.509562:0.404255:0.509562:0.000000
Restricción de la producción de  : 0 ≤   ≤ 3 500. :@0.427990:0.526060:0.773551:0.526060:0.773551:0.509562:0.427990:0.509562:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.656996:0.526175:0.665974:0.526175:0.665974:0.509707:0.656996:0.509707:0.000000
a:@0.700459:0.526175:0.709436:0.526175:0.709436:0.509707:0.700459:0.509707:0.000000
 :@0.404255:0.543411:0.408397:0.543411:0.408397:0.526913:0.404255:0.526913:0.000000
Restricción de la producción de  : 0 ≤   ≤ 4 500. :@0.427990:0.543411:0.774129:0.543411:0.774129:0.526913:0.427990:0.526913:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
b:@0.656996:0.543526:0.666263:0.543526:0.666263:0.527057:0.656996:0.527057:0.000000
b:@0.700748:0.543526:0.710014:0.543526:0.710014:0.527057:0.700748:0.527057:0.000000
b):@0.404255:0.575307:0.420265:0.575307:0.420265:0.558592:0.404255:0.558592:0.000000:0.000000
 :@0.420265:0.575090:0.424407:0.575090:0.424407:0.558592:0.420265:0.558592:0.000000
Función objetivo:@0.427990:0.575307:0.552635:0.575307:0.552635:0.558592:0.427990:0.558592:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.404255:0.592441:0.408397:0.592441:0.408397:0.575943:0.404255:0.575943:0.000000
Denotamos con   la utilidad neta que debemos maximizar con la :@0.427990:0.592441:0.895980:0.592441:0.895980:0.575943:0.427990:0.575943:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
U:@0.546778:0.592557:0.558722:0.592557:0.558722:0.576088:0.546778:0.576088:0.000000
producción de   y  . La utilidad neta de cada unidad de   es $ 3,5, :@0.427990:0.609792:0.895972:0.609792:0.895972:0.593294:0.427990:0.593294:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a b:@0.536492:0.609907:0.570303:0.609907:0.570303:0.593439:0.536492:0.593439:0.000000:0.000000:0.000000
a:@0.825866:0.609907:0.834844:0.609907:0.834844:0.593439:0.825866:0.593439:0.000000
y la utilidad de cada unidad de   es $ 2,5. Por lo tanto, la función :@0.427990:0.627142:0.895920:0.627142:0.895920:0.610645:0.427990:0.610645:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
b:@0.654087:0.627258:0.663354:0.627258:0.663354:0.610789:0.654087:0.610789:0.000000
objetivo está definida como U = 3,5  + 2,5 .:@0.427990:0.644493:0.742338:0.644493:0.742338:0.627995:0.427990:0.627995:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.682500:0.644609:0.691477:0.644609:0.691477:0.628140:0.682500:0.628140:0.000000
b:@0.730316:0.644609:0.739583:0.644609:0.739583:0.628140:0.730316:0.628140:0.000000
 :@0.404255:0.668972:0.408397:0.668972:0.408397:0.652474:0.404255:0.652474:0.000000
De a) y b) obtenemos el siguiente modelo matemático::@0.427990:0.668972:0.819169:0.668972:0.819169:0.652474:0.427990:0.652474:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.404255:0.686323:0.408397:0.686323:0.408397:0.669825:0.404255:0.669825:0.000000
máx:@0.427990:0.686439:0.459219:0.686439:0.459219:0.669970:0.427990:0.669970:0.000000:0.000000:0.000000
{3,5  + 2,5 },:@0.459219:0.686323:0.550517:0.686323:0.550517:0.669825:0.459219:0.669825:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.484823:0.686439:0.493800:0.686439:0.493800:0.669970:0.484823:0.669970:0.000000
b:@0.532639:0.686439:0.541906:0.686439:0.541906:0.669970:0.532639:0.669970:0.000000
 :@0.404255:0.710802:0.408397:0.710802:0.408397:0.694304:0.404255:0.694304:0.000000
 :@0.428000:0.710802:0.432142:0.710802:0.432142:0.694304:0.428000:0.694304:0.000000
0 ≤   ≤ 3 500, :@0.518229:0.710802:0.618909:0.710802:0.618909:0.694304:0.518229:0.694304:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.545817:0.710918:0.554794:0.710918:0.554794:0.694449:0.545817:0.694449:0.000000
( ):@0.689189:0.710802:0.710072:0.710802:0.710072:0.694304:0.689189:0.694304:0.000000:0.000000:0.000000
a:@0.695142:0.710918:0.704119:0.710918:0.704119:0.694449:0.695142:0.694449:0.000000
   sujeto a :@0.404275:0.728153:0.487173:0.728153:0.487173:0.711655:0.404275:0.711655:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
0 ≤   ≤ 4 500, :@0.518229:0.728153:0.619198:0.728153:0.619198:0.711655:0.518229:0.711655:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
b:@0.545817:0.728268:0.555083:0.728268:0.555083:0.711800:0.545817:0.711800:0.000000
( ):@0.689189:0.728153:0.710361:0.728153:0.710361:0.711655:0.689189:0.711655:0.000000:0.000000:0.000000
b:@0.695142:0.728268:0.704408:0.728268:0.704408:0.711800:0.695142:0.711800:0.000000
0,03  + 0,01  ≤ 120. :@0.518248:0.745503:0.663547:0.745503:0.663547:0.729006:0.518248:0.729006:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.546491:0.745619:0.555468:0.745619:0.555468:0.729150:0.546491:0.729150:0.000000
b:@0.602803:0.745619:0.612070:0.745619:0.612070:0.729150:0.602803:0.729150:0.000000
( ):@0.689208:0.745503:0.708300:0.745503:0.708300:0.729006:0.689208:0.729006:0.000000:0.000000:0.000000
c:@0.695161:0.745619:0.702347:0.745619:0.702347:0.729150:0.695161:0.729150:0.000000
 :@0.404294:0.769982:0.408436:0.769982:0.408436:0.753485:0.404294:0.753485:0.000000
La restricción ( ) es equivalente a 3  +   ≤ 12 000.:@0.428029:0.769982:0.780525:0.769982:0.780525:0.753485:0.428029:0.753485:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
c:@0.532235:0.770098:0.539420:0.770098:0.539420:0.753629:0.532235:0.753629:0.000000
a b:@0.674720:0.770098:0.712056:0.770098:0.712056:0.753629:0.674720:0.753629:0.000000:0.000000:0.000000
c):@0.404294:0.801879:0.418627:0.801879:0.418627:0.785164:0.404294:0.785164:0.000000:0.000000
 :@0.418627:0.801662:0.422769:0.801662:0.422769:0.785164:0.418627:0.785164:0.000000
Determinación de la región de soluciones factibles y vértices:@0.428029:0.801879:0.872012:0.801879:0.872012:0.785164:0.428029:0.785164:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.404294:0.819013:0.408436:0.819013:0.408436:0.802515:0.404294:0.802515:0.000000
Graficamos la región de soluciones :@0.428029:0.819013:0.688586:0.819013:0.688586:0.802515:0.428029:0.802515:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
factibles:@0.689106:0.819230:0.752467:0.819230:0.752467:0.802515:0.689106:0.802515:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 que se muestra en :@0.752706:0.819013:0.895964:0.819013:0.895964:0.802515:0.752706:0.802515:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
la Figura 5.11. La región   de soluciones factibles es la región :@0.428029:0.836364:0.895961:0.836364:0.895961:0.819866:0.428029:0.819866:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
S:@0.613825:0.836479:0.621704:0.836479:0.621704:0.820010:0.613825:0.820010:0.000000
poligonal de vértices  ,  ,  ,   y  . Los vértices  ,  ,   están de-:@0.428029:0.853714:0.891821:0.853714:0.891821:0.837217:0.428029:0.837217:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
O A B C D:@0.582594:0.853830:0.675163:0.853830:0.675163:0.837361:0.582594:0.837361:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
O A D:@0.770912:0.853830:0.820385:0.853830:0.820385:0.837361:0.770912:0.837361:0.000000:0.000000:0.000000:0.000000:0.000000
terminados. Nos queda, entonces, obtener los vértices   y  .   es :@0.428029:0.871065:0.895943:0.871065:0.895943:0.854567:0.428029:0.854567:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
B C C:@0.822080:0.871181:0.873442:0.871181:0.873442:0.854712:0.822080:0.854712:0.000000:0.000000:0.000000:0.000000:0.000000
C:@0.428010:0.888531:0.438047:0.888531:0.438047:0.872063:0.428010:0.872063:0.000000
 = (2 500, 4 500), y   es   = (3 500, 1 500). Tomando en conside-:@0.438278:0.888416:0.891743:0.888416:0.891743:0.871918:0.438278:0.871918:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
B:@0.571150:0.888531:0.580340:0.888531:0.580340:0.872063:0.571150:0.872063:0.000000
B:@0.602765:0.888531:0.611954:0.888531:0.611954:0.872063:0.602765:0.872063:0.000000
ración las restricciones y estos últimos resultados, obtenemos la :@0.428010:0.905767:0.895943:0.905767:0.895943:0.889269:0.428010:0.889269:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
región de soluciones factibles, que se muestra en la Figura 5.12.:@0.428010:0.923117:0.886752:0.923117:0.886752:0.906620:0.428010:0.906620:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p:@0.143847:0.856016:0.155327:0.856016:0.155327:0.845991:0.143847:0.845991:0.000000
 :@0.155327:0.856724:0.158209:0.856724:0.158209:0.845247:0.155327:0.845247:0.000000
Figura 5.11.:@0.158209:0.856724:0.212688:0.856724:0.212688:0.845247:0.158209:0.845247:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
L:@0.241714:0.741887:0.247851:0.741887:0.247851:0.728998:0.241714:0.728998:0.000000
1:@0.247851:0.744361:0.251727:0.744361:0.251727:0.736834:0.247851:0.736834:0.000000
L:@0.314938:0.765090:0.321074:0.765090:0.321074:0.752202:0.314938:0.752202:0.000000
2:@0.321074:0.767565:0.324950:0.767565:0.324950:0.760037:0.321074:0.760037:0.000000
0:@0.178993:0.828050:0.186012:0.828050:0.186012:0.814422:0.178993:0.814422:0.000000
x:@0.352130:0.829448:0.358735:0.829448:0.358735:0.815819:0.352130:0.815819:0.000000
1 500:@0.164029:0.806652:0.183920:0.806652:0.183920:0.798044:0.164029:0.798044:0.000000:0.000000:0.000000:0.000000:0.000000
12 000:@0.159596:0.699711:0.183920:0.699711:0.183920:0.691103:0.159596:0.691103:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
8 000:@0.164029:0.737430:0.183920:0.737430:0.183920:0.728822:0.164029:0.728822:0.000000:0.000000:0.000000:0.000000:0.000000
4 000:@0.164029:0.777661:0.183920:0.777661:0.183920:0.769053:0.164029:0.769053:0.000000:0.000000:0.000000:0.000000:0.000000
4 000:@0.248621:0.821950:0.268513:0.821950:0.268513:0.813343:0.248621:0.813343:0.000000:0.000000:0.000000:0.000000:0.000000
4 500:@0.164029:0.768669:0.183920:0.768669:0.183920:0.760061:0.164029:0.760061:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.176042:0.674440:0.182503:0.674440:0.182503:0.660811:0.176042:0.660811:0.000000
L:@0.203288:0.715481:0.209424:0.715481:0.209424:0.702592:0.203288:0.702592:0.000000
D:@0.193367:0.768303:0.202474:0.768303:0.202474:0.755414:0.193367:0.755414:0.000000
C:@0.224155:0.768303:0.232010:0.768303:0.232010:0.755414:0.224155:0.755414:0.000000
B:@0.243137:0.805826:0.250329:0.805826:0.250329:0.792937:0.243137:0.792937:0.000000
A:@0.224034:0.825685:0.232854:0.825685:0.232854:0.812796:0.224034:0.812796:0.000000
Competencia :@0.199646:0.428471:0.297269:0.428471:0.297269:0.412999:0.199646:0.412999:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
matemática:@0.199646:0.441039:0.283709:0.441039:0.283709:0.425567:0.199646:0.425567:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Para la solución de un :@0.199884:0.465514:0.346178:0.465514:0.346178:0.450451:0.199884:0.450451:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
problema de programación :@0.153341:0.481356:0.335360:0.481356:0.335360:0.466293:0.153341:0.466293:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
lineal, es necesaria la construc-:@0.153341:0.497198:0.348168:0.497198:0.348168:0.482135:0.153341:0.482135:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ción del modelo matemático :@0.153341:0.513040:0.345684:0.513040:0.345684:0.497977:0.153341:0.497977:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
que implica dos elementos :@0.153341:0.528882:0.331418:0.528882:0.331418:0.513819:0.153341:0.513819:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
básicos: las restricciones y la :@0.153341:0.544724:0.336572:0.544724:0.336572:0.529661:0.153341:0.529661:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
función objetivo.:@0.153341:0.560566:0.262890:0.560566:0.262890:0.545503:0.153341:0.545503:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Define:@0.153341:0.583735:0.198035:0.583735:0.198035:0.568474:0.153341:0.568474:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 con tus palabras estos :@0.198035:0.583537:0.347847:0.583537:0.347847:0.568474:0.198035:0.568474:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
elementos básicos.:@0.153341:0.599379:0.274022:0.599379:0.274022:0.584316:0.153341:0.584316:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000