155:@0.916858:0.966074:0.945034:0.966074:0.945034:0.949450:0.916858:0.949450:0.000000:0.000000:0.000000 ii):@0.108233:0.096194:0.121815:0.096194:0.121815:0.079697:0.108233:0.079697:0.000000:0.000000:0.000000 :@0.121816:0.096194:0.125958:0.096194:0.125958:0.079697:0.121816:0.079697:0.000000 Vértices de la región factible:@0.131968:0.096411:0.340046:0.096411:0.340046:0.079697:0.131968:0.079697:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.108233:0.113545:0.112375:0.113545:0.112375:0.097047:0.108233:0.097047:0.000000 Los vértices , , están determinados así: = (0, 0), = , 0 ,:@0.131968:0.113545:0.595677:0.113545:0.595677:0.097047:0.131968:0.097047:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 O A E:@0.216791:0.113661:0.261026:0.113661:0.261026:0.097192:0.216791:0.097192:0.000000:0.000000:0.000000:0.000000:0.000000 O:@0.433043:0.113661:0.444949:0.113661:0.444949:0.097192:0.433043:0.097192:0.000000 A:@0.505949:0.113661:0.517219:0.113661:0.517219:0.097192:0.505949:0.097192:0.000000 :@0.108214:0.138025:0.112356:0.138025:0.112356:0.121527:0.108214:0.121527:0.000000 E:@0.131949:0.138140:0.139906:0.138140:0.139906:0.121672:0.131949:0.121672:0.000000 = (0, 20). Nos queda determinar el vértice . Se tiene = { }, :@0.139713:0.138025:0.599917:0.138025:0.599917:0.121527:0.139713:0.121527:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 B:@0.432424:0.138140:0.441613:0.138140:0.441613:0.121672:0.432424:0.121672:0.000000 L:@0.505983:0.138140:0.513823:0.138140:0.513823:0.121672:0.505983:0.121672:0.000000 1:@0.513680:0.141301:0.518633:0.141301:0.518633:0.131683:0.513680:0.131683:0.000000 :@0.522316:0.137808:0.538364:0.137808:0.538364:0.123161:0.522316:0.123161:0.000000 L:@0.541967:0.138140:0.549808:0.138140:0.549808:0.121672:0.541967:0.121672:0.000000 2:@0.549629:0.141301:0.554582:0.141301:0.554582:0.131683:0.549629:0.131683:0.000000 B:@0.578340:0.138140:0.587529:0.138140:0.587529:0.121672:0.578340:0.121672:0.000000 es decir que es solución del sistema de ecuaciones lineales :@0.131983:0.155375:0.535775:0.155375:0.535775:0.138878:0.131983:0.138878:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 –0,5 + ≤ 20,:@0.141481:0.179854:0.244820:0.179854:0.244820:0.163357:0.141481:0.163357:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x y:@0.171727:0.179970:0.205981:0.179970:0.205981:0.163501:0.171727:0.163501:0.000000:0.000000:0.000000 1,5 + ≤ 50,:@0.141481:0.197205:0.234320:0.197205:0.234320:0.180707:0.141481:0.180707:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x y:@0.161228:0.197321:0.195481:0.197321:0.195481:0.180852:0.161228:0.180852:0.000000:0.000000:0.000000 iii):@0.108248:0.231907:0.125645:0.231907:0.125645:0.215409:0.108248:0.215409:0.000000:0.000000:0.000000:0.000000 :@0.125644:0.231906:0.129786:0.231906:0.129786:0.215408:0.125644:0.215408:0.000000 Determinación del valor extremo:@0.131983:0.232123:0.376898:0.232123:0.376898:0.215408:0.131983:0.215408:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Calculemos = 200 + 70 en los vértices de .:@0.131983:0.249257:0.465229:0.249257:0.465229:0.232759:0.131983:0.232759:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 C:@0.219004:0.249372:0.229041:0.249372:0.229041:0.232904:0.219004:0.232904:0.000000 x:@0.273621:0.249372:0.281096:0.249372:0.281096:0.232904:0.273621:0.232904:0.000000 y:@0.317180:0.249372:0.324867:0.249372:0.324867:0.232904:0.317180:0.232904:0.000000 S:@0.454595:0.249372:0.462475:0.249372:0.462475:0.232904:0.454595:0.232904:0.000000 Tenemos = 200 + 70 = en = , = 0, es decir, :@0.131983:0.357888:0.578525:0.357888:0.578525:0.341390:0.131983:0.341390:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 C:@0.200798:0.358003:0.210836:0.358003:0.210836:0.341534:0.200798:0.341534:0.000000 �:@0.204085:0.361190:0.211227:0.361190:0.211227:0.343054:0.204085:0.343054:0.000000 x:@0.256331:0.358003:0.263806:0.358003:0.263806:0.341534:0.256331:0.341534:0.000000 �:@0.257061:0.363704:0.264203:0.363704:0.264203:0.345569:0.257061:0.345569:0.000000 y:@0.300811:0.358003:0.308498:0.358003:0.308498:0.341534:0.300811:0.341534:0.000000 �:@0.301753:0.363704:0.308895:0.363704:0.308895:0.345569:0.301753:0.345569:0.000000 x:@0.408190:0.358003:0.415665:0.358003:0.415665:0.341534:0.408190:0.341534:0.000000 �:@0.408922:0.363704:0.416063:0.363704:0.416063:0.345569:0.408922:0.345569:0.000000 y:@0.475713:0.358003:0.483400:0.358003:0.483400:0.341534:0.475713:0.341534:0.000000 �:@0.476655:0.363704:0.483797:0.363704:0.483797:0.345569:0.476655:0.345569:0.000000 :@0.108242:0.382367:0.112384:0.382367:0.112384:0.365870:0.108242:0.365870:0.000000 C:@0.131978:0.382483:0.142015:0.382483:0.142015:0.366014:0.131978:0.366014:0.000000 �:@0.135271:0.385668:0.142413:0.385668:0.142413:0.367533:0.135271:0.367533:0.000000 = máx C = , valor que alcanza en el vértice .:@0.142936:0.382366:0.518279:0.382366:0.518279:0.365868:0.142936:0.365868:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A:@0.504254:0.382482:0.515524:0.382482:0.515524:0.366013:0.504254:0.366013:0.000000 Como ≥ 0, ≥ 0, entonces, = 200 + 70 ≥ 0. Sea > 0.:@0.131975:0.417067:0.546098:0.417067:0.546098:0.400570:0.131975:0.400570:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.181120:0.417183:0.188595:0.417183:0.188595:0.400714:0.181120:0.400714:0.000000 y:@0.223080:0.417183:0.230767:0.417183:0.230767:0.400714:0.223080:0.400714:0.000000 C:@0.337109:0.417183:0.347146:0.417183:0.347146:0.400714:0.337109:0.400714:0.000000 x:@0.391726:0.417183:0.399201:0.417183:0.399201:0.400714:0.391726:0.400714:0.000000 y:@0.435285:0.417183:0.442972:0.417183:0.442972:0.400714:0.435285:0.400714:0.000000 C:@0.505719:0.417183:0.515756:0.417183:0.515756:0.400714:0.505719:0.400714:0.000000 Definimos = {( , ) | 200 + 70 = }.:@0.131975:0.451769:0.449449:0.451769:0.449449:0.435271:0.131975:0.435271:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 D:@0.209941:0.451885:0.221577:0.451885:0.221577:0.435416:0.209941:0.435416:0.000000 x y:@0.252479:0.451885:0.274537:0.451885:0.274537:0.435416:0.252479:0.435416:0.000000:0.000000:0.000000 :@0.284631:0.451250:0.299283:0.451250:0.299283:0.437877:0.284631:0.437877:0.000000 R:@0.303425:0.450682:0.316730:0.450682:0.316730:0.437820:0.303425:0.437820:0.000000 2:@0.316730:0.445417:0.321683:0.445417:0.321683:0.435799:0.316730:0.435799:0.000000 x:@0.360463:0.451885:0.367938:0.451885:0.367938:0.435416:0.360463:0.435416:0.000000 y C:@0.404022:0.451885:0.440838:0.451885:0.440838:0.435416:0.404022:0.435416:0.000000:0.000000:0.000000 :@0.108224:0.486470:0.112366:0.486470:0.112366:0.469973:0.108224:0.469973:0.000000 La pendiente de la recta es :@0.131958:0.486470:0.341078:0.486470:0.341078:0.469973:0.131958:0.469973:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 D:@0.306786:0.486586:0.318422:0.486586:0.318422:0.470117:0.306786:0.470117:0.000000 m:@0.341078:0.486586:0.355874:0.486586:0.355874:0.470117:0.341078:0.470117:0.000000 D:@0.355892:0.489816:0.362676:0.489816:0.362676:0.480215:0.355892:0.480215:0.000000 = – . Sea ( , ) .:@0.362677:0.486470:0.529717:0.486470:0.529717:0.469973:0.362677:0.469973:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x y:@0.458230:0.486586:0.485242:0.486586:0.485242:0.470117:0.458230:0.470117:0.000000:0.000000:0.000000 0:@0.465704:0.489748:0.470657:0.489748:0.470657:0.480130:0.465704:0.480130:0.000000 0:@0.485241:0.489748:0.490194:0.489748:0.490194:0.480130:0.485241:0.480130:0.000000 :@0.500289:0.485952:0.514942:0.485952:0.514942:0.472579:0.500289:0.472579:0.000000 S:@0.519083:0.486586:0.526963:0.486586:0.526963:0.470117:0.519083:0.470117:0.000000 :@0.108232:0.521172:0.112374:0.521172:0.112374:0.504674:0.108232:0.504674:0.000000 La ecuación cartesiana de la recta que pasa por ( , ) y tiene::@0.131968:0.521172:0.580892:0.521172:0.580892:0.504674:0.131968:0.504674:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 L:@0.373685:0.521288:0.381526:0.521288:0.381526:0.504819:0.373685:0.504819:0.000000 x y:@0.488543:0.521288:0.515563:0.521288:0.515563:0.504819:0.488543:0.504819:0.000000:0.000000:0.000000 0:@0.496026:0.524450:0.500979:0.524450:0.500979:0.514832:0.496026:0.514832:0.000000 0:@0.515563:0.524450:0.520516:0.524450:0.520516:0.514832:0.515563:0.514832:0.000000 pendiente:@0.131973:0.547429:0.204485:0.547429:0.204485:0.530932:0.131973:0.530932:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 m:@0.208629:0.547545:0.223425:0.547545:0.223425:0.531076:0.208629:0.531076:0.000000 D:@0.223428:0.550777:0.230211:0.550777:0.230211:0.541176:0.223428:0.541176:0.000000 = – está definida como – = – ( – ):@0.230212:0.547433:0.577735:0.547433:0.577735:0.530936:0.230212:0.530936:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y y:@0.429450:0.547549:0.463607:0.547549:0.463607:0.531080:0.429450:0.531080:0.000000:0.000000:0.000000 0:@0.463605:0.550710:0.468558:0.550710:0.468558:0.541092:0.463605:0.541092:0.000000 x x:@0.533097:0.547549:0.566831:0.547549:0.566831:0.531080:0.533097:0.531080:0.000000:0.000000:0.000000 0:@0.566828:0.550710:0.571781:0.550710:0.571781:0.541092:0.566828:0.541092:0.000000 :@0.108240:0.571912:0.112382:0.571912:0.112382:0.555414:0.108240:0.555414:0.000000 y de esta obtenemos 20 + 7 = 20 + 7 , y multiplicando por :@0.131975:0.571912:0.589291:0.571912:0.589291:0.555414:0.131975:0.555414:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.300890:0.572027:0.308365:0.572027:0.308365:0.555559:0.300890:0.555559:0.000000 y:@0.335953:0.572027:0.343640:0.572027:0.343640:0.555559:0.335953:0.555559:0.000000 x:@0.379724:0.572027:0.387199:0.572027:0.387199:0.555559:0.379724:0.555559:0.000000 0:@0.387197:0.575190:0.392150:0.575190:0.392150:0.565571:0.387197:0.565571:0.000000 y:@0.419739:0.572027:0.427426:0.572027:0.427426:0.555559:0.419739:0.555559:0.000000 0:@0.427425:0.575190:0.432378:0.575190:0.432378:0.565571:0.427425:0.565571:0.000000 10 para obtener la función objetivo, resulta:@0.131974:0.589262:0.436053:0.589262:0.436053:0.572765:0.131974:0.572765:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 200 + 70 = 200 + 70 .:@0.259394:0.619438:0.444609:0.619438:0.444609:0.602940:0.259394:0.602941:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.284882:0.619554:0.292357:0.619554:0.292357:0.603085:0.284882:0.603085:0.000000 y:@0.328441:0.619554:0.336128:0.619554:0.336128:0.603085:0.328441:0.603085:0.000000 x:@0.380707:0.619554:0.388182:0.619554:0.388182:0.603085:0.380707:0.603085:0.000000 0:@0.388177:0.622716:0.393131:0.622716:0.393131:0.613097:0.388177:0.613097:0.000000 y:@0.429215:0.619553:0.436902:0.619553:0.436902:0.603085:0.429215:0.603085:0.000000 0:@0.436900:0.622716:0.441853:0.622716:0.441853:0.613097:0.436900:0.613097:0.000000 Ponemos = 200 + 70 ≥ 0. Así, para ( , ) se tiene::@0.131971:0.654139:0.548230:0.654139:0.548230:0.637641:0.131971:0.637641:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 C:@0.202598:0.654255:0.212635:0.654255:0.212635:0.637786:0.202598:0.637786:0.000000 0:@0.212639:0.657417:0.217592:0.657417:0.217592:0.647799:0.212639:0.647799:0.000000 x:@0.262173:0.654255:0.269647:0.654255:0.269647:0.637786:0.262173:0.637786:0.000000 0:@0.269646:0.657417:0.274599:0.657417:0.274599:0.647799:0.269646:0.647799:0.000000 y:@0.310683:0.654255:0.318370:0.654255:0.318370:0.637786:0.310683:0.637786:0.000000 0:@0.318368:0.657417:0.323322:0.657417:0.323322:0.647799:0.318368:0.647799:0.000000 x y:@0.428241:0.654255:0.450299:0.654255:0.450299:0.637786:0.428241:0.637786:0.000000:0.000000:0.000000 :@0.460390:0.653620:0.475043:0.653620:0.475043:0.640247:0.460390:0.640247:0.000000 S:@0.479186:0.654255:0.487065:0.654255:0.487065:0.637786:0.479186:0.637786:0.000000 200 + 70 = .:@0.295222:0.684315:0.408785:0.684314:0.408785:0.667817:0.295222:0.667817:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.320710:0.684431:0.328184:0.684431:0.328184:0.667962:0.320710:0.667962:0.000000 y C:@0.364268:0.684431:0.401084:0.684431:0.401084:0.667962:0.364268:0.667962:0.000000:0.000000:0.000000 0:@0.401077:0.687592:0.406030:0.687592:0.406030:0.677974:0.401077:0.677974:0.000000 :@0.108228:0.701665:0.112370:0.701665:0.112370:0.685167:0.108228:0.685167:0.000000 :@0.108227:0.719016:0.112369:0.719016:0.112369:0.702518:0.108227:0.702518:0.000000 Para cada punto ( , ) obtenemos una recta de ecuación :@0.131963:0.719016:0.599954:0.719016:0.599954:0.702518:0.131963:0.702518:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x y:@0.264410:0.719132:0.293376:0.719132:0.293376:0.702663:0.264410:0.702663:0.000000:0.000000:0.000000 0:@0.271875:0.722294:0.276829:0.722294:0.276829:0.712676:0.271875:0.712676:0.000000 0:@0.293369:0.722294:0.298322:0.722294:0.298322:0.712676:0.293369:0.712676:0.000000 :@0.310374:0.718497:0.325027:0.718497:0.325027:0.705124:0.310374:0.705124:0.000000 S:@0.331133:0.719132:0.339012:0.719132:0.339012:0.702663:0.331133:0.702663:0.000000 cartesiana:@0.131988:0.736367:0.202923:0.736367:0.202923:0.719869:0.131988:0.719869:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 200 + 70 = 200 + 70 = ≥ 0.:@0.228565:0.766542:0.475443:0.766542:0.475443:0.750044:0.228565:0.750045:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.254053:0.766658:0.261528:0.766658:0.261528:0.750189:0.254053:0.750189:0.000000 y:@0.297611:0.766658:0.305298:0.766658:0.305298:0.750189:0.297611:0.750189:0.000000 x:@0.349878:0.766658:0.357353:0.766658:0.357353:0.750189:0.349878:0.750189:0.000000 0:@0.357343:0.769820:0.362296:0.769820:0.362296:0.760202:0.357343:0.760202:0.000000 y:@0.398380:0.766658:0.406067:0.766658:0.406067:0.750189:0.398380:0.750189:0.000000 0:@0.406066:0.769820:0.411019:0.769820:0.411019:0.760202:0.406066:0.760202:0.000000 C:@0.430111:0.766658:0.440148:0.766658:0.440148:0.750189:0.430111:0.750189:0.000000 0:@0.440148:0.769820:0.445101:0.769820:0.445101:0.760202:0.440148:0.760202:0.000000 :@0.108229:0.801243:0.112371:0.801243:0.112371:0.784746:0.108229:0.784746:0.000000 Particularmente para ( , ) que yacen en la recta, se tiene:@0.131963:0.801243:0.565102:0.801243:0.565102:0.784746:0.131963:0.784746:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x y:@0.290805:0.801359:0.312864:0.801359:0.312864:0.784890:0.290805:0.784890:0.000000:0.000000:0.000000 :@0.322970:0.800725:0.337623:0.800725:0.337623:0.787351:0.322970:0.787351:0.000000 S:@0.341764:0.801359:0.349643:0.801359:0.349643:0.784890:0.341764:0.784890:0.000000 200 + 70 = ≥ 0.:@0.281425:0.831419:0.422579:0.831419:0.422579:0.814921:0.281425:0.814922:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.306913:0.831535:0.314388:0.831535:0.314388:0.815066:0.306913:0.815066:0.000000 y C:@0.350472:0.831535:0.387288:0.831535:0.387288:0.815066:0.350472:0.815066:0.000000:0.000000:0.000000 0:@0.387283:0.834696:0.392236:0.834696:0.392236:0.825078:0.387283:0.825078:0.000000 :@0.108228:0.866120:0.112370:0.866120:0.112370:0.849622:0.108228:0.849622:0.000000 En la Figura 5.10., se han trazado rectas paralelas que pasan por :@0.131963:0.866120:0.599852:0.866120:0.599852:0.849622:0.131963:0.849622:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 cada uno de los vértices. Nota que el valor máximo se obtiene en :@0.131963:0.883471:0.599910:0.883471:0.599910:0.866973:0.131963:0.866973:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 el vértice , el más alejado de todos.:@0.131963:0.900822:0.387838:0.900822:0.387838:0.884324:0.131963:0.884324:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A:@0.199543:0.900937:0.210814:0.900937:0.210814:0.884468:0.199543:0.884468:0.000000 p:@0.787313:0.792819:0.798794:0.792819:0.798794:0.782794:0.787313:0.782794:0.000000 :@0.798794:0.793527:0.801675:0.793527:0.801675:0.782050:0.798794:0.782050:0.000000 Figura 5.10.:@0.801675:0.793527:0.856154:0.793527:0.856154:0.782050:0.801675:0.782050:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 100:@0.541251:0.105952:0.567124:0.105952:0.567124:0.089454:0.541251:0.089454:0.000000:0.000000:0.000000 3:@0.549939:0.122291:0.558435:0.122291:0.558435:0.105793:0.549939:0.105793:0.000000 cuya solución es = 27,5 y = 15. Así, = (15; 27,5).:@0.256269:0.189758:0.598150:0.189758:0.598150:0.173260:0.256269:0.173260:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.369662:0.189873:0.377349:0.189873:0.377349:0.173404:0.369662:0.173404:0.000000 x:@0.435320:0.189873:0.442795:0.189873:0.442795:0.173404:0.435320:0.173404:0.000000 B:@0.508836:0.189873:0.518026:0.189873:0.518026:0.173404:0.508836:0.173404:0.000000 Punto = (0, 0),:@0.138567:0.274476:0.245408:0.274476:0.245408:0.259413:0.138567:0.259413:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 O:@0.181908:0.274581:0.192779:0.274581:0.192779:0.259545:0.181908:0.259545:0.000000 C:@0.305953:0.274581:0.315118:0.274581:0.315118:0.259545:0.305953:0.259545:0.000000 = 200 × 0 + 70 × 0 = 0.:@0.315118:0.274476:0.466849:0.274476:0.466849:0.259413:0.315118:0.259413:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Punto = ((100)/3), 0),:@0.138567:0.291902:0.290175:0.291902:0.290175:0.276839:0.138567:0.276839:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A:@0.181908:0.292008:0.192199:0.292008:0.192199:0.276971:0.181908:0.276971:0.000000 C:@0.305953:0.292008:0.315118:0.292008:0.315118:0.276971:0.305953:0.276971:0.000000 = 200 × ((100)/3) + 70×0 = 20 000/3.:@0.315118:0.291902:0.558405:0.291902:0.558405:0.276839:0.315118:0.276839:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Punto = (15; 27,5),:@0.138567:0.309328:0.268715:0.309328:0.268715:0.294265:0.138567:0.294265:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 B:@0.181908:0.309434:0.190299:0.309434:0.190299:0.294397:0.181908:0.294397:0.000000 C:@0.305953:0.309434:0.315118:0.309434:0.315118:0.294397:0.305953:0.294397:0.000000 = 200 × 15 + 70 × 27,5 = 4 925.:@0.315118:0.309328:0.519690:0.309328:0.519690:0.294265:0.315118:0.294265:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Punto = (0, 20),:@0.138567:0.326754:0.249560:0.326754:0.249560:0.311691:0.138567:0.311691:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 E:@0.181908:0.326860:0.189173:0.326860:0.189173:0.311823:0.181908:0.311823:0.000000 C:@0.305953:0.326860:0.315118:0.326860:0.315118:0.311823:0.305953:0.311823:0.000000 = 200 × 0 + 70 × 20 = 1 400.:@0.315118:0.326754:0.501660:0.326754:0.501660:0.311691:0.315118:0.311691:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 20 000:@0.329569:0.350309:0.376962:0.350309:0.376962:0.333811:0.329569:0.333811:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 3:@0.349008:0.366647:0.357504:0.366647:0.357504:0.350150:0.349008:0.350150:0.000000 20 000:@0.230795:0.374732:0.278188:0.374732:0.278188:0.358234:0.230795:0.358234:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 3:@0.250234:0.391070:0.258730:0.391070:0.258730:0.374573:0.250234:0.374573:0.000000 100:@0.434617:0.350309:0.460490:0.350309:0.460490:0.333811:0.434617:0.333811:0.000000:0.000000:0.000000 3:@0.443305:0.366647:0.451801:0.366647:0.451801:0.350150:0.443305:0.350150:0.000000 20:@0.396433:0.478939:0.413618:0.478939:0.413618:0.462442:0.396433:0.462442:0.000000:0.000000 7:@0.400768:0.495278:0.409264:0.495278:0.409264:0.478780:0.400768:0.478780:0.000000 20:@0.502528:0.539586:0.519712:0.539586:0.519712:0.523089:0.502528:0.523089:0.000000:0.000000 7:@0.506862:0.555925:0.515358:0.555925:0.515358:0.539427:0.506862:0.539427:0.000000 20:@0.263957:0.539942:0.281141:0.539942:0.281141:0.523445:0.263957:0.523445:0.000000:0.000000 7:@0.268291:0.556281:0.276787:0.556281:0.276787:0.539783:0.268291:0.539783:0.000000 ( , ):@0.158792:0.390890:0.180943:0.390890:0.180943:0.380131:0.158792:0.380131:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x y:@0.162674:0.390966:0.177060:0.390966:0.177060:0.380225:0.162674:0.380225:0.000000:0.000000:0.000000 :@0.180942:0.390598:0.190710:0.390598:0.190710:0.381683:0.180942:0.381683:0.000000 S:@0.190710:0.390966:0.195849:0.390966:0.195849:0.380225:0.190710:0.380225:0.000000 Simbología matemática:@0.684804:0.200129:0.851007:0.200129:0.851007:0.184657:0.684804:0.184657:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 •:@0.638503:0.241701:0.643991:0.241701:0.643991:0.226440:0.638503:0.226440:0.000000 :@0.643991:0.240451:0.646513:0.240451:0.646513:0.230427:0.643991:0.230427:0.000000 máx U::@0.655123:0.241609:0.700928:0.241609:0.700928:0.226572:0.655123:0.226572:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 valor máximo de:@0.700928:0.241503:0.814595:0.241503:0.814595:0.226440:0.700928:0.226440:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 la función objetivo:@0.638502:0.264474:0.776757:0.264474:0.776757:0.249411:0.638502:0.249411:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 •:@0.638501:0.287643:0.643989:0.287643:0.643989:0.272382:0.638501:0.272382:0.000000 :@0.643991:0.286392:0.646513:0.286392:0.646513:0.276367:0.643991:0.276367:0.000000 mín U: :@0.655123:0.287549:0.701543:0.287549:0.701543:0.272512:0.655123:0.272512:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 valor mínimo de:@0.701543:0.287444:0.809193:0.287444:0.809193:0.272380:0.701543:0.272380:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 la función objetivo:@0.638502:0.310414:0.776757:0.310414:0.776757:0.295351:0.638502:0.295351:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 •:@0.638501:0.333583:0.643989:0.333583:0.643989:0.318322:0.638501:0.318322:0.000000 :@0.643991:0.332331:0.646513:0.332331:0.646513:0.322307:0.643991:0.322307:0.000000 L:@0.655123:0.333488:0.662283:0.333488:0.662283:0.318452:0.655123:0.318452:0.000000 1:@0.662283:0.336376:0.666806:0.336376:0.666806:0.327594:0.662283:0.327594:0.000000 : recta:@0.666805:0.333383:0.705855:0.333383:0.705855:0.318320:0.666805:0.318320:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 •:@0.638503:0.356552:0.643991:0.356552:0.643991:0.341291:0.638503:0.341291:0.000000 :@0.643991:0.355301:0.646513:0.355301:0.646513:0.345276:0.643991:0.345276:0.000000 m::@0.655123:0.356458:0.671429:0.356458:0.671429:0.341421:0.655123:0.341421:0.000000:0.000000 pendiente de la recta:@0.671429:0.356352:0.812464:0.356352:0.812464:0.341289:0.671429:0.341289:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 •:@0.638501:0.379521:0.643989:0.379521:0.643989:0.364260:0.638501:0.364260:0.000000 :@0.643991:0.378272:0.646513:0.378272:0.646513:0.368247:0.643991:0.368247:0.000000 :@0.655123:0.378974:0.669078:0.378974:0.669078:0.366238:0.655123:0.366238:0.000000 : pertenece al conjunto:@0.669078:0.379323:0.818363:0.379323:0.818363:0.364260:0.669078:0.364260:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ( , ):@0.653649:0.248166:0.673873:0.248166:0.673873:0.238343:0.653649:0.238343:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x y:@0.657194:0.248235:0.670328:0.248235:0.670328:0.238429:0.657194:0.238429:0.000000:0.000000:0.000000 :@0.673873:0.247899:0.682791:0.247899:0.682791:0.239760:0.673873:0.239760:0.000000 S:@0.682792:0.248235:0.687483:0.248235:0.687483:0.238429:0.682792:0.238429:0.000000 ( , ):@0.653655:0.293942:0.673879:0.293942:0.673879:0.284119:0.653655:0.284119:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x y:@0.657199:0.294011:0.670334:0.294011:0.670334:0.284205:0.657199:0.284205:0.000000:0.000000:0.000000 :@0.673873:0.293678:0.682791:0.293678:0.682791:0.285538:0.673873:0.285538:0.000000 S:@0.682792:0.294013:0.687483:0.294013:0.687483:0.284207:0.682792:0.284207:0.000000 B:@0.729933:0.680817:0.737125:0.680817:0.737125:0.667929:0.729933:0.667929:0.000000 S:@0.715142:0.719845:0.721309:0.719845:0.721309:0.706956:0.715142:0.706956:0.000000 E:@0.678414:0.710860:0.684641:0.710860:0.684641:0.697972:0.678414:0.697972:0.000000 0:@0.681405:0.745444:0.685837:0.745444:0.685837:0.736836:0.681405:0.736836:0.000000 x:@0.840666:0.751399:0.847271:0.751399:0.847271:0.737770:0.840666:0.737770:0.000000 10:@0.709036:0.748001:0.717901:0.748001:0.717901:0.739394:0.709036:0.739394:0.000000:0.000000 15:@0.723038:0.745074:0.731903:0.745074:0.731903:0.736467:0.723038:0.736467:0.000000:0.000000 20:@0.735160:0.748001:0.744025:0.748001:0.744025:0.739394:0.735160:0.739394:0.000000:0.000000 30:@0.761273:0.748001:0.770139:0.748001:0.770139:0.739394:0.761273:0.739394:0.000000:0.000000 40:@0.787387:0.748001:0.796252:0.748001:0.796252:0.739394:0.787387:0.739394:0.000000:0.000000 50:@0.813501:0.748001:0.822366:0.748001:0.822366:0.739394:0.813501:0.739394:0.000000:0.000000 –10:@0.654055:0.748001:0.668398:0.748001:0.668398:0.739394:0.654055:0.739394:0.000000:0.000000:0.000000 10:@0.673635:0.719908:0.682500:0.719908:0.682500:0.711300:0.673635:0.711300:0.000000:0.000000 20:@0.673635:0.700309:0.682500:0.700309:0.682500:0.691702:0.673635:0.691702:0.000000:0.000000 30:@0.673635:0.680160:0.682500:0.680160:0.682500:0.671552:0.673635:0.671552:0.000000:0.000000 27,5:@0.667765:0.686436:0.682500:0.686436:0.682500:0.677829:0.667765:0.677829:0.000000:0.000000:0.000000:0.000000 40:@0.673635:0.661104:0.682500:0.661104:0.682500:0.652496:0.673635:0.652496:0.000000:0.000000 y:@0.674628:0.640393:0.681090:0.640393:0.681090:0.626765:0.674628:0.626765:0.000000 A:@0.774344:0.736236:0.783164:0.736236:0.783164:0.723348:0.774344:0.723348:0.000000 Competencia :@0.684804:0.426517:0.782426:0.426517:0.782426:0.411045:0.684804:0.411045:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 socioemocional:@0.684804:0.439085:0.795179:0.439085:0.795179:0.423613:0.684804:0.423613:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 La gratitud es uno de los :@0.685042:0.463560:0.847763:0.463560:0.847763:0.448497:0.685042:0.448497:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 sentimientos más nobles, nos :@0.638498:0.479402:0.832831:0.479402:0.832831:0.464339:0.638498:0.464339:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ayuda a valorar lo que somos y :@0.638498:0.495244:0.842275:0.495244:0.842275:0.480181:0.638498:0.480181:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 lo que tenemos. Piensa en tres :@0.638498:0.511086:0.841589:0.511086:0.841589:0.496023:0.638498:0.496023:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 cosas de las que puedas dar :@0.638498:0.526928:0.821695:0.526928:0.821695:0.511865:0.638498:0.511865:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 gracias, repite este ejercicio cada :@0.638498:0.542770:0.850423:0.542770:0.850423:0.527707:0.638498:0.527707:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 día de la semana y verás que :@0.638498:0.558612:0.825709:0.558612:0.825709:0.543549:0.638498:0.543549:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 eres una persona privilegiada. :@0.638498:0.574454:0.832039:0.574454:0.832039:0.559391:0.638498:0.559391:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Debate:@0.638498:0.590494:0.687311:0.590494:0.687311:0.575233:0.638498:0.575233:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 con tus compañeros :@0.687311:0.590296:0.827714:0.590296:0.827714:0.575233:0.687311:0.575233:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 acerca de la gratitud.:@0.638498:0.606138:0.771811:0.606138:0.771811:0.591075:0.638498:0.591075:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ©:@0.079553:0.731952:0.079553:0.720342:0.061505:0.720342:0.061505:0.731952:0.000000:0.000000 maya:@0.080774:0.720340:0.080774:0.684191:0.055786:0.684191:0.055786:0.720340:0.000000:0.000000:0.000000:0.000000 ®EDUCACIÓN – Libro resuelto solo para fines didácticos – Prohibida su reproducción :@0.079553:0.684191:0.079553:0.268044:0.061505:0.268044:0.061505:0.684191:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000