86:@0.058783:0.510692:0.077690:0.510692:0.077690:0.494068:0.058783:0.494068:0.000000:0.000000 Tema:@0.047190:0.135475:0.083321:0.135475:0.083321:0.113749:0.047190:0.113749:0.000000:0.000000:0.000000:0.000000 Determina:@0.540847:0.828428:0.622537:0.828428:0.622537:0.811804:0.540847:0.811804:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 gráficamente el conjunto de las :@0.630645:0.828428:0.883619:0.828428:0.883619:0.812039:0.630645:0.812039:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 soluciones factibles.:@0.540847:0.845024:0.686864:0.845024:0.686864:0.828636:0.540847:0.828636:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1. :@0.115519:0.828428:0.134260:0.828428:0.134260:0.811292:0.115519:0.811292:0.000000:0.000000:0.000000 Considera:@0.148762:0.828428:0.225642:0.828428:0.225642:0.811804:0.148762:0.811804:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 las desigualdades::@0.225642:0.828428:0.362062:0.828428:0.362062:0.812039:0.225642:0.812039:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ≥:@0.172318:0.877612:0.182434:0.877612:0.182434:0.862040:0.172318:0.862040:0.000000 ≥:@0.172318:0.898635:0.182434:0.898635:0.182434:0.883062:0.172318:0.883062:0.000000 ⎧:@0.148767:0.854945:0.157870:0.854945:0.157870:0.839372:0.148767:0.839372:0.000000 ⎨:@0.148767:0.879784:0.157870:0.879784:0.157870:0.864211:0.148767:0.864211:0.000000 ⎪:@0.148767:0.868429:0.157870:0.868429:0.157870:0.852856:0.148767:0.852856:0.000000 ⎩:@0.148760:0.904607:0.157864:0.904607:0.157864:0.889034:0.148760:0.889034:0.000000 ⎪:@0.148760:0.893253:0.157864:0.893253:0.157864:0.877680:0.148760:0.877680:0.000000 ( ):@0.357484:0.858481:0.382084:0.858481:0.382084:0.840308:0.357484:0.840308:0.000000:0.000000:0.000000:0.000000:0.000000 ( ):@0.196294:0.877724:0.380773:0.877724:0.380773:0.859551:0.196294:0.859551:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ( ):@0.196294:0.898746:0.379980:0.898746:0.379980:0.880573:0.196294:0.880573:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 b:@0.364759:0.876936:0.374028:0.876936:0.374028:0.860575:0.364759:0.860575:0.000000 x:@0.159383:0.876936:0.166846:0.876936:0.166846:0.860575:0.159383:0.860575:0.000000 c:@0.365128:0.897958:0.372794:0.897958:0.372794:0.881597:0.365128:0.881597:0.000000 y:@0.159383:0.897958:0.166865:0.897958:0.166865:0.881597:0.159383:0.881597:0.000000 2:@0.321285:0.849301:0.326625:0.849301:0.326625:0.838769:0.321285:0.838769:0.000000 :@0.306994:0.857376:0.320298:0.857376:0.320298:0.840628:0.306994:0.840628:0.000000 0:@0.186403:0.876932:0.195396:0.876932:0.195396:0.860543:0.186403:0.860543:0.000000 0:@0.186403:0.897954:0.195396:0.897954:0.195396:0.881565:0.186403:0.881565:0.000000 3x y 2, :@0.156937:0.856643:0.234554:0.856643:0.234554:0.840254:0.156937:0.840254:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 + ≤:@0.177871:0.857321:0.214284:0.857321:0.214284:0.841748:0.177871:0.841748:0.000000:0.000000:0.000000 (x, y :@0.253222:0.856048:0.308707:0.856048:0.308707:0.839660:0.253222:0.839660:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ) ∈:@0.281361:0.856726:0.304672:0.856726:0.304672:0.841153:0.281361:0.841153:0.000000:0.000000:0.000000 ,:@0.326177:0.856643:0.329512:0.856643:0.329512:0.840282:0.326177:0.840282:0.000000 :@0.329512:0.856643:0.333548:0.856643:0.333548:0.840254:0.329512:0.840254:0.000000 a:@0.366054:0.857888:0.375323:0.857888:0.375323:0.841527:0.366054:0.841527:0.000000 :@0.375323:0.857888:0.379359:0.857888:0.379359:0.841499:0.375323:0.841499:0.000000 Taller:@0.175844:0.787180:0.236739:0.787180:0.236739:0.753233:0.175844:0.753233:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 I.M.5.8.1. Utiliza métodos gráficos y analíticos para la resolución de sistemas de ecuaciones lineales y de inecuaciones, para determinar :@0.256865:0.769926:0.877554:0.769926:0.877554:0.759497:0.256865:0.759497:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 el conjunto de soluciones factibles y la solución óptima de un problema de programación lineal. (I.3.):@0.256865:0.780487:0.726477:0.780487:0.726477:0.770058:0.256865:0.770058:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Actividad resuelta:@0.115354:0.384369:0.272476:0.384369:0.272476:0.365932:0.115354:0.365932:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Consideramos:@0.115354:0.429724:0.225017:0.429724:0.225017:0.413100:0.115354:0.413100:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 las desigualdades :@0.225017:0.429724:0.362266:0.429724:0.362266:0.413335:0.225017:0.413335:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 +:@0.388124:0.409298:0.398240:0.409298:0.398240:0.391277:0.388124:0.391277:0.000000 ≤ ⎧:@0.424297:0.409298:0.374727:0.407652:0.374727:0.389631:0.424297:0.391277:0.000000:0.000000:0.000000 ∈:@0.510944:0.409298:0.434414:0.409298:0.434414:0.391277:0.510944:0.391277:0.000000 ≥:@0.389174:0.430320:0.399291:0.430320:0.399291:0.412299:0.389174:0.412299:0.000000 ≥:@0.389174:0.451342:0.399291:0.451342:0.399291:0.433321:0.389174:0.433321:0.000000 ⎨:@0.365624:0.432491:0.374727:0.432491:0.374727:0.414471:0.365624:0.414471:0.000000 ⎪:@0.365624:0.421137:0.374727:0.421137:0.374727:0.403116:0.365624:0.403116:0.000000 ⎩:@0.365614:0.457313:0.374717:0.457313:0.374717:0.439292:0.365614:0.439292:0.000000 ⎪:@0.365614:0.445958:0.374717:0.445958:0.374717:0.427937:0.365614:0.427937:0.000000 (:@0.453716:0.409488:0.474407:0.409488:0.474407:0.391315:0.453716:0.391315:0.000000:0.000000:0.000000:0.000000 ):@0.501094:0.409488:0.507230:0.409488:0.507230:0.391315:0.501094:0.391315:0.000000 ( ):@0.552660:0.409488:0.594710:0.409488:0.594710:0.391315:0.552660:0.391315:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ( ):@0.413138:0.430510:0.597636:0.430510:0.597636:0.412337:0.413138:0.412337:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ( ):@0.413138:0.451532:0.596851:0.451532:0.596851:0.433359:0.413138:0.433359:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.539314:0.401498:0.544654:0.401498:0.544654:0.390966:0.539314:0.390966:0.000000 x:@0.376240:0.408703:0.383703:0.408703:0.383703:0.392342:0.376240:0.392342:0.000000 y:@0.411366:0.408703:0.418848:0.408703:0.418848:0.392342:0.411366:0.392342:0.000000 xy:@0.476230:0.408703:0.499412:0.408703:0.499412:0.392342:0.476230:0.392342:0.000000:0.000000 a:@0.578676:0.408703:0.587945:0.408703:0.587945:0.392342:0.578676:0.392342:0.000000 x:@0.376240:0.429724:0.383703:0.429724:0.383703:0.413363:0.376240:0.413363:0.000000 b:@0.581616:0.429724:0.590885:0.429724:0.590885:0.413363:0.581616:0.413363:0.000000 y:@0.376240:0.450746:0.383721:0.450746:0.383721:0.434385:0.376240:0.434385:0.000000 c:@0.581984:0.450746:0.589650:0.450746:0.589650:0.434385:0.581984:0.434385:0.000000 :@0.525023:0.409575:0.538327:0.409575:0.538327:0.392826:0.525023:0.392826:0.000000 3:@0.401521:0.408703:0.410513:0.408703:0.410513:0.392314:0.401521:0.392314:0.000000 4,:@0.439109:0.408703:0.451106:0.408703:0.451106:0.392314:0.439109:0.392314:0.000000:0.000000 ,:@0.485383:0.408703:0.488589:0.408703:0.488589:0.392314:0.485383:0.392314:0.000000 ,:@0.546843:0.408703:0.550049:0.408703:0.550049:0.392314:0.546843:0.392314:0.000000 0:@0.403253:0.429725:0.412245:0.429725:0.412245:0.413336:0.403253:0.413336:0.000000 0:@0.403253:0.450747:0.412245:0.450747:0.412245:0.434359:0.403253:0.434359:0.000000 Determinamos:@0.115354:0.477172:0.229826:0.477172:0.229826:0.460548:0.115354:0.460548:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 gráficamente el conjunto de las soluciones factibles.:@0.229826:0.477172:0.615513:0.477172:0.615513:0.460783:0.229826:0.460783:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Comenzamos :@0.115354:0.500891:0.220557:0.500891:0.220557:0.484267:0.115354:0.484267:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 con la ecuación + 3 = 4 y la :@0.219986:0.500891:0.429471:0.500891:0.429471:0.484502:0.219986:0.484502:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.332763:0.500891:0.340226:0.500891:0.340226:0.484530:0.332763:0.484530:0.000000 y:@0.366007:0.500891:0.373488:0.500891:0.373488:0.484530:0.366007:0.484530:0.000000 colocamos :@0.428882:0.500891:0.512119:0.500891:0.512119:0.484267:0.428882:0.484267:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 de tal forma que esté en función de :@0.511585:0.500891:0.773368:0.500891:0.773368:0.484502:0.511585:0.484502:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.629596:0.500891:0.637077:0.500891:0.637077:0.484530:0.629596:0.484530:0.000000 x, y:@0.772778:0.500891:0.793095:0.500891:0.793095:0.484530:0.772778:0.484530:0.000000:0.000000:0.000000:0.000000 = 4 3 – 3. :@0.792726:0.500891:0.883934:0.500891:0.883934:0.484502:0.792726:0.484502:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.818857:0.501472:0.828070:0.501472:0.828070:0.483866:0.818857:0.483866:0.000000 x:@0.852109:0.500891:0.859573:0.500891:0.859573:0.484530:0.852109:0.484530:0.000000 :@0.859222:0.501472:0.868436:0.501472:0.868436:0.483866:0.859222:0.483866:0.000000 Esta ecuación tiene una recta de pendiente – y corta los ejes en los puntos = (4, 0) y = (0, 4 3).:@0.115354:0.523047:0.848123:0.523040:0.848123:0.506651:0.115354:0.506658:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1 :@0.450565:0.514036:0.465786:0.514036:0.465786:0.497647:0.450565:0.497647:0.000000:0.000000:0.000000 3:@0.450565:0.534989:0.461751:0.534989:0.461751:0.518600:0.450565:0.518600:0.000000:0.000000 A:@0.683693:0.523040:0.693589:0.523040:0.693589:0.506678:0.683693:0.506678:0.000000 B:@0.763816:0.523040:0.772662:0.523040:0.772662:0.506678:0.763816:0.506678:0.000000 :@0.821827:0.523621:0.831040:0.523621:0.831040:0.506015:0.821827:0.506015:0.000000 Las variables que intervienen en los problemas de programación lineal son no negativas. Escribimos :@0.115200:0.213006:0.883928:0.213006:0.883928:0.196617:0.115200:0.196617:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.879892:0.213006:0.883928:0.213006:0.883928:0.196617:0.879892:0.196617:0.000000 x:@0.115200:0.229602:0.122664:0.229602:0.122664:0.213241:0.115200:0.213241:0.000000 ≥ 0, ≥ 0, para cada una de estas variables y las asociamos a un subconjunto de 2. :@0.122664:0.229602:0.739437:0.229602:0.739437:0.213213:0.122664:0.213213:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.157952:0.229602:0.165434:0.229602:0.165434:0.213241:0.157952:0.213241:0.000000 R:@0.713817:0.228745:0.727121:0.228745:0.727121:0.215882:0.713817:0.215882:0.000000 1 = x, y 2 | ≥ 0:@0.115200:0.253321:0.309962:0.253321:0.309962:0.236932:0.115200:0.236932:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 S:@0.147486:0.253321:0.155557:0.253321:0.155557:0.236960:0.147486:0.236960:0.000000 {(:@0.178481:0.253999:0.193463:0.253999:0.193463:0.238426:0.178481:0.238426:0.000000:0.000000 ) ∈:@0.216718:0.253999:0.240029:0.253999:0.240029:0.238426:0.216718:0.238426:0.000000:0.000000:0.000000 R:@0.244065:0.252464:0.257370:0.252464:0.257370:0.239601:0.244065:0.239601:0.000000 y:@0.274434:0.253321:0.281915:0.253321:0.281915:0.236960:0.274434:0.236960:0.000000 }:@0.309962:0.253999:0.318807:0.253999:0.318807:0.238426:0.309962:0.238426:0.000000 Así, 2 = x, y 2 | ≥ 0:@0.115200:0.273486:0.310976:0.273486:0.310976:0.257097:0.115200:0.257097:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 S:@0.143800:0.273486:0.155188:0.273486:0.155188:0.257124:0.143800:0.257124:0.000000:0.000000 {(:@0.179513:0.274163:0.194494:0.274163:0.194494:0.258590:0.179513:0.258590:0.000000:0.000000 ) ∈:@0.217750:0.274163:0.241061:0.274163:0.241061:0.258590:0.217750:0.258590:0.000000:0.000000:0.000000 R:@0.245097:0.272628:0.258402:0.272628:0.258402:0.259766:0.245097:0.259766:0.000000 x:@0.275466:0.273486:0.282929:0.273486:0.282929:0.257124:0.275466:0.257124:0.000000 }:@0.310976:0.274163:0.319821:0.274163:0.319821:0.258590:0.310976:0.258590:0.000000 3 = 1 2 = x, y 2 | ≥ 0, ≥ 0:@0.115200:0.293650:0.420546:0.293650:0.420546:0.277261:0.115200:0.277261:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 S:@0.147486:0.293650:0.155557:0.293650:0.155557:0.277289:0.147486:0.277289:0.000000 S:@0.179752:0.293650:0.187824:0.293650:0.187824:0.277289:0.179752:0.277289:0.000000 ∩:@0.195729:0.294328:0.209882:0.294328:0.209882:0.278755:0.195729:0.278755:0.000000 S:@0.213917:0.293650:0.221989:0.293650:0.221989:0.277289:0.213917:0.277289:0.000000 {(:@0.246313:0.294328:0.261295:0.294328:0.261295:0.278755:0.246313:0.278755:0.000000:0.000000 ) ∈:@0.284550:0.294328:0.307861:0.294328:0.307861:0.278755:0.284550:0.278755:0.000000:0.000000:0.000000 R:@0.311897:0.292793:0.325202:0.292793:0.325202:0.279931:0.311897:0.279931:0.000000 x:@0.342266:0.293650:0.349729:0.293650:0.349729:0.277289:0.342266:0.277289:0.000000 y:@0.385018:0.293650:0.392499:0.293650:0.392499:0.277289:0.385018:0.277289:0.000000 }:@0.420546:0.294328:0.429392:0.294328:0.429392:0.278755:0.420546:0.278755:0.000000 S:@0.115200:0.317369:0.123272:0.317369:0.123272:0.301008:0.115200:0.301008:0.000000 1 representa un semiplano que se extiende del eje hacia arriba, según la dirección del eje :@0.123272:0.317369:0.883928:0.317369:0.883928:0.300980:0.123272:0.300980:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.537156:0.317369:0.544620:0.317369:0.544620:0.301008:0.537156:0.301008:0.000000 y.:@0.862329:0.317369:0.879927:0.317369:0.879927:0.301008:0.862329:0.301008:0.000000:0.000000:0.000000 :@0.879892:0.317369:0.883928:0.317369:0.883928:0.300980:0.879892:0.300980:0.000000 S:@0.115200:0.333966:0.123272:0.333966:0.123272:0.317604:0.115200:0.317604:0.000000 2 representa un semiplano que se extiende del eje hacia la derecha, según la dirección positiva del eje :@0.123087:0.333966:0.869075:0.333966:0.869075:0.317577:0.123087:0.317577:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.487035:0.333966:0.494517:0.333966:0.494517:0.317604:0.487035:0.317604:0.000000 x. :@0.869241:0.333966:0.883170:0.333966:0.883170:0.317604:0.869241:0.317604:0.000000:0.000000:0.000000 S:@0.115200:0.350562:0.123272:0.350562:0.123272:0.334201:0.115200:0.334201:0.000000 3 representa la intersección de los dos semiplanos.:@0.123272:0.350562:0.489661:0.350562:0.489661:0.334173:0.123272:0.334173:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Problema de la programación lineal. Conjunto :@0.115891:0.141978:0.795720:0.141978:0.795720:0.101242:0.115891:0.101242:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 de soluciones factibles:@0.115891:0.182224:0.455277:0.182224:0.455277:0.141488:0.115891:0.141488:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 M.5.2.25. Reconocer un subconjunto convexo en 2 y determinar el conjunto de soluciones factibles, de forma gráfica y analítica, para resolver problemas de :@0.125388:0.069719:0.877686:0.069719:0.877686:0.059289:0.125388:0.059289:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 R:@0.360659:0.069173:0.369125:0.069173:0.369125:0.060988:0.360659:0.060988:0.000000 programación lineal simple (minimización en un conjunto de soluciones factibles de un funcional lineal definido en 2).:@0.125388:0.080280:0.683097:0.080280:0.683097:0.069851:0.125388:0.069851:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 R:@0.666252:0.079734:0.674719:0.079734:0.674719:0.071549:0.666252:0.071549:0.000000 5:@0.054209:0.122645:0.076302:0.122645:0.076302:0.065614:0.054209:0.065614:0.000000 0:@0.170649:0.681245:0.176976:0.681245:0.176976:0.670119:0.170649:0.670119:0.000000 3:@0.164729:0.577981:0.171056:0.577981:0.171056:0.566855:0.164729:0.566855:0.000000 2:@0.164729:0.610027:0.171056:0.610027:0.171056:0.598901:0.164729:0.598901:0.000000 1:@0.164729:0.641285:0.171056:0.641285:0.171056:0.630159:0.164729:0.630159:0.000000 –1:@0.157021:0.705608:0.169514:0.705608:0.169514:0.694482:0.157021:0.694482:0.000000:0.000000 –1:@0.128950:0.684605:0.141444:0.684605:0.141444:0.673479:0.128950:0.673479:0.000000:0.000000 –2:@0.157021:0.737274:0.169515:0.737274:0.169515:0.726148:0.157021:0.726148:0.000000:0.000000 –2:@0.087486:0.684606:0.099980:0.684606:0.099980:0.673479:0.087486:0.673479:0.000000:0.000000 –3:@0.044961:0.684606:0.057455:0.684606:0.057455:0.673479:0.044961:0.673479:0.000000:0.000000 –3:@0.157021:0.769070:0.169515:0.769070:0.169515:0.757944:0.157021:0.757944:0.000000:0.000000 –4:@0.002464:0.684601:0.014958:0.684601:0.014958:0.673475:0.002464:0.673475:0.000000:0.000000 5:@0.389186:0.684601:0.395513:0.684601:0.395513:0.673475:0.389186:0.673475:0.000000 4:@0.347425:0.684601:0.353752:0.684601:0.353752:0.673475:0.347425:0.673475:0.000000 3:@0.304530:0.684601:0.310857:0.684601:0.310857:0.673475:0.304530:0.673475:0.000000 2:@0.261561:0.684601:0.267888:0.684601:0.267888:0.673475:0.261561:0.673475:0.000000 1:@0.218617:0.684601:0.224943:0.684601:0.224943:0.673475:0.218617:0.673475:0.000000 B:@0.183902:0.620808:0.190587:0.620808:0.190587:0.609682:0.183902:0.609682:0.000000 y:@0.183902:0.555597:0.188909:0.555597:0.188909:0.544647:0.183902:0.544647:0.000000 x:@0.422403:0.665674:0.427398:0.665674:0.427398:0.654724:0.422403:0.654724:0.000000 A:@0.167141:0.668793:0.174689:0.668793:0.174689:0.657667:0.167141:0.657667:0.000000 C:@0.347515:0.665674:0.354669:0.665674:0.354669:0.654548:0.347515:0.654548:0.000000 Las soluciones factibles :@0.459635:0.554364:0.641995:0.554364:0.641995:0.537975:0.459635:0.537975:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 encontramos:@0.645883:0.554364:0.747456:0.554364:0.747456:0.537740:0.645883:0.537740:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 gráficamente de :@0.747456:0.554364:0.883911:0.554364:0.883911:0.537975:0.747456:0.537975:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 acuerdo a las restricciones dadas: :@0.459635:0.570960:0.706489:0.570960:0.706489:0.554572:0.459635:0.554572:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 • :@0.459635:0.591125:0.469586:0.591125:0.469586:0.573989:0.459635:0.573989:0.000000:0.000000 Las condiciones ≥ 0, ≥ 0 indican que las soluciones :@0.492878:0.591125:0.883986:0.591125:0.883986:0.574736:0.492878:0.574736:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.612308:0.591125:0.619771:0.591125:0.619771:0.574764:0.612308:0.574764:0.000000 y:@0.652848:0.591125:0.660330:0.591125:0.660330:0.574764:0.652848:0.574764:0.000000 factibles son positivas.:@0.492878:0.607721:0.655369:0.607721:0.655369:0.591333:0.492878:0.591333:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 • :@0.459635:0.627886:0.469586:0.627886:0.469586:0.610750:0.459635:0.610750:0.000000:0.000000 Al despejar de la inecuación :@0.492878:0.627886:0.713254:0.627886:0.713254:0.611497:0.492878:0.611497:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y :@0.578327:0.627886:0.589126:0.627886:0.589126:0.611525:0.578327:0.611525:0.000000:0.000000 obtenemos:@0.713254:0.627886:0.801318:0.627886:0.801318:0.611262:0.713254:0.611262:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.801318:0.627886:0.809389:0.627886:0.809389:0.611497:0.801318:0.611497:0.000000:0.000000 y:@0.492878:0.644482:0.500360:0.644482:0.500360:0.628121:0.492878:0.628121:0.000000 ≤ 4 3 – 3, lo que indica que las soluciones :@0.500360:0.644482:0.833421:0.644482:0.833421:0.628094:0.500360:0.628094:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.528407:0.645063:0.537620:0.645063:0.537620:0.627457:0.528407:0.627457:0.000000 x:@0.563898:0.644482:0.571361:0.644482:0.571361:0.628121:0.563898:0.628121:0.000000 :@0.571361:0.645063:0.580575:0.645063:0.580575:0.627457:0.571361:0.627457:0.000000 factibles están por debajo de la recta formada por la :@0.492878:0.661079:0.878029:0.661079:0.878029:0.644690:0.492878:0.644690:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ecuación = 4 3 – 3.:@0.492878:0.677675:0.663868:0.677675:0.663868:0.661286:0.492878:0.661286:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.563972:0.677675:0.571454:0.677675:0.571454:0.661314:0.563972:0.661314:0.000000 :@0.599500:0.678256:0.608714:0.678256:0.608714:0.660650:0.599500:0.660650:0.000000 x:@0.634992:0.677675:0.642455:0.677675:0.642455:0.661314:0.634992:0.661314:0.000000 :@0.642455:0.678256:0.651669:0.678256:0.651669:0.660650:0.642455:0.660650:0.000000 Al juntar todas las restricciones tenemos el conjunto de :@0.459635:0.701394:0.883872:0.701394:0.883872:0.685005:0.459635:0.685005:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 las soluciones factibles delimitado por los puntos A, B y C.:@0.459635:0.717991:0.879949:0.717991:0.879949:0.701602:0.459635:0.701602:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 S:@0.555375:0.875332:0.563446:0.875332:0.563446:0.858970:0.555375:0.858970:0.000000 1 = :@0.563446:0.875332:0.586370:0.875332:0.586370:0.858943:0.563446:0.858943:0.000000:0.000000:0.000000:0.000000 {(:@0.586370:0.876009:0.601352:0.876009:0.601352:0.860436:0.586370:0.860436:0.000000:0.000000 x, y:@0.601352:0.875332:0.622949:0.875332:0.622949:0.858970:0.601352:0.858970:0.000000:0.000000:0.000000:0.000000 ) ∈:@0.622949:0.876009:0.646260:0.876009:0.646260:0.860436:0.622949:0.860436:0.000000:0.000000:0.000000 2 | ≤ 2 – 3:@0.629085:0.875332:0.742470:0.875332:0.742470:0.858943:0.629085:0.858943:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 R:@0.650295:0.874474:0.663600:0.874474:0.663600:0.861612:0.650295:0.861612:0.000000 y:@0.680664:0.875332:0.688146:0.875332:0.688146:0.858970:0.680664:0.858970:0.000000 x:@0.742470:0.875332:0.749934:0.875332:0.749934:0.858970:0.742470:0.858970:0.000000 }:@0.749934:0.876009:0.758779:0.876009:0.758779:0.860436:0.749934:0.860436:0.000000 La solución es la región delimitada por :@0.555375:0.896921:0.841554:0.896921:0.841554:0.880532:0.555375:0.880532:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 los puntos ABC.:@0.555375:0.913517:0.669919:0.913517:0.669919:0.897128:0.555375:0.897128:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000