157:@0.916858:0.966074:0.945034:0.966074:0.945034:0.949450:0.916858:0.949450:0.000000:0.000000:0.000000
Calculemos   = 3,5  + 2,5  en los vértices de  .:@0.108233:0.096194:0.443483:0.096194:0.443483:0.079697:0.108233:0.079697:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
U:@0.195252:0.096310:0.207197:0.096310:0.207197:0.079841:0.195252:0.079841:0.000000
a:@0.246035:0.096310:0.255013:0.096310:0.255013:0.079841:0.246035:0.079841:0.000000
b:@0.293852:0.096310:0.303118:0.096310:0.303118:0.079841:0.293852:0.079841:0.000000
S:@0.432849:0.096310:0.440728:0.096310:0.440728:0.079841:0.432849:0.079841:0.000000
Vemos que el valor extremo es alcanzado en el vértice   = (2 500, 4 500).:@0.108233:0.113545:0.595779:0.113545:0.595779:0.097047:0.108233:0.097047:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
C:@0.476450:0.113661:0.486487:0.113661:0.486487:0.097192:0.476450:0.097192:0.000000
Así,   = 3,5 × 2 500 + 2,5 × 4 500 = 20 000.:@0.108233:0.145225:0.409869:0.145225:0.409869:0.128727:0.108233:0.128727:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Ú:@0.137343:0.145340:0.149287:0.145340:0.149287:0.128871:0.137343:0.128871:0.000000
De este resultado se concluye que deben producirse 2 500 unidades :@0.108233:0.162575:0.599934:0.162575:0.599934:0.146078:0.108233:0.146078:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
del tipo 1 y 4 500 unidades del tipo 2 para obtener un beneficio máxi-:@0.108233:0.179926:0.595827:0.179926:0.595827:0.163428:0.108233:0.163428:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
mo de $ 20 000.:@0.108233:0.197277:0.220858:0.197277:0.220858:0.180779:0.108233:0.180779:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Modelo en la industria química:@0.108233:0.233380:0.358568:0.233380:0.358568:0.215698:0.108233:0.215698:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Una industria alimenticia modifica la producción de dos artículos   y :@0.108233:0.250088:0.599915:0.250088:0.599915:0.233590:0.108233:0.233590:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.572905:0.250204:0.584176:0.250204:0.584176:0.233735:0.572905:0.233735:0.000000
B:@0.108233:0.267554:0.117423:0.267554:0.117423:0.251086:0.108233:0.251086:0.000000
 que requieren de tres procesos dominantes: mezclado, evaporado, :@0.117423:0.267439:0.599973:0.267439:0.599973:0.250941:0.117423:0.250941:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
pasteurizado-envasado. En la tabla se muestran los tiempos que ne-:@0.108233:0.284789:0.595785:0.284789:0.595785:0.268292:0.108233:0.268292:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cesitan 500 unidades de cada producto y cada proceso.:@0.108233:0.302140:0.501200:0.302140:0.501200:0.285642:0.108233:0.285642:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
La utilidad neta de   es $ 8,5 y la de   es $ 12 por cada 500 unidades.:@0.108233:0.415296:0.595290:0.415296:0.595290:0.398798:0.108233:0.398798:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.244841:0.415412:0.256111:0.415412:0.256111:0.398943:0.244841:0.398943:0.000000
B:@0.365054:0.415412:0.374244:0.415412:0.374244:0.398943:0.365054:0.398943:0.000000
¿Cuál es la estrategia que se debe seguir para que la utilidad sea máxima?:@0.108233:0.432647:0.595698:0.432647:0.595698:0.416149:0.108233:0.416149:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Solución:@0.108233:0.467811:0.175162:0.467811:0.175162:0.450865:0.108233:0.450865:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Designamos con   ≥ 0 al número de 500 unidades de  , y con   ≥ 0 al :@0.108233:0.484699:0.599823:0.484699:0.599823:0.468201:0.108233:0.468201:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.229643:0.484815:0.237118:0.484815:0.237118:0.468346:0.229643:0.468346:0.000000
A:@0.485406:0.484815:0.496677:0.484815:0.496677:0.468346:0.485406:0.468346:0.000000
y:@0.545649:0.484815:0.553336:0.484815:0.553336:0.468346:0.545649:0.468346:0.000000
número de 500 unidades de  .:@0.108233:0.502050:0.323946:0.502050:0.323946:0.485552:0.108233:0.485552:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
B:@0.312002:0.502165:0.321191:0.502165:0.321191:0.485697:0.312002:0.485697:0.000000
a):@0.108233:0.533946:0.122778:0.533946:0.122778:0.517232:0.108233:0.517232:0.000000:0.000000
 :@0.122779:0.533730:0.126921:0.533730:0.126921:0.517232:0.122779:0.517232:0.000000
Restricciones:@0.131968:0.533947:0.228564:0.533947:0.228564:0.517232:0.131968:0.517232:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.108233:0.551081:0.112375:0.551081:0.112375:0.534583:0.108233:0.534583:0.000000
Restricción del tiempo de mezclado: 4  + 3  ≤ 80.:@0.131968:0.551081:0.483902:0.551081:0.483902:0.534583:0.131968:0.534583:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.402313:0.551196:0.409788:0.551196:0.409788:0.534728:0.402313:0.534728:0.000000
y:@0.437376:0.551196:0.445063:0.551196:0.445063:0.534728:0.437376:0.534728:0.000000
 :@0.108233:0.568431:0.112375:0.568431:0.112375:0.551934:0.108233:0.551934:0.000000
Restricción del tiempo de evaporación: 5  + 6  ≤ 120. :@0.131968:0.568431:0.515867:0.568431:0.515867:0.551934:0.131968:0.551934:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.421640:0.568547:0.429115:0.568547:0.429115:0.552078:0.421640:0.552078:0.000000
y:@0.456703:0.568547:0.464390:0.568547:0.464390:0.552078:0.456703:0.552078:0.000000
 :@0.108233:0.585782:0.112375:0.585782:0.112375:0.569285:0.108233:0.569285:0.000000
Restricción del tiempo de pasteurizado-envasado: 8  + 12,5  ≤ 240.:@0.131968:0.585782:0.594796:0.585782:0.594796:0.569285:0.131968:0.569285:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.487847:0.585898:0.495322:0.585898:0.495322:0.569429:0.487847:0.569429:0.000000
y:@0.541123:0.585898:0.548810:0.585898:0.548810:0.569429:0.541123:0.569429:0.000000
b):@0.108233:0.617679:0.124242:0.617679:0.124242:0.600964:0.108233:0.600964:0.000000:0.000000
 :@0.124243:0.617461:0.128385:0.617461:0.128385:0.600963:0.124243:0.600963:0.000000
Función objetivo:@0.131968:0.617678:0.256612:0.617678:0.256612:0.600963:0.131968:0.600963:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.108233:0.634812:0.112375:0.634812:0.112375:0.618314:0.108233:0.618314:0.000000
La utilidad neta de   es 8,5  y la de   es 12 . La función objetivo   :@0.131968:0.634812:0.599821:0.634812:0.599821:0.618314:0.131968:0.618314:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.267266:0.634928:0.278536:0.634928:0.278536:0.618459:0.267266:0.618459:0.000000
x:@0.320284:0.634928:0.327759:0.634928:0.327759:0.618459:0.320284:0.618459:0.000000
B:@0.380353:0.634928:0.389542:0.634928:0.389542:0.618459:0.380353:0.618459:0.000000
y:@0.428535:0.634928:0.436222:0.634928:0.436222:0.618459:0.428535:0.618459:0.000000
U:@0.583734:0.634928:0.595679:0.634928:0.595679:0.618459:0.583734:0.618459:0.000000
está definida como:   = 8,5  + 12 ,:@0.131968:0.652163:0.380162:0.652163:0.380162:0.635665:0.131968:0.635665:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
U:@0.275378:0.652278:0.287323:0.652278:0.287323:0.635810:0.275378:0.635810:0.000000
x:@0.326162:0.652278:0.333637:0.652278:0.333637:0.635810:0.326162:0.635810:0.000000
y:@0.369720:0.652278:0.377407:0.652278:0.377407:0.635810:0.369720:0.635810:0.000000
máx  = 8,5  + 12:@0.131968:0.669513:0.257192:0.669513:0.257192:0.653016:0.131968:0.653016:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
U:@0.162850:0.669629:0.174795:0.669629:0.174795:0.653160:0.162850:0.653160:0.000000
x:@0.213633:0.669629:0.221108:0.669629:0.221108:0.653160:0.213633:0.653160:0.000000
y.:@0.257192:0.669629:0.267576:0.669629:0.267576:0.653160:0.257192:0.653160:0.000000:0.000000
 :@0.108233:0.686864:0.112375:0.686864:0.112375:0.670366:0.108233:0.670366:0.000000
De a) y b) se obtiene:@0.131968:0.686864:0.279441:0.686864:0.279441:0.670366:0.131968:0.670366:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.108233:0.704215:0.112375:0.704215:0.112375:0.687717:0.108233:0.687717:0.000000
el modelo matemático   sujeto a:@0.131968:0.704215:0.353202:0.704299:0.353202:0.687801:0.131968:0.687717:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
c):@0.108233:0.749443:0.122566:0.749443:0.122566:0.732728:0.108233:0.732728:0.000000:0.000000
 :@0.122566:0.749226:0.126708:0.749226:0.126708:0.732729:0.122566:0.732729:0.000000
Conjunto de soluciones factibles:@0.131968:0.749443:0.372414:0.749443:0.372414:0.732729:0.131968:0.732729:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.108233:0.766577:0.112375:0.766577:0.112375:0.750079:0.108233:0.750079:0.000000
El conjunto de restricciones se encuentra representado en la Figu-:@0.131968:0.766577:0.595812:0.766577:0.595812:0.750079:0.131968:0.750079:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ra 5.13.:@0.131968:0.783928:0.180767:0.783928:0.180767:0.767430:0.131968:0.767430:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
d):@0.108233:0.815824:0.124435:0.815824:0.124435:0.799110:0.108233:0.799110:0.000000:0.000000
 :@0.124436:0.815607:0.128578:0.815607:0.128578:0.799109:0.124436:0.799109:0.000000
Cálculo del valor óptimo:@0.131968:0.815824:0.314658:0.815824:0.314658:0.799109:0.131968:0.799109:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.108233:0.832958:0.112375:0.832958:0.112375:0.816460:0.108233:0.816460:0.000000
La función objetivo está definida como   = 8,5  + 12  cuyo valor :@0.131968:0.832958:0.599921:0.832958:0.599921:0.816460:0.131968:0.816460:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
U:@0.415186:0.833073:0.427131:0.833073:0.427131:0.816604:0.415186:0.816604:0.000000
x:@0.466182:0.833073:0.473656:0.833073:0.473656:0.816604:0.466182:0.816604:0.000000
y:@0.509962:0.833073:0.517649:0.833073:0.517649:0.816604:0.509962:0.816604:0.000000
máximo es alcanzado en  .:@0.131968:0.850308:0.324040:0.850308:0.324040:0.833811:0.131968:0.833811:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
C:@0.311248:0.850424:0.321286:0.850424:0.321286:0.833955:0.311248:0.833955:0.000000
 :@0.108233:0.867659:0.112375:0.867659:0.112375:0.851161:0.108233:0.851161:0.000000
C:@0.131968:0.867775:0.142005:0.867775:0.142005:0.851306:0.131968:0.851306:0.000000
 = (4,138; 16,55),     = 8,5 × 4,138 + 12 × 16,55 ≈ 233,773. :@0.142005:0.867659:0.546807:0.867659:0.546807:0.851161:0.142005:0.851161:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
U:@0.268559:0.867775:0.280503:0.867775:0.280503:0.851306:0.268559:0.851306:0.000000
De estos resultados se concluye que el jefe de planta debe producir, apro-:@0.108233:0.899339:0.595719:0.899339:0.595719:0.882841:0.108233:0.882841:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ximadamente, 4 números de cada 500 unidades de  , y 16 números de :@0.108233:0.916689:0.599921:0.916689:0.599921:0.900192:0.108233:0.900192:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.462288:0.916805:0.473558:0.916805:0.473558:0.900336:0.462288:0.900336:0.000000
cada 500 unidades de   para una utilidad máxima aproximada de $ 234,00.:@0.108233:0.934040:0.595723:0.934040:0.595723:0.917542:0.108233:0.917542:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
B:@0.253722:0.934156:0.262912:0.934156:0.262912:0.917687:0.253722:0.917687:0.000000
Proceso:@0.178628:0.332250:0.228619:0.332250:0.228619:0.316923:0.178628:0.316923:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A h:@0.319348:0.332012:0.343658:0.332012:0.343658:0.316976:0.319348:0.316976:0.000000:0.000000:0.000000
( ):@0.329639:0.331907:0.349093:0.331907:0.349093:0.316844:0.329639:0.316844:0.000000:0.000000:0.000000
B h:@0.391538:0.332012:0.413948:0.332012:0.413948:0.316976:0.391538:0.316976:0.000000:0.000000:0.000000
( ):@0.399928:0.331907:0.419383:0.331907:0.419383:0.316844:0.399928:0.316844:0.000000:0.000000:0.000000
Disponibilidad ( ):@0.459347:0.331907:0.577146:0.331907:0.577146:0.316844:0.459347:0.316844:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
h:@0.563127:0.332012:0.571711:0.332012:0.571711:0.316976:0.563127:0.316976:0.000000
Mezclado:@0.172067:0.349676:0.235214:0.349676:0.235214:0.334349:0.172067:0.334349:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
4:@0.330360:0.349333:0.338117:0.349333:0.338117:0.334270:0.330360:0.334270:0.000000
3:@0.401582:0.349333:0.409339:0.349333:0.409339:0.334270:0.401582:0.334270:0.000000
80:@0.510482:0.349333:0.525996:0.349333:0.525996:0.334270:0.510482:0.334270:0.000000:0.000000
Evaporado:@0.168215:0.367102:0.239050:0.367102:0.239050:0.351775:0.168215:0.351775:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.330342:0.366759:0.338099:0.366759:0.338099:0.351696:0.330342:0.351696:0.000000
6:@0.401564:0.366759:0.409321:0.366759:0.409321:0.351696:0.401564:0.351696:0.000000
120:@0.506594:0.366759:0.529866:0.366759:0.529866:0.351696:0.506594:0.351696:0.000000:0.000000:0.000000
Pasteurizado-envasado:@0.127846:0.384529:0.279400:0.384529:0.279400:0.369201:0.127846:0.369201:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
8:@0.330342:0.384185:0.338099:0.384185:0.338099:0.369122:0.330342:0.369122:0.000000
12,5:@0.392558:0.384185:0.418345:0.384185:0.418345:0.369122:0.392558:0.369122:0.000000:0.000000:0.000000:0.000000
240:@0.506594:0.384185:0.529866:0.384185:0.529866:0.369122:0.506594:0.369122:0.000000:0.000000:0.000000
x:@0.381493:0.680903:0.388968:0.680903:0.388968:0.664435:0.381493:0.664435:0.000000
 ≥ 0,    ≥ 0,:@0.388968:0.680788:0.465625:0.680788:0.465625:0.664290:0.388968:0.664290:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.427595:0.680903:0.435282:0.680903:0.435282:0.664435:0.427595:0.664435:0.000000
4  + 3  ≤ 80,:@0.381493:0.698138:0.471577:0.698138:0.471577:0.681641:0.381493:0.681641:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.389989:0.698254:0.397464:0.698254:0.397464:0.681785:0.389989:0.681785:0.000000
y:@0.425052:0.698254:0.432739:0.698254:0.432739:0.681785:0.425052:0.681785:0.000000
5  + 6  ≤ 120,:@0.381493:0.715489:0.480073:0.715489:0.480073:0.698991:0.381493:0.698991:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.389989:0.715605:0.397464:0.715605:0.397464:0.699136:0.389989:0.699136:0.000000
y:@0.425052:0.715605:0.432739:0.715605:0.432739:0.699136:0.425052:0.699136:0.000000
8  + 12,5  ≤ 240.:@0.381493:0.732840:0.499820:0.732840:0.499820:0.716342:0.381493:0.716342:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.389989:0.732956:0.397464:0.732956:0.397464:0.716487:0.389989:0.716487:0.000000
y:@0.444799:0.732956:0.452486:0.732956:0.452486:0.716487:0.444799:0.716487:0.000000
p:@0.629006:0.285231:0.640487:0.285231:0.640487:0.275207:0.629006:0.275207:0.000000
 :@0.640487:0.285939:0.643368:0.285939:0.643368:0.274463:0.640487:0.274463:0.000000
Figura 5.12.:@0.643368:0.285939:0.697847:0.285939:0.697847:0.274463:0.643368:0.274463:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p:@0.629006:0.791458:0.640487:0.791458:0.640487:0.781434:0.629006:0.781434:0.000000
 :@0.640487:0.792166:0.643368:0.792166:0.643368:0.780690:0.640487:0.780690:0.000000
Figura 5.13.:@0.643368:0.792166:0.697847:0.792166:0.697847:0.780690:0.643368:0.780690:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Los vértices de la región de :@0.638503:0.828287:0.816405:0.828287:0.816405:0.813224:0.638503:0.813224:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
soluciones factibles son: :@0.638503:0.844129:0.797617:0.844129:0.797617:0.829066:0.638503:0.829066:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
O:@0.638503:0.868987:0.649374:0.868987:0.649374:0.853951:0.638503:0.853951:0.000000
 = (0, 0),     = (20, 0),:@0.649374:0.868882:0.784026:0.868882:0.784026:0.853819:0.649374:0.853819:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.713349:0.868987:0.723639:0.868987:0.723639:0.853951:0.713349:0.853951:0.000000
B:@0.638503:0.891958:0.646894:0.891958:0.646894:0.876922:0.638503:0.876922:0.000000
 =         ,        ,:@0.646894:0.891853:0.728105:0.891853:0.728105:0.876790:0.646894:0.876790:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
C:@0.638503:0.918494:0.647668:0.918494:0.647668:0.903457:0.638503:0.903457:0.000000
 = (4,138; 16,55),:@0.647668:0.918388:0.751871:0.918388:0.751871:0.903325:0.647668:0.903325:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
D:@0.638503:0.934336:0.649128:0.934336:0.649128:0.919299:0.638503:0.919299:0.000000
 = (0; 19,2).:@0.649128:0.934230:0.719787:0.934230:0.719787:0.919167:0.649128:0.919167:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
40 80:@0.672271:0.884884:0.717149:0.884884:0.717149:0.869821:0.672271:0.869821:0.000000:0.000000:0.000000:0.000000:0.000000
3:@0.676141:0.901228:0.683898:0.901228:0.683898:0.886165:0.676141:0.886165:0.000000
9:@0.705505:0.901228:0.713262:0.901228:0.713262:0.886165:0.705505:0.886165:0.000000
S:@0.643943:0.754140:0.650109:0.754140:0.650109:0.741252:0.643943:0.741252:0.000000
1:@0.650109:0.756615:0.653986:0.756615:0.653986:0.749088:0.650109:0.749088:0.000000
0:@0.647484:0.769166:0.654503:0.769166:0.654503:0.755537:0.647484:0.755537:0.000000
x:@0.842393:0.770563:0.848997:0.770563:0.848997:0.756935:0.842393:0.756935:0.000000
10:@0.701060:0.769762:0.712881:0.769762:0.712881:0.758286:0.701060:0.758286:0.000000:0.000000
20:@0.749495:0.769762:0.761315:0.769762:0.761315:0.758286:0.749495:0.758286:0.000000:0.000000
30:@0.797929:0.769762:0.809750:0.769762:0.809750:0.758286:0.797929:0.758286:0.000000:0.000000
10:@0.640591:0.728654:0.652411:0.728654:0.652411:0.717177:0.640591:0.717177:0.000000:0.000000
20:@0.640591:0.696577:0.652411:0.696577:0.652411:0.685101:0.640591:0.685101:0.000000:0.000000
30:@0.640591:0.664501:0.652411:0.664501:0.652411:0.653025:0.640591:0.653025:0.000000:0.000000
y:@0.646208:0.650760:0.652669:0.650760:0.652669:0.637131:0.646208:0.637131:0.000000
A:@0.735763:0.756487:0.744583:0.756487:0.744583:0.743598:0.735763:0.743598:0.000000
B:@0.716630:0.739196:0.723822:0.739196:0.723822:0.726308:0.716630:0.726308:0.000000
C:@0.669529:0.713894:0.677384:0.713894:0.677384:0.701006:0.669529:0.701006:0.000000
D:@0.648481:0.706573:0.657588:0.706573:0.657588:0.693684:0.648481:0.693684:0.000000
C:@0.759580:0.154258:0.767435:0.154258:0.767435:0.141370:0.759580:0.141370:0.000000
B:@0.788392:0.213349:0.795584:0.213349:0.795584:0.200460:0.788392:0.200460:0.000000
0:@0.685482:0.250642:0.689915:0.250642:0.689915:0.242034:0.685482:0.242034:0.000000
x:@0.848094:0.255340:0.854699:0.255340:0.854699:0.241711:0.848094:0.241711:0.000000
–2 000 –1 000:@0.629571:0.251898:0.676654:0.251898:0.676654:0.244725:0.629571:0.244725:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1 000:@0.710033:0.251898:0.726609:0.251898:0.726609:0.244725:0.710033:0.244725:0.000000:0.000000:0.000000:0.000000:0.000000
2 000:@0.736359:0.251898:0.752936:0.251898:0.752936:0.244725:0.736359:0.244725:0.000000:0.000000:0.000000:0.000000:0.000000
3 000:@0.762216:0.251898:0.778793:0.251898:0.778793:0.244725:0.762216:0.244725:0.000000:0.000000:0.000000:0.000000:0.000000
4 000:@0.788543:0.251898:0.805119:0.251898:0.805119:0.244725:0.788543:0.244725:0.000000:0.000000:0.000000:0.000000:0.000000
1 000:@0.670011:0.224118:0.686588:0.224118:0.686588:0.216945:0.670011:0.216945:0.000000:0.000000:0.000000:0.000000:0.000000
2 000:@0.670011:0.204516:0.686588:0.204516:0.686588:0.197343:0.670011:0.197343:0.000000:0.000000:0.000000:0.000000:0.000000
3 000:@0.670011:0.184915:0.686588:0.184915:0.686588:0.177742:0.670011:0.177742:0.000000:0.000000:0.000000:0.000000:0.000000
4 000:@0.670011:0.165314:0.686588:0.165314:0.686588:0.158141:0.670011:0.158141:0.000000:0.000000:0.000000:0.000000:0.000000
5 000:@0.670011:0.145712:0.686588:0.145712:0.686588:0.138539:0.670011:0.138539:0.000000:0.000000:0.000000:0.000000:0.000000
4 500:@0.670011:0.155513:0.686588:0.155513:0.686588:0.148340:0.670011:0.148340:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.678706:0.127989:0.685167:0.127989:0.685167:0.114360:0.678706:0.114360:0.000000
S:@0.731509:0.198363:0.737676:0.198363:0.737676:0.185475:0.731509:0.185475:0.000000
D:@0.695339:0.154006:0.704446:0.154006:0.704446:0.141117:0.695339:0.141117:0.000000
A:@0.786089:0.241057:0.794909:0.241057:0.794909:0.228169:0.786089:0.228169:0.000000
Glosario:@0.684820:0.557140:0.752286:0.557140:0.752286:0.539458:0.684820:0.539458:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
factible: :@0.685058:0.583953:0.741978:0.583953:0.741978:0.568692:0.685058:0.568692:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
que se puede :@0.741978:0.583755:0.832758:0.583755:0.832758:0.568692:0.741978:0.568692:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
hacer.:@0.638515:0.599597:0.675489:0.599597:0.675489:0.584534:0.638515:0.584534:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.632085:0.560872:0.643489:0.559363:0.638287:0.537218:0.626882:0.538727:0.000000
c:@0.635466:0.571841:0.646066:0.570439:0.640983:0.548804:0.630384:0.550206:0.000000
b:@0.645842:0.564623:0.658555:0.562941:0.653424:0.541098:0.640710:0.542781:0.000000
Interdisciplinariedad:@0.684408:0.345560:0.831193:0.345560:0.831193:0.330087:0.684408:0.330087:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Matemática y Química:@0.684646:0.374610:0.834826:0.374610:0.834826:0.359137:0.684646:0.359137:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
La química es una ciencia :@0.638103:0.390029:0.806438:0.390029:0.806438:0.374966:0.638103:0.374966:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
que interacciona con muchas :@0.638103:0.405871:0.833368:0.405871:0.833368:0.390808:0.638103:0.390808:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
disciplinas como la física, la agri-:@0.638103:0.421713:0.845681:0.421713:0.845681:0.406650:0.638103:0.406650:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cultura, la geología, la biología :@0.638103:0.437555:0.836024:0.437555:0.836024:0.422492:0.638103:0.422492:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y muchas más, pero siempre, :@0.638103:0.453397:0.828476:0.453397:0.828476:0.438334:0.638103:0.438334:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
como un eje centralizado está :@0.638103:0.469239:0.836058:0.469239:0.836058:0.454176:0.638103:0.454176:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
presente la matemática.:@0.638103:0.485081:0.792258:0.485081:0.792258:0.470018:0.638103:0.470018:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 ©:@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