154:@0.054582:0.966558:0.078778:0.966558:0.078778:0.950778:0.054582:0.950778:0.000000:0.000000:0.000000
M.5.2.26. Realizar un proceso de solución gráfica y analítica del problema de programación lineal, graficando las inecuaciones lineales, determinando los puntos extremos del :@0.148948:0.940888:0.888553:0.940888:0.888553:0.930846:0.148948:0.930846:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
conjunto de soluciones factibles, y encontrar la solución óptima.:@0.148948:0.949689:0.427264:0.949689:0.427264:0.939647:0.148948:0.939647:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Puntos extremos y solución óptima:@0.404235:0.117192:0.835692:0.117192:0.835692:0.072532:0.404235:0.072532:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Procedimiento de solución gráfica:@0.404236:0.147650:0.677810:0.147650:0.677810:0.129967:0.404236:0.129967:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Ejercicios resueltos:@0.404236:0.164733:0.534891:0.164733:0.534891:0.147947:0.404236:0.147947:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1.:@0.404236:0.181925:0.416508:0.181925:0.416508:0.165211:0.404236:0.165211:0.000000:0.000000
  La función objetivo   está definida como   = 3  + 2 , sujeta a :@0.416508:0.181708:0.873686:0.181708:0.873686:0.165211:0.416508:0.165211:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
U:@0.569896:0.181824:0.581841:0.181824:0.581841:0.165355:0.569896:0.165355:0.000000
U:@0.726634:0.181824:0.738579:0.181824:0.738579:0.165355:0.726634:0.165355:0.000000
x:@0.766167:0.181824:0.773642:0.181824:0.773642:0.165355:0.766167:0.165355:0.000000
y:@0.801230:0.181824:0.808916:0.181824:0.808916:0.165355:0.801230:0.165355:0.000000
la restricción   = {( ,  )     |   =   + 1       [1, 3]}. Determinar :@0.427971:0.199059:0.886698:0.199059:0.886698:0.182561:0.427971:0.182561:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
S:@0.521658:0.199175:0.529537:0.199175:0.529537:0.182706:0.521658:0.182706:0.000000
1:@0.529546:0.202337:0.534499:0.202337:0.534499:0.192719:0.529546:0.192719:0.000000
x y:@0.565399:0.199175:0.587458:0.199175:0.587458:0.182706:0.565399:0.182706:0.000000:0.000000:0.000000
:@0.597552:0.198540:0.612205:0.198540:0.612205:0.185167:0.597552:0.185167:0.000000
R:@0.616347:0.197972:0.629651:0.197972:0.629651:0.185110:0.616347:0.185110:0.000000
2:@0.629650:0.192707:0.634603:0.192707:0.634603:0.183089:0.629650:0.183089:0.000000
y x:@0.647896:0.199175:0.682150:0.199175:0.682150:0.182706:0.647896:0.182706:0.000000:0.000000:0.000000
x:@0.722164:0.199175:0.729639:0.199175:0.729639:0.182706:0.722164:0.182706:0.000000
:@0.733779:0.198540:0.748432:0.198540:0.748432:0.185167:0.733779:0.185167:0.000000
mín   y máx   :@0.427973:0.216410:0.541599:0.216410:0.541599:0.199912:0.427973:0.199912:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
U:@0.460454:0.216525:0.472398:0.216525:0.472398:0.200057:0.460454:0.200057:0.000000
U.:@0.523528:0.216525:0.537457:0.216525:0.537457:0.200057:0.523528:0.200057:0.000000:0.000000
 :@0.404238:0.251111:0.408380:0.251111:0.408380:0.234614:0.404238:0.234614:0.000000
De la definición del conjunto   tenemos la equivalencia::@0.427973:0.251111:0.823887:0.251111:0.823887:0.234614:0.427973:0.234614:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
S:@0.639077:0.251227:0.646957:0.251227:0.646957:0.234758:0.639077:0.234758:0.000000
( ,  )         =   + 1;        [1, 3].:@0.526900:0.268462:0.769102:0.268462:0.769102:0.251964:0.526900:0.251964:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.532853:0.268578:0.554911:0.268578:0.554911:0.252109:0.532853:0.252109:0.000000:0.000000:0.000000
:@0.565012:0.267943:0.579665:0.267943:0.579665:0.254570:0.565012:0.254570:0.000000
S:@0.583806:0.268578:0.591685:0.268578:0.591685:0.252109:0.583806:0.252109:0.000000
⇔:@0.595827:0.267818:0.615028:0.267818:0.615028:0.250876:0.595827:0.250876:0.000000
y x:@0.619170:0.268578:0.653424:0.268578:0.653424:0.252109:0.619170:0.252109:0.000000:0.000000:0.000000
x:@0.700335:0.268578:0.707810:0.268578:0.707810:0.252109:0.700335:0.252109:0.000000
:@0.711949:0.267943:0.726602:0.267943:0.726602:0.254570:0.711949:0.254570:0.000000
 :@0.404237:0.300142:0.408379:0.300142:0.408379:0.283644:0.404237:0.283644:0.000000
Al reemplazar   en la función objetivo  , obtenemos::@0.427972:0.300142:0.804966:0.300142:0.804966:0.283644:0.427972:0.283644:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.530943:0.300257:0.538629:0.300257:0.538629:0.283789:0.530943:0.283789:0.000000
U:@0.701824:0.300257:0.713768:0.300257:0.713768:0.283789:0.701824:0.283789:0.000000
U:@0.476674:0.317608:0.488619:0.317608:0.488619:0.301139:0.476674:0.301139:0.000000
 = 3  + 2  = 3  + 2(  + 1) = 5  + 2;        [1, 3].:@0.488619:0.317492:0.819322:0.317497:0.819322:0.300999:0.488619:0.300995:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.516207:0.317608:0.523682:0.317608:0.523682:0.301139:0.516207:0.301139:0.000000
y:@0.551269:0.317608:0.558956:0.317608:0.558956:0.301139:0.551269:0.301139:0.000000
x:@0.586544:0.317608:0.594019:0.317608:0.594019:0.301139:0.586544:0.301139:0.000000
x:@0.627560:0.317608:0.635035:0.317608:0.635035:0.301139:0.627560:0.301139:0.000000
x:@0.696163:0.317608:0.703638:0.317608:0.703638:0.301139:0.696163:0.301139:0.000000
x:@0.750549:0.317608:0.758024:0.317608:0.758024:0.301139:0.750549:0.301139:0.000000
:@0.762171:0.316978:0.776824:0.316978:0.776824:0.303605:0.762171:0.303605:0.000000
 :@0.404233:0.349176:0.408375:0.349176:0.408375:0.332679:0.404233:0.332679:0.000000
Puesto que     [1, 3], entonces, :@0.427968:0.349176:0.656148:0.349181:0.656148:0.332683:0.427968:0.332679:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.511367:0.349292:0.518842:0.349292:0.518842:0.332823:0.511367:0.332823:0.000000
:@0.522994:0.348662:0.537646:0.348662:0.537646:0.335289:0.522994:0.335289:0.000000
1 ≤   ≤ 3   5 ≤ 5  ≤ 15   7 ≤ 5  + 2 ≤ 17   7 ≤   ≤ 17.:@0.442824:0.366532:0.853178:0.366532:0.853178:0.350034:0.442824:0.350034:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.470411:0.366647:0.477886:0.366647:0.477886:0.350178:0.470411:0.350178:0.000000
⇔:@0.509622:0.365887:0.528824:0.365887:0.528824:0.348945:0.509622:0.348945:0.000000
x:@0.569050:0.366647:0.576525:0.366647:0.576525:0.350178:0.569050:0.350178:0.000000
⇔:@0.616749:0.365887:0.635950:0.365887:0.635950:0.348945:0.616749:0.348945:0.000000
x:@0.676176:0.366647:0.683651:0.366647:0.683651:0.350178:0.676176:0.350178:0.000000
⇔:@0.751463:0.365887:0.770665:0.365887:0.770665:0.348945:0.751463:0.348945:0.000000
U:@0.802395:0.366647:0.814339:0.366647:0.814339:0.350178:0.802395:0.350178:0.000000
En  = 1 se tiene   = 2 y   = 3 × 1 + 2 × 2 = 7 ≤  .:@0.427974:0.398211:0.787583:0.398216:0.787583:0.381718:0.427974:0.381713:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.449956:0.398327:0.457431:0.398327:0.457431:0.381858:0.449956:0.381858:0.000000
y:@0.547571:0.398327:0.555258:0.398327:0.555258:0.381858:0.547571:0.381858:0.000000
U:@0.598952:0.398327:0.610896:0.398327:0.610896:0.381858:0.598952:0.381858:0.000000
0:@0.610900:0.401493:0.615854:0.401493:0.615854:0.391875:0.610900:0.391875:0.000000
U:@0.772884:0.398331:0.784828:0.398331:0.784828:0.381862:0.772884:0.381862:0.000000
 :@0.404243:0.415566:0.408385:0.415566:0.408385:0.399069:0.404243:0.399069:0.000000
Luego, mín   = 7, valor que alcanza en el punto (1, 2).:@0.427978:0.415566:0.808426:0.415566:0.808426:0.399069:0.427978:0.399069:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
U:@0.510568:0.415682:0.522512:0.415682:0.522512:0.399213:0.510568:0.399213:0.000000
 :@0.404243:0.440045:0.408385:0.440045:0.408385:0.423548:0.404243:0.423548:0.000000
En forma similar, para   = 3, se tiene   = 4 y   =  3 × 3 + 2 × 4 = :@0.427978:0.440045:0.886085:0.440045:0.886085:0.423547:0.427978:0.423548:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.583851:0.440161:0.591326:0.440161:0.591326:0.423692:0.583851:0.423692:0.000000
y:@0.684221:0.440161:0.691908:0.440161:0.691908:0.423692:0.684221:0.423692:0.000000
U:@0.735601:0.440161:0.747546:0.440161:0.747546:0.423692:0.735601:0.423692:0.000000
1:@0.747546:0.443323:0.752500:0.443323:0.752500:0.433704:0.747546:0.433704:0.000000
17 ≥   Luego, máx   = 17, valor que alcanza en el punto (3, 4).:@0.427977:0.457395:0.873619:0.457395:0.873619:0.440898:0.427977:0.440898:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
U.:@0.464061:0.457511:0.477989:0.457511:0.477989:0.441042:0.464061:0.441042:0.000000:0.000000
U:@0.567265:0.457511:0.579209:0.457511:0.579209:0.441042:0.567265:0.441042:0.000000
2.:@0.404242:0.490810:0.416514:0.490810:0.416514:0.474096:0.404242:0.474096:0.000000:0.000000
  Sea la función objetivo   = 200  + 70 , sujeta a las restricciones: :@0.416514:0.490593:0.881766:0.490593:0.881766:0.474096:0.416514:0.474096:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
C:@0.593600:0.490709:0.603637:0.490709:0.603637:0.474240:0.593600:0.474240:0.000000
x:@0.648217:0.490709:0.655692:0.490709:0.655692:0.474240:0.648217:0.474240:0.000000
y:@0.691776:0.490709:0.699463:0.490709:0.699463:0.474240:0.691776:0.474240:0.000000
 :@0.423238:0.507944:0.427380:0.507944:0.427380:0.491446:0.423238:0.491446:0.000000
x:@0.446972:0.508060:0.454447:0.508060:0.454447:0.491591:0.446972:0.491591:0.000000
 ≥ 0 :@0.454447:0.507944:0.486177:0.507944:0.486177:0.491446:0.454447:0.491446:0.000000:0.000000:0.000000:0.000000:0.000000
( ):@0.594178:0.507944:0.615062:0.507944:0.615062:0.491446:0.594178:0.491446:0.000000:0.000000:0.000000
a:@0.600131:0.508060:0.609109:0.508060:0.609109:0.491591:0.600131:0.491591:0.000000
 :@0.423218:0.525295:0.427360:0.525295:0.427360:0.508797:0.423218:0.508797:0.000000
y:@0.446953:0.525410:0.454640:0.525410:0.454640:0.508942:0.446953:0.508942:0.000000
 ≥ 0 :@0.454640:0.525295:0.486370:0.525295:0.486370:0.508797:0.454640:0.508797:0.000000:0.000000:0.000000:0.000000:0.000000
( ):@0.594159:0.525295:0.615331:0.525295:0.615331:0.508797:0.594159:0.508797:0.000000:0.000000:0.000000
b:@0.600112:0.525410:0.609378:0.525410:0.609378:0.508942:0.600112:0.508942:0.000000
–0,5  +   ≤ 20 :@0.446934:0.542645:0.551660:0.542645:0.551660:0.526148:0.446934:0.526148:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.477180:0.542761:0.511434:0.542761:0.511434:0.526292:0.477180:0.526292:0.000000:0.000000:0.000000
( ):@0.594140:0.542645:0.613232:0.542645:0.613232:0.526148:0.594140:0.526148:0.000000:0.000000:0.000000
c:@0.600093:0.542761:0.607279:0.542761:0.607279:0.526292:0.600093:0.526292:0.000000
1,5  +   ≤ 50 :@0.446915:0.559996:0.541141:0.559996:0.541141:0.543499:0.446915:0.543499:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.466661:0.560112:0.500915:0.560112:0.500915:0.543643:0.466661:0.543643:0.000000:0.000000:0.000000
( ):@0.594120:0.559996:0.615197:0.559996:0.615197:0.543499:0.594120:0.543499:0.000000:0.000000:0.000000
d:@0.600073:0.560112:0.609244:0.560112:0.609244:0.543643:0.600073:0.543643:0.000000
Hallar ,   soluciones factibles, tales que   = máx;   = 200  + 70 .:@0.427900:0.593194:0.891770:0.593184:0.891770:0.576686:0.427900:0.576696:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.473308:0.593310:0.496356:0.593300:0.496356:0.576831:0.473308:0.576841:0.000000:0.000000:0.000000
� �:@0.474127:0.599001:0.496761:0.599001:0.496761:0.580865:0.474127:0.580865:0.000000:0.000000:0.000000
C:@0.713764:0.593300:0.723801:0.593300:0.723801:0.576831:0.713764:0.576831:0.000000
�:@0.717092:0.596486:0.724234:0.596486:0.724234:0.578351:0.717092:0.578351:0.000000
C:@0.781571:0.593300:0.791609:0.593300:0.791609:0.576831:0.781571:0.576831:0.000000
xx:@0.836150:0.593300:0.843394:0.593300:0.843394:0.576831:0.836150:0.576831:0.000000:0.000000
�:@0.836683:0.599001:0.843824:0.599001:0.843824:0.580865:0.836683:0.580865:0.000000
y:@0.880394:0.593300:0.888081:0.593300:0.888081:0.576831:0.880394:0.576831:0.000000
�:@0.881351:0.599001:0.888493:0.599001:0.888493:0.580865:0.881351:0.580865:0.000000
i):@0.404244:0.626382:0.414011:0.626382:0.414011:0.609884:0.404244:0.609884:0.000000:0.000000
 :@0.414011:0.626382:0.418153:0.626382:0.418153:0.609884:0.414011:0.609884:0.000000
Determinación gráfica del conjunto de soluciones factibles:@0.427979:0.626599:0.860499:0.626599:0.860499:0.609884:0.427979:0.609884:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.404244:0.643732:0.408386:0.643732:0.408386:0.627235:0.404244:0.627235:0.000000
Comenzamos con las condiciones ( ) y ( ) que nos muestran que :@0.427979:0.643732:0.895874:0.643732:0.895874:0.627235:0.427979:0.627235:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.678369:0.643848:0.687347:0.643848:0.687347:0.627379:0.678369:0.627379:0.000000
b:@0.714434:0.643848:0.723700:0.643848:0.723700:0.627379:0.714434:0.627379:0.000000
las soluciones factibles tienen que ser no negativas.:@0.427979:0.661083:0.788848:0.661083:0.788848:0.644586:0.427979:0.644586:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.404244:0.692763:0.408386:0.692763:0.408386:0.676265:0.404244:0.676265:0.000000
Analizamos la condición ( ). Este conjunto representa una recta :@0.427979:0.692763:0.895912:0.692763:0.895912:0.676265:0.427979:0.676265:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
c:@0.616239:0.692878:0.623425:0.692878:0.623425:0.676410:0.616239:0.676410:0.000000
que tiene una pendiente :@0.427979:0.710114:0.607336:0.710114:0.607336:0.693616:0.427979:0.693616:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
m:@0.607586:0.710229:0.622382:0.710229:0.622382:0.693760:0.607586:0.693760:0.000000
1:@0.622361:0.713391:0.627314:0.713391:0.627314:0.703773:0.622361:0.703773:0.000000
 = 0,5. Corta a los ejes del lado positi-:@0.627314:0.710113:0.891823:0.710113:0.891823:0.693615:0.627314:0.693615:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
vo, en el punto (0, 20), y satisface todos los puntos del semiplano :@0.427977:0.727464:0.895870:0.727464:0.895870:0.710966:0.427977:0.710966:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
que parten de la recta   hacia abajo. :@0.427977:0.744814:0.691238:0.744814:0.691238:0.728317:0.427977:0.728317:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
L:@0.588050:0.744930:0.595891:0.744930:0.595891:0.728461:0.588050:0.728461:0.000000
1:@0.595892:0.748092:0.600845:0.748092:0.600845:0.738474:0.595892:0.738474:0.000000
 :@0.404244:0.776494:0.408386:0.776494:0.408386:0.759996:0.404244:0.759996:0.000000
Analizamos la condición ( ). Este conjunto es una recta que tiene :@0.427979:0.776494:0.895912:0.776494:0.895912:0.759996:0.427979:0.759996:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
d:@0.611615:0.776610:0.620785:0.776610:0.620785:0.760141:0.611615:0.760141:0.000000
una pendiente   = –1,5. Sus puntos de corte con los ejes del lado:@0.427979:0.793845:0.891827:0.793849:0.891827:0.777351:0.427979:0.777347:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
m:@0.534533:0.793960:0.549328:0.793960:0.549328:0.777492:0.534533:0.777492:0.000000
2:@0.549314:0.797127:0.554267:0.797127:0.554267:0.787509:0.549314:0.787509:0.000000
 :@0.404229:0.818328:0.408372:0.818328:0.408372:0.801831:0.404229:0.801831:0.000000
positivo son           , 0   y (0, 50). La desigualdad muestra que son:@0.427964:0.818328:0.879634:0.818328:0.879634:0.801831:0.427964:0.801831:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.404229:0.842807:0.408372:0.842807:0.408372:0.826310:0.404229:0.826310:0.000000
todos los puntos del semiplano que parten de   hacia abajo.:@0.427964:0.842807:0.858766:0.842807:0.858766:0.826310:0.427964:0.826310:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
L:@0.759708:0.842923:0.767549:0.842923:0.767549:0.826454:0.759708:0.826454:0.000000
2:@0.767562:0.846085:0.772515:0.846085:0.772515:0.836467:0.767562:0.836467:0.000000
 :@0.404241:0.877509:0.408383:0.877509:0.408383:0.861011:0.404241:0.861011:0.000000
En la Figura 5.9., se muestra el conjunto de soluciones factibles. :@0.427976:0.877509:0.895902:0.877509:0.895902:0.861011:0.427976:0.861011:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Observamos que es una región poligonal cuyos vértices son los :@0.427976:0.894859:0.895923:0.894859:0.895923:0.878362:0.427976:0.878362:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
puntos  ,  ,  ,  .:@0.427976:0.912210:0.546419:0.912210:0.546419:0.895713:0.427976:0.895713:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
O A B E:@0.482651:0.912326:0.543664:0.912326:0.543664:0.895857:0.482651:0.895857:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
( ,  ):@0.426081:0.225254:0.448232:0.225254:0.448232:0.214494:0.426081:0.214494:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.429964:0.225329:0.444350:0.225329:0.444350:0.214589:0.429964:0.214589:0.000000:0.000000:0.000000
:@0.448231:0.224961:0.458000:0.224961:0.458000:0.216046:0.448231:0.216046:0.000000
S:@0.458000:0.225329:0.463138:0.225329:0.463138:0.214589:0.458000:0.214589:0.000000
( ,  ):@0.486395:0.225254:0.508546:0.225254:0.508546:0.214494:0.486395:0.214494:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.490277:0.225329:0.504663:0.225329:0.504663:0.214589:0.490277:0.214589:0.000000:0.000000:0.000000
:@0.508540:0.224961:0.518308:0.224961:0.518308:0.216046:0.508540:0.216046:0.000000
S:@0.518308:0.225329:0.523447:0.225329:0.523447:0.214589:0.518308:0.214589:0.000000
( ,  ):@0.474107:0.422967:0.496258:0.422967:0.496258:0.412208:0.474107:0.412208:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.477989:0.423043:0.492376:0.423043:0.492376:0.412302:0.477989:0.412302:0.000000:0.000000:0.000000
:@0.496259:0.422674:0.506027:0.422674:0.506027:0.413759:0.496259:0.413759:0.000000
S:@0.506027:0.423042:0.511166:0.423042:0.511166:0.412302:0.506027:0.412302:0.000000
( ,  ):@0.529120:0.465768:0.551271:0.465768:0.551271:0.455009:0.529120:0.455009:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.533003:0.465844:0.547389:0.465844:0.547389:0.455103:0.533003:0.455103:0.000000:0.000000:0.000000
:@0.551265:0.465472:0.561034:0.465472:0.561034:0.456556:0.551265:0.456556:0.000000
S:@0.561034:0.465839:0.566172:0.465839:0.566172:0.455099:0.561034:0.455099:0.000000
( ,  ):@0.741819:0.601146:0.763970:0.601146:0.763970:0.590387:0.741819:0.590387:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.745701:0.601222:0.760087:0.601222:0.760087:0.590481:0.745701:0.590481:0.000000:0.000000:0.000000
:@0.763969:0.600854:0.773737:0.600854:0.773737:0.591939:0.763969:0.591939:0.000000
S:@0.773737:0.601222:0.778876:0.601222:0.778876:0.590481:0.773737:0.590481:0.000000
100:@0.527227:0.813222:0.553100:0.813222:0.553100:0.796724:0.527227:0.796724:0.000000:0.000000:0.000000
3:@0.535916:0.829560:0.544412:0.829560:0.544412:0.813063:0.535916:0.813063:0.000000
p:@0.143847:0.899982:0.155327:0.899982:0.155327:0.889958:0.143847:0.889958:0.000000
 :@0.155327:0.900690:0.158209:0.900690:0.158209:0.889214:0.155327:0.889214:0.000000
Figura 5.9.:@0.158209:0.900690:0.206777:0.900690:0.206777:0.889214:0.158209:0.889214:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
L:@0.317219:0.822997:0.323356:0.822997:0.323356:0.810108:0.317219:0.810108:0.000000
1:@0.323356:0.825471:0.327232:0.825471:0.327232:0.817944:0.323356:0.817944:0.000000
L:@0.254063:0.806686:0.260199:0.806686:0.260199:0.793797:0.254063:0.793797:0.000000
2:@0.260199:0.809160:0.264075:0.809160:0.264075:0.801633:0.260199:0.801633:0.000000
S:@0.263109:0.858993:0.269276:0.858993:0.269276:0.846104:0.263109:0.846104:0.000000
A:@0.308401:0.865681:0.317221:0.865681:0.317221:0.852792:0.308401:0.852792:0.000000
E:@0.234583:0.837233:0.240810:0.837233:0.240810:0.824344:0.234583:0.824344:0.000000
0:@0.236253:0.876869:0.240686:0.876869:0.240686:0.868262:0.236253:0.868262:0.000000
x:@0.356983:0.882826:0.363587:0.882826:0.363587:0.869197:0.356983:0.869197:0.000000
10:@0.256760:0.879428:0.265625:0.879428:0.265625:0.870820:0.256760:0.870820:0.000000:0.000000
–10:@0.216031:0.879428:0.230375:0.879428:0.230375:0.870820:0.216031:0.870820:0.000000:0.000000:0.000000
–20:@0.197034:0.879428:0.211378:0.879428:0.211378:0.870820:0.197034:0.870820:0.000000:0.000000:0.000000
–30:@0.178037:0.879428:0.192380:0.879428:0.192380:0.870820:0.178037:0.870820:0.000000:0.000000:0.000000
–40:@0.159040:0.879428:0.173383:0.879428:0.173383:0.870820:0.159040:0.870820:0.000000:0.000000:0.000000
20:@0.275747:0.879428:0.284612:0.879428:0.284612:0.870820:0.275747:0.870820:0.000000:0.000000
30:@0.294744:0.879428:0.303610:0.879428:0.303610:0.870820:0.294744:0.870820:0.000000:0.000000
40:@0.313741:0.879428:0.322607:0.879428:0.322607:0.870820:0.313741:0.870820:0.000000:0.000000
50:@0.332739:0.879428:0.341604:0.879428:0.341604:0.870820:0.332739:0.870820:0.000000:0.000000
10:@0.228485:0.856683:0.237350:0.856683:0.237350:0.848076:0.228485:0.848076:0.000000:0.000000
20:@0.228485:0.842426:0.237350:0.842426:0.237350:0.833818:0.228485:0.833818:0.000000:0.000000
30:@0.228485:0.828168:0.237350:0.828168:0.237350:0.819560:0.228485:0.819560:0.000000:0.000000
40:@0.228485:0.813910:0.237350:0.813910:0.237350:0.805303:0.228485:0.805303:0.000000:0.000000
50:@0.228485:0.799652:0.237350:0.799652:0.237350:0.791045:0.228485:0.791045:0.000000:0.000000
y:@0.229475:0.776848:0.235937:0.776848:0.235937:0.763219:0.229475:0.763219:0.000000
B:@0.271143:0.824422:0.278335:0.824422:0.278335:0.811534:0.271143:0.811534:0.000000
Saberes previos:@0.199646:0.115710:0.307805:0.115710:0.307805:0.100238:0.199646:0.100238:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿Qué entiendes por :@0.199884:0.144338:0.331297:0.144338:0.331297:0.129274:0.199884:0.129274:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
solución óptima?:@0.153341:0.160180:0.264719:0.160180:0.264719:0.145116:0.153341:0.145116:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Desequilibrio cognitivo:@0.199646:0.207331:0.363493:0.207331:0.363493:0.191858:0.199646:0.191858:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿Las soluciones factibles :@0.199884:0.235958:0.365279:0.235958:0.365279:0.220895:0.199884:0.220895:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de un problema de programa-:@0.153341:0.251800:0.361482:0.251800:0.361482:0.236737:0.153341:0.236737:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ción lineal pueden ser negativas?:@0.153341:0.267642:0.361517:0.267642:0.361517:0.252579:0.153341:0.252579:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Interdisciplinariedad:@0.199644:0.346293:0.346429:0.346293:0.346429:0.330820:0.199644:0.330820:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Matemática :@0.199880:0.375343:0.288217:0.375343:0.288217:0.359870:0.199880:0.359870:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y Nutrición:@0.153337:0.391185:0.232739:0.391185:0.232739:0.375712:0.153337:0.375712:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Uno de los problemas más :@0.153337:0.406604:0.330571:0.406604:0.330571:0.391541:0.153337:0.391541:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
conocidos y difundidos de :@0.153337:0.422446:0.329586:0.422446:0.329586:0.407383:0.153337:0.407383:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
aplicación de la programación :@0.153337:0.438288:0.352753:0.438288:0.352753:0.423225:0.153337:0.423225:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
lineal se relaciona con las dietas. :@0.153337:0.454130:0.363269:0.454130:0.363269:0.439067:0.153337:0.439067:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
En términos generales, el pro-:@0.153337:0.469972:0.343906:0.469972:0.343906:0.454909:0.153337:0.454909:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
blema consiste en encontrar la :@0.153337:0.485814:0.354530:0.485814:0.354530:0.470751:0.153337:0.470751:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
dieta que contenga los requeri-:@0.153337:0.501656:0.355091:0.501656:0.355091:0.486593:0.153337:0.486593:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
mientos nutricionales al menor :@0.153337:0.517498:0.359088:0.517498:0.359088:0.502435:0.153337:0.502435:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
costo posible.:@0.153337:0.533340:0.241954:0.533340:0.241954:0.518277:0.153337:0.518277:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Investiga escribe:@0.153344:0.708663:0.274961:0.708663:0.274961:0.693401:0.153344:0.693401:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 y :@0.212693:0.708465:0.227398:0.708465:0.227398:0.693401:0.212693:0.693401:0.000000:0.000000:0.000000
 otros :@0.274961:0.708465:0.315999:0.708465:0.315999:0.693401:0.274961:0.693401:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ejemplos de aplicaciones de la :@0.153344:0.724307:0.353022:0.724307:0.353022:0.709243:0.153344:0.709243:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
programación lineal.:@0.153344:0.740149:0.284882:0.740149:0.284882:0.725085:0.153344:0.725085:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Shutterstock, 537604240:@0.386145:0.683221:0.386145:0.615048:0.374677:0.615048:0.374677:0.683221:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000