90:@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
Actividad resuelta:@0.115891:0.302246:0.273013:0.302246:0.273013:0.283809:0.115891:0.283809:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sea la función objetivo   = 5  + 3 , sujeta a las siguientes :@0.115891:0.322093:0.536938:0.322093:0.536938:0.305704:0.115891:0.305704:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
C:@0.286897:0.322093:0.296811:0.322093:0.296811:0.305732:0.286897:0.305732:0.000000
x:@0.324858:0.322093:0.332321:0.322093:0.332321:0.305732:0.324858:0.305732:0.000000
y:@0.360368:0.322093:0.367850:0.322093:0.367850:0.305732:0.360368:0.305732:0.000000
restricciones:  :@0.115891:0.375021:0.219104:0.375021:0.219104:0.358633:0.115891:0.358633:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.231614:0.344254:0.240607:0.344254:0.240607:0.327865:0.231614:0.327865:0.000000
18,:@0.294488:0.344254:0.315274:0.344254:0.315274:0.327865:0.294488:0.327865:0.000000:0.000000:0.000000
2:@0.231614:0.365276:0.240607:0.365276:0.240607:0.348887:0.231614:0.348887:0.000000
3:@0.267161:0.365276:0.276154:0.365276:0.276154:0.348887:0.267161:0.348887:0.000000
42,:@0.304750:0.365276:0.325536:0.365276:0.325536:0.348887:0.304750:0.348887:0.000000:0.000000:0.000000
0:@0.260104:0.386298:0.269096:0.386298:0.269096:0.369909:0.260104:0.369909:0.000000
0:@0.260104:0.407320:0.269096:0.407320:0.269096:0.390931:0.260104:0.390931:0.000000
     ( ):@0.317893:0.345042:0.364550:0.345042:0.364550:0.326869:0.317893:0.326869:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
   ( ):@0.328157:0.366064:0.365233:0.366064:0.365233:0.347891:0.328157:0.347891:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
                ( ):@0.269999:0.387087:0.366180:0.387087:0.366180:0.368913:0.269999:0.368913:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
                ( ):@0.269999:0.408109:0.368117:0.408109:0.368117:0.389936:0.269999:0.389936:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.241879:0.344254:0.249342:0.344254:0.249342:0.327893:0.241879:0.327893:0.000000
y:@0.268636:0.344254:0.276117:0.344254:0.276117:0.327893:0.268636:0.327893:0.000000
a:@0.348523:0.344254:0.357792:0.344254:0.357792:0.327893:0.348523:0.327893:0.000000
x:@0.241879:0.365276:0.249342:0.365276:0.249342:0.348915:0.241879:0.348915:0.000000
y:@0.277002:0.365276:0.284483:0.365276:0.284483:0.348915:0.277002:0.348915:0.000000
b:@0.349194:0.365276:0.358463:0.365276:0.358463:0.348915:0.349194:0.348915:0.000000
x:@0.233080:0.386296:0.240543:0.386296:0.240543:0.369934:0.233080:0.369934:0.000000
c:@0.351294:0.386296:0.358959:0.386296:0.358959:0.369934:0.351294:0.369934:0.000000
y:@0.233080:0.407318:0.240562:0.407318:0.240562:0.390956:0.233080:0.390956:0.000000
d:@0.351294:0.407318:0.360563:0.407318:0.360563:0.390956:0.351294:0.390956:0.000000
+ ≤:@0.253761:0.344849:0.291667:0.344849:0.291667:0.326828:0.253761:0.326828:0.000000:0.000000:0.000000
+:@0.253761:0.365871:0.263878:0.365871:0.263878:0.347850:0.253761:0.347850:0.000000
≤:@0.289935:0.365871:0.300051:0.365871:0.300051:0.347850:0.289935:0.347850:0.000000
≥:@0.246003:0.386893:0.256120:0.386893:0.256120:0.368872:0.246003:0.368872:0.000000
≥:@0.246003:0.407915:0.256120:0.407915:0.256120:0.389894:0.246003:0.389894:0.000000
⎧:@0.222453:0.344268:0.231556:0.344268:0.231556:0.326247:0.222453:0.326247:0.000000
⎨:@0.222453:0.377779:0.231556:0.377779:0.231556:0.359758:0.222453:0.359758:0.000000
⎪:@0.222453:0.357739:0.231556:0.357739:0.231556:0.339718:0.222453:0.339718:0.000000
⎪:@0.222453:0.367282:0.231556:0.367282:0.231556:0.349261:0.222453:0.349261:0.000000
⎩:@0.222456:0.411288:0.231559:0.411288:0.231559:0.393267:0.222456:0.393267:0.000000
⎪:@0.222456:0.391249:0.231559:0.391249:0.231559:0.373229:0.222456:0.373229:0.000000
⎪:@0.222456:0.404720:0.231559:0.404720:0.231559:0.386699:0.222456:0.386699:0.000000
Encontremos:@0.115891:0.431859:0.217556:0.431859:0.217556:0.415235:0.115891:0.415235:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.217556:0.431859:0.221591:0.431859:0.221591:0.415470:0.217556:0.415470:0.000000
x, y:@0.221591:0.431859:0.243189:0.431859:0.243189:0.415498:0.221591:0.415498:0.000000:0.000000:0.000000:0.000000
 soluciones factibles, tales que, :@0.243189:0.431859:0.470858:0.431859:0.470858:0.415470:0.243189:0.415470:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
C:@0.115891:0.448455:0.125805:0.448455:0.125805:0.432094:0.115891:0.432094:0.000000
max:@0.125805:0.450362:0.144090:0.450362:0.144090:0.440807:0.125805:0.440807:0.000000:0.000000:0.000000
 = 5  + 3:@0.144090:0.448455:0.207647:0.448455:0.207647:0.432066:0.144090:0.432066:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.172137:0.448455:0.179600:0.448455:0.179600:0.432094:0.172137:0.432094:0.000000
y:@0.207647:0.448455:0.215128:0.448455:0.215128:0.432094:0.207647:0.432094:0.000000
Solución:@0.115896:0.475743:0.185110:0.475743:0.185110:0.458842:0.115896:0.458842:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Para resolver gráficamente un problema de programación lineal seguimos los siguientes pasos::@0.115214:0.167755:0.810372:0.167755:0.810372:0.151366:0.115214:0.151366:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a) :@0.115214:0.187920:0.133936:0.187920:0.133936:0.171019:0.115214:0.171019:0.000000:0.000000:0.000000
Dibujamos:@0.148457:0.187920:0.231824:0.187920:0.231824:0.171296:0.148457:0.171296:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 la región factible utilizando las ecuaciones de las rectas que resultan de convertir las :@0.231824:0.187920:0.884031:0.187920:0.884031:0.171531:0.231824:0.171531:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.879905:0.187920:0.883941:0.187920:0.883941:0.171531:0.879905:0.171531:0.000000
restricciones en igualdades.:@0.148457:0.204516:0.350439:0.204516:0.350439:0.188127:0.148457:0.188127:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
b) :@0.115214:0.224681:0.135245:0.224681:0.135245:0.207780:0.115214:0.207780:0.000000:0.000000:0.000000
Determinamos:@0.148457:0.224681:0.262930:0.224681:0.262930:0.208057:0.148457:0.208057:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 los puntos extremos de la región factible: puntos de intersección entre las rectas :@0.262930:0.224681:0.884022:0.224681:0.884022:0.208292:0.262930:0.208292:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.879905:0.224681:0.883941:0.224681:0.883941:0.208292:0.879905:0.208292:0.000000
y que pertenecen a la región factible.:@0.148457:0.241277:0.420296:0.241277:0.420296:0.224888:0.148457:0.224888:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
c) :@0.115214:0.261442:0.132849:0.261442:0.132849:0.244541:0.115214:0.244541:0.000000:0.000000:0.000000
Evaluamos:@0.148457:0.261442:0.231234:0.261442:0.231234:0.244818:0.148457:0.244818:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 la función objetivo en los puntos extremos y :@0.231234:0.261442:0.564791:0.261442:0.564791:0.245053:0.231234:0.245053:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
determinamos:@0.564791:0.261442:0.677310:0.261442:0.677310:0.244818:0.564791:0.244818:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 el de valor óptimo.:@0.677310:0.261442:0.818392:0.261442:0.818392:0.245053:0.677310:0.245053:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Puntos extremos y solución óptima:@0.115891:0.141978:0.642033:0.141978:0.642033:0.101242:0.115891:0.101242:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
M.5.2.26. Realizar un proceso de solución gráfica y analítica del problema de programación lineal graficando las inecuaciones lineales, determinando los puntos :@0.125388:0.069719:0.877666:0.069719:0.877666:0.059289:0.125388:0.059289:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
extremos del conjunto de soluciones factibles, y encontrar la solución óptima.:@0.125388:0.080280:0.488183:0.080280:0.488183:0.069851:0.125388:0.069851:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
6:@0.054104:0.122645:0.076408:0.122645:0.076408:0.065614:0.054104:0.065614:0.000000
0:@0.623619:0.442149:0.629807:0.442149:0.629807:0.431268:0.623619:0.431268:0.000000
20:@0.608469:0.309121:0.620845:0.309121:0.620845:0.298240:0.608469:0.298240:0.000000:0.000000
y:@0.639215:0.300422:0.644112:0.300422:0.644112:0.289713:0.639215:0.289713:0.000000
x:@0.861934:0.426506:0.866819:0.426506:0.866819:0.415797:0.861934:0.415797:0.000000
15:@0.608469:0.340027:0.620845:0.340027:0.620845:0.329146:0.608469:0.329146:0.000000:0.000000
10:@0.608469:0.371367:0.620845:0.371367:0.620845:0.360486:0.608469:0.360486:0.000000:0.000000
5:@0.614657:0.401937:0.620845:0.401937:0.620845:0.391056:0.614657:0.391056:0.000000
–5:@0.608625:0.464843:0.620844:0.464843:0.620844:0.453962:0.608625:0.453962:0.000000:0.000000
5:@0.587360:0.444303:0.593548:0.444303:0.593548:0.433421:0.587360:0.433421:0.000000
–10:@0.602437:0.495812:0.620843:0.495812:0.620843:0.484930:0.602437:0.484930:0.000000:0.000000:0.000000
10:@0.545301:0.444303:0.557676:0.444303:0.557676:0.433421:0.545301:0.433421:0.000000:0.000000
15:@0.503712:0.444303:0.516087:0.444303:0.516087:0.433421:0.503712:0.433421:0.000000:0.000000
–15:@0.602437:0.526907:0.620843:0.526907:0.620843:0.516026:0.602437:0.516026:0.000000:0.000000:0.000000
–10:@0.602437:0.589904:0.620843:0.589904:0.620843:0.579023:0.602437:0.579023:0.000000:0.000000:0.000000
–12:@0.602437:0.621045:0.620843:0.621045:0.620843:0.610164:0.602437:0.610164:0.000000:0.000000:0.000000
–20:@0.602437:0.559315:0.620843:0.559315:0.620843:0.548434:0.602437:0.548434:0.000000:0.000000:0.000000
20:@0.462153:0.444299:0.474528:0.444299:0.474528:0.433418:0.462153:0.433418:0.000000:0.000000
25:@0.416004:0.444299:0.428380:0.444299:0.428380:0.433418:0.416004:0.433418:0.000000:0.000000
30:@0.375887:0.444299:0.388262:0.444299:0.388262:0.433418:0.375887:0.433418:0.000000:0.000000
35:@0.333454:0.444299:0.345829:0.444299:0.345829:0.433418:0.333454:0.433418:0.000000:0.000000
25:@0.837344:0.444299:0.849720:0.444299:0.849720:0.433418:0.837344:0.433418:0.000000:0.000000
20:@0.796503:0.444299:0.808879:0.444299:0.808879:0.433418:0.796503:0.433418:0.000000:0.000000
15:@0.754553:0.444299:0.766928:0.444299:0.766928:0.433418:0.754553:0.433418:0.000000:0.000000
10:@0.712530:0.444299:0.724905:0.444299:0.724905:0.433418:0.712530:0.433418:0.000000:0.000000
5:@0.666007:0.444299:0.672195:0.444299:0.672195:0.433418:0.666007:0.433418:0.000000
C = (3, 12):@0.662441:0.351867:0.720880:0.351867:0.720880:0.338266:0.662441:0.338266:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
B = (0, 14):@0.569339:0.352908:0.627206:0.352908:0.627206:0.339307:0.569339:0.339307:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A = (0, 0):@0.578567:0.427897:0.630131:0.427897:0.630131:0.414296:0.578567:0.414296:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
D = (9, 0):@0.705833:0.427071:0.758211:0.427071:0.758211:0.413470:0.705833:0.413470:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Soluciones factibles:@0.115354:0.510125:0.287614:0.510125:0.287614:0.491688:0.115354:0.491688:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
• :@0.115354:0.529971:0.125121:0.529971:0.125121:0.512835:0.115354:0.512835:0.000000:0.000000
La condición ( ) representa una recta con pendiente :@0.148597:0.529971:0.518311:0.529971:0.518311:0.513582:0.148597:0.513582:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.246540:0.529971:0.255809:0.529971:0.255809:0.513610:0.246540:0.513610:0.000000
m:@0.517943:0.529971:0.532574:0.529971:0.532574:0.513610:0.517943:0.513610:0.000000
1:@0.532198:0.531878:0.537440:0.531878:0.537440:0.522323:0.532198:0.522323:0.000000
 = –2 y corta los ejes en los puntos (0,18) y (9, 0).:@0.537225:0.529971:0.868812:0.529971:0.868812:0.513582:0.537225:0.513582:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
• :@0.115361:0.553690:0.125128:0.553690:0.125128:0.536554:0.115361:0.536554:0.000000:0.000000
La condición ( ) representa una recta con pendiente :@0.148605:0.553690:0.508920:0.553690:0.508920:0.537301:0.148605:0.537301:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
b:@0.243968:0.553690:0.253237:0.553690:0.253237:0.537329:0.243968:0.537329:0.000000
m:@0.508367:0.553690:0.522999:0.553690:0.522999:0.537329:0.508367:0.537329:0.000000
2:@0.522431:0.555602:0.527674:0.555602:0.527674:0.546047:0.522431:0.546047:0.000000
 = –2 3 y corta los ejes en los puntos (0,14) y (21, 0).:@0.527351:0.553695:0.874896:0.553695:0.874896:0.537306:0.527351:0.537306:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.561848:0.554276:0.571062:0.554276:0.571062:0.536670:0.561848:0.536670:0.000000
• :@0.115346:0.577414:0.125297:0.577414:0.125297:0.560278:0.115346:0.560278:0.000000:0.000000
Las condiciones ( ) y ( ) nos indican que las soluciones factibles son positivas.:@0.148590:0.577414:0.715258:0.577414:0.715258:0.561025:0.148590:0.561025:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
c:@0.274377:0.577414:0.282043:0.577414:0.282043:0.561053:0.274377:0.561053:0.000000
d:@0.307989:0.577414:0.317258:0.577414:0.317258:0.561053:0.307989:0.561053:0.000000
Vértices de la región factible:@0.115354:0.610095:0.360766:0.610095:0.360766:0.591658:0.115354:0.591658:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Los vértices:@0.115354:0.629942:0.200637:0.629942:0.200637:0.613553:0.115354:0.613553:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 A, B, D:@0.200637:0.629942:0.247259:0.629942:0.247259:0.613580:0.200637:0.613580:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 están determinados así   = (0, 0),    = (0, 14),    = (9, 0). :@0.247259:0.629942:0.656386:0.629942:0.656386:0.613553:0.247259:0.613553:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.425174:0.629942:0.435070:0.629942:0.435070:0.613580:0.425174:0.613580:0.000000
B:@0.500396:0.629942:0.509241:0.629942:0.509241:0.613580:0.500396:0.613580:0.000000
D:@0.583560:0.629942:0.595096:0.629942:0.595096:0.613580:0.583560:0.613580:0.000000
El vértice   se obtiene al resolver el siguiente sistema de ecuaciones:  :@0.115354:0.664490:0.623786:0.664490:0.623786:0.648101:0.115354:0.648101:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
C:@0.185619:0.664490:0.195533:0.664490:0.195533:0.648129:0.185619:0.648129:0.000000
2  +   = 18:@0.631204:0.654893:0.703960:0.654893:0.703960:0.639994:0.631204:0.639994:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.639380:0.654893:0.646164:0.654893:0.646164:0.640019:0.639380:0.640019:0.000000
y:@0.663486:0.654893:0.670288:0.654893:0.670288:0.640019:0.663486:0.640019:0.000000
2  + 3  = 42:@0.631204:0.673539:0.712135:0.673539:0.712135:0.658640:0.631204:0.658640:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.639380:0.673539:0.646164:0.673539:0.646164:0.658665:0.639380:0.658665:0.000000
y:@0.671661:0.673539:0.678463:0.673539:0.678463:0.658665:0.671661:0.658665:0.000000
 :@0.722967:0.664485:0.727003:0.664485:0.727003:0.648096:0.722967:0.648096:0.000000
cuya solución es:    = 3,    = 12,    = (3, 12):@0.115353:0.681081:0.422652:0.681081:0.422652:0.664692:0.115353:0.664692:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.247110:0.681081:0.254574:0.681081:0.254574:0.664720:0.247110:0.664720:0.000000
y:@0.293898:0.681081:0.301380:0.681081:0.301380:0.664720:0.293898:0.664720:0.000000
C:@0.349697:0.681081:0.359611:0.681081:0.359611:0.664720:0.349697:0.664720:0.000000
Valor óptimo:@0.115354:0.730354:0.228393:0.730354:0.228393:0.711917:0.115354:0.711917:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Calculamos:@0.115354:0.750199:0.203567:0.750199:0.203567:0.733575:0.115354:0.733575:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
   = 5  + 3  en los vértices del polígono.:@0.203567:0.750199:0.497742:0.750199:0.497742:0.733810:0.203567:0.733810:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
C:@0.207603:0.750199:0.217517:0.750199:0.217517:0.733838:0.207603:0.733838:0.000000
x:@0.245564:0.750199:0.253027:0.750199:0.253027:0.733838:0.245564:0.733838:0.000000
y:@0.281074:0.750199:0.288556:0.750199:0.288556:0.733838:0.281074:0.733838:0.000000
A:@0.417368:0.774675:0.426364:0.774675:0.426364:0.759801:0.417368:0.759801:0.000000
 =  0, 0:@0.426364:0.774675:0.472199:0.774675:0.472199:0.759776:0.426364:0.759776:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(:@0.443686:0.775291:0.449265:0.775291:0.449265:0.761134:0.443686:0.761134:0.000000
):@0.472199:0.775291:0.477778:0.775291:0.477778:0.761134:0.472199:0.761134:0.000000
C:@0.516677:0.774675:0.525689:0.774675:0.525689:0.759801:0.516677:0.759801:0.000000
 = 0:@0.525689:0.774675:0.551187:0.774675:0.551187:0.759776:0.525689:0.759776:0.000000:0.000000:0.000000:0.000000
B:@0.417368:0.794402:0.425410:0.794402:0.425410:0.779528:0.417368:0.779528:0.000000
 =  0, 14:@0.425410:0.794402:0.479419:0.794402:0.479419:0.779503:0.425410:0.779503:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(:@0.442732:0.795018:0.448310:0.795018:0.448310:0.780861:0.442732:0.780861:0.000000
):@0.479419:0.795018:0.484998:0.795018:0.484998:0.780861:0.479419:0.780861:0.000000
C:@0.516677:0.794402:0.525689:0.794402:0.525689:0.779528:0.516677:0.779528:0.000000
 = 42:@0.525689:0.794402:0.559362:0.794402:0.559362:0.779503:0.525689:0.779503:0.000000:0.000000:0.000000:0.000000:0.000000
C:@0.417368:0.814129:0.426381:0.814129:0.426381:0.799255:0.417368:0.799255:0.000000
 =  3, 12:@0.426381:0.814129:0.480391:0.814129:0.480391:0.799230:0.426381:0.799230:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(:@0.443703:0.814745:0.449282:0.814745:0.449282:0.800588:0.443703:0.800588:0.000000
):@0.480391:0.814745:0.485969:0.814745:0.485969:0.800588:0.480391:0.800588:0.000000
C:@0.516677:0.814129:0.525689:0.814129:0.525689:0.799255:0.516677:0.799255:0.000000
 = 51:@0.525689:0.814129:0.559362:0.814129:0.559362:0.799230:0.525689:0.799230:0.000000:0.000000:0.000000:0.000000:0.000000
D:@0.417368:0.833856:0.427855:0.833856:0.427855:0.818982:0.417368:0.818982:0.000000
 =  9, 0:@0.427855:0.833856:0.473690:0.833856:0.473690:0.818957:0.427855:0.818957:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(:@0.445177:0.834472:0.450756:0.834472:0.450756:0.820315:0.445177:0.820315:0.000000
):@0.473690:0.834472:0.479268:0.834472:0.479268:0.820315:0.473690:0.820315:0.000000
C:@0.516677:0.833856:0.525689:0.833856:0.525689:0.818982:0.516677:0.818982:0.000000
 = 45:@0.525689:0.833856:0.559362:0.833856:0.559362:0.818957:0.525689:0.818957:0.000000:0.000000:0.000000:0.000000:0.000000
De la tabla :@0.115354:0.859815:0.197210:0.859815:0.197210:0.843426:0.115354:0.843426:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
obtenemos:@0.197210:0.859815:0.285275:0.859815:0.285275:0.843191:0.197210:0.843191:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 que los valores   = 3,    = 12 proporcionan el valor  :@0.285275:0.859815:0.662745:0.859815:0.662745:0.843426:0.285275:0.843426:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.402162:0.859815:0.409625:0.859815:0.409625:0.843454:0.402162:0.843454:0.000000
y:@0.448950:0.859815:0.456431:0.859815:0.456431:0.843454:0.448950:0.843454:0.000000
máximo :@0.115354:0.876412:0.179501:0.876412:0.179501:0.860023:0.115354:0.860023:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
C  :@0.179501:0.876412:0.211016:0.876412:0.211016:0.860050:0.179501:0.860050:0.000000:0.000000:0.000000
max:@0.189413:0.878318:0.207699:0.878318:0.207699:0.868780:0.189413:0.868780:0.000000:0.000000:0.000000
= 5(3) + 3(12) = 51:@0.211016:0.876412:0.346625:0.876412:0.346625:0.860023:0.211016:0.860023:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Shutterstock, 324410132.:@0.894842:0.913425:0.894842:0.825599:0.880946:0.825599:0.880946:0.913425:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000