65:@0.942817:0.963886:0.964167:0.963886:0.964167:0.945448:0.942817:0.945448:0.000000:0.000000
Ejemplo:@0.096359:0.132503:0.153719:0.132503:0.153719:0.117390:0.096359:0.117390:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Un fabricante de:@0.096359:0.156542:0.218954:0.156542:0.218954:0.140872:0.096359:0.140872:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 jeans:@0.218954:0.156542:0.259016:0.156542:0.259016:0.140180:0.218954:0.140180:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 obtiene una ganancia de $ 30 por cada :@0.259016:0.156542:0.555452:0.156542:0.555452:0.140872:0.259016:0.140872:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
jean:@0.555631:0.156542:0.585834:0.156542:0.585834:0.140180:0.555631:0.140180:0.000000:0.000000:0.000000:0.000000
 de marca Blue :@0.585834:0.156542:0.698729:0.156542:0.698729:0.140872:0.585834:0.140872:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y $ 15 por cada :@0.096359:0.173138:0.210979:0.173138:0.210979:0.157468:0.096359:0.157468:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
jean:@0.210721:0.173138:0.240924:0.173138:0.240924:0.156777:0.210721:0.156777:0.000000:0.000000:0.000000:0.000000
 de marca Victoria. Para la fabricación de sus pantalones, utiliza :@0.240924:0.173138:0.698705:0.173138:0.698705:0.157468:0.240924:0.157468:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
dos máquinas: A y B. Para la fabricación del pantalón de marca Blue, la máquina :@0.096359:0.189734:0.698759:0.189734:0.698759:0.174065:0.096359:0.174065:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A demora 15 minutos y la máquina B, 9 minutos. Para la elaboración del pantalón :@0.096359:0.206331:0.698777:0.206331:0.698777:0.190661:0.096359:0.190661:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de marca Victoria, la máquina A demora 5 minutos y la máquina B, 3 minutos.  :@0.096359:0.222927:0.698740:0.222927:0.698740:0.207257:0.096359:0.207257:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Si diariamente cuenta con la máquina A un máximo de 200 minutos y con la B, :@0.096359:0.239523:0.698775:0.239523:0.698775:0.223854:0.096359:0.223854:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
un máximo de 90 minutos, ¿cuántos pantalones de cada tipo debe producir para :@0.096359:0.256120:0.698740:0.256120:0.698740:0.240450:0.096359:0.240450:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
obtener la máxima utilidad?:@0.096359:0.272716:0.300685:0.272716:0.300685:0.257046:0.096359:0.257046:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Identificamos las variables y organizamos en una tabla.:@0.096359:0.296435:0.497083:0.296435:0.497083:0.280765:0.096359:0.280765:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Solución:@0.096359:0.314778:0.157020:0.314778:0.157020:0.299665:0.096359:0.299665:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.197977:0.340456:0.201361:0.340456:0.201361:0.324878:0.197977:0.324878:0.000000
Máquina A :@0.329752:0.340456:0.413564:0.340456:0.413564:0.324878:0.329752:0.324878:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Máquina B:@0.458410:0.340456:0.537967:0.340456:0.537967:0.324878:0.458410:0.324878:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Ganancia:@0.591474:0.340456:0.661349:0.340456:0.661349:0.324878:0.591474:0.324878:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Pantalones marca Blue :@0.103996:0.361842:0.258085:0.361842:0.258085:0.346730:0.103996:0.346730:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(x):@0.257750:0.361842:0.273983:0.361842:0.273983:0.346717:0.257750:0.346717:0.000000:0.000000:0.000000
15:@0.361799:0.361842:0.378149:0.361842:0.378149:0.347597:0.361799:0.347597:0.000000:0.000000
9:@0.494109:0.361842:0.502285:0.361842:0.502285:0.347597:0.494109:0.347597:0.000000
$ 30:@0.612314:0.361842:0.640509:0.361842:0.640509:0.347597:0.612314:0.347597:0.000000:0.000000:0.000000:0.000000
Pantalones marca Victoria :@0.103996:0.383229:0.278389:0.383229:0.278389:0.368116:0.103996:0.368116:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(y):@0.278054:0.383229:0.294287:0.383229:0.294287:0.368104:0.278054:0.368104:0.000000:0.000000:0.000000
5:@0.365887:0.383229:0.374062:0.383229:0.374062:0.368984:0.365887:0.368984:0.000000
3:@0.494109:0.383229:0.502285:0.383229:0.502285:0.368984:0.494109:0.368984:0.000000
$ 15:@0.612314:0.383229:0.640509:0.383229:0.640509:0.368984:0.612314:0.368984:0.000000:0.000000:0.000000:0.000000
Tiempo disponible :@0.103996:0.404616:0.232370:0.404616:0.232370:0.389503:0.103996:0.389503:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(min):@0.232035:0.404616:0.266528:0.404616:0.266528:0.389490:0.232035:0.389490:0.000000:0.000000:0.000000:0.000000:0.000000
200:@0.357711:0.404616:0.382237:0.404616:0.382237:0.390371:0.357711:0.390371:0.000000:0.000000:0.000000
90:@0.490022:0.404616:0.506372:0.404616:0.506372:0.390371:0.490022:0.390371:0.000000:0.000000
Como la producción de un artículo no puede ser negativa tenemos:   ≥ 0,   ≥ 0.  :@0.096359:0.449659:0.698740:0.449659:0.698740:0.433989:0.096359:0.433989:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.608353:0.449659:0.615834:0.449659:0.615834:0.433297:0.608353:0.433297:0.000000
x:@0.653998:0.449659:0.661461:0.449659:0.661461:0.433297:0.653998:0.433297:0.000000
Al referirse el problema a la máxima ganancia, significa menor o igual ≤. Entonces, :@0.096359:0.466255:0.698814:0.466255:0.698814:0.450585:0.096359:0.450585:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
15  + 5  ≤ 200; 9  + 3  ≤ 90:@0.096359:0.489974:0.299634:0.489974:0.299634:0.474304:0.096359:0.474304:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.114344:0.489974:0.121808:0.489974:0.121808:0.473613:0.114344:0.473613:0.000000
y:@0.149855:0.489974:0.157336:0.489974:0.157336:0.473613:0.149855:0.473613:0.000000
x:@0.219603:0.489974:0.227066:0.489974:0.227066:0.473613:0.219603:0.473613:0.000000
y:@0.255113:0.489974:0.262595:0.489974:0.262595:0.473613:0.255113:0.473613:0.000000
Por lo tanto, el sistema de inecuaciones es::@0.096359:0.513693:0.407526:0.513693:0.407526:0.498023:0.096359:0.498023:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.123511:0.537900:0.131417:0.537900:0.136010:0.522230:0.128105:0.522230:0.000000
y:@0.157234:0.537900:0.165342:0.537900:0.169935:0.522230:0.161827:0.522230:0.000000
x:@0.116656:0.558645:0.124562:0.558645:0.129155:0.542975:0.121249:0.542975:0.000000
y:@0.150379:0.558645:0.158487:0.558645:0.163080:0.542975:0.154972:0.542975:0.000000
y:@0.108235:0.579391:0.116343:0.579391:0.120936:0.563721:0.112828:0.563721:0.000000
x:@0.107498:0.600136:0.115403:0.600136:0.119996:0.584466:0.112091:0.584466:0.000000
15:@0.106987:0.537900:0.124769:0.537900:0.124769:0.522230:0.106987:0.522230:0.000000:0.000000
5:@0.148762:0.537900:0.157755:0.537900:0.157755:0.522230:0.148762:0.522230:0.000000
200:@0.184733:0.537900:0.211305:0.537900:0.211305:0.522230:0.184733:0.522230:0.000000:0.000000:0.000000
9:@0.108147:0.558645:0.117140:0.558645:0.117140:0.542975:0.108147:0.542975:0.000000
3:@0.141907:0.558645:0.150900:0.558645:0.150900:0.542975:0.141907:0.542975:0.000000
90:@0.177878:0.558645:0.195660:0.558645:0.195660:0.542975:0.177878:0.542975:0.000000:0.000000
0:@0.135734:0.579391:0.144726:0.579391:0.144726:0.563721:0.135734:0.563721:0.000000
0:@0.134223:0.600136:0.143215:0.600136:0.143215:0.584466:0.134223:0.584466:0.000000
+:@0.136637:0.538577:0.146753:0.538577:0.146753:0.523005:0.136637:0.523005:0.000000
≤:@0.172073:0.538577:0.182190:0.538577:0.182190:0.523005:0.172073:0.523005:0.000000
+:@0.129781:0.559323:0.139898:0.559323:0.139898:0.543750:0.129781:0.543750:0.000000
≤:@0.165218:0.559323:0.175335:0.559323:0.175335:0.543750:0.165218:0.543750:0.000000
≥:@0.123074:0.580068:0.133191:0.580068:0.133191:0.564495:0.123074:0.564495:0.000000
≥:@0.121563:0.600814:0.131680:0.600814:0.131680:0.585241:0.121563:0.585241:0.000000
Graficando las rectas, obtenemos: :@0.096391:0.622514:0.347003:0.622514:0.347003:0.606844:0.096391:0.606844:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(Ilustración 1):@0.347003:0.622514:0.441682:0.622514:0.441682:0.606152:0.347003:0.606152:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sombreamos la solución de cada inecuación; recuerda que la solución del sistema es :@0.096391:0.646233:0.698731:0.646233:0.698731:0.630563:0.096391:0.630563:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
la intersección de las regiones sombreadas (región factible). :@0.096391:0.662829:0.525146:0.662829:0.525146:0.647159:0.096391:0.647159:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(Ilustración 2):@0.524962:0.662829:0.619643:0.662829:0.619643:0.646468:0.524962:0.646468:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Verificamos la solución tomando un punto de la intersección de las regiones :@0.096391:0.686548:0.698696:0.686548:0.698696:0.670878:0.096391:0.670878:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
sombreadas. P (0, 10):@0.096391:0.703144:0.250444:0.703144:0.250444:0.687475:0.096391:0.687475:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
15(0)5(10) 200 50 200:@0.120102:0.725215:0.323996:0.725215:0.323996:0.709545:0.120102:0.709545:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
9(0) 3(10)90:@0.121245:0.745947:0.233020:0.745950:0.233020:0.730281:0.121245:0.730277:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
10 0:@0.120102:0.766696:0.162449:0.766696:0.162449:0.751026:0.120102:0.751026:0.000000:0.000000:0.000000:0.000000
;:@0.250352:0.756166:0.253558:0.756166:0.253558:0.740496:0.250352:0.740496:0.000000
30 90:@0.264069:0.745950:0.315206:0.745950:0.315206:0.730281:0.264069:0.730281:0.000000:0.000000:0.000000:0.000000:0.000000
10 0:@0.262916:0.766696:0.305263:0.766696:0.305263:0.751026:0.262916:0.751026:0.000000:0.000000:0.000000:0.000000
+:@0.158790:0.725893:0.168907:0.725893:0.168907:0.710320:0.158790:0.710320:0.000000
≤:@0.209411:0.725893:0.219528:0.725893:0.219528:0.710320:0.209411:0.710320:0.000000
+:@0.151935:0.746624:0.162052:0.746624:0.162052:0.731051:0.151935:0.731051:0.000000
≤:@0.202556:0.746624:0.212673:0.746624:0.212673:0.731051:0.202556:0.731051:0.000000
≥:@0.140781:0.767374:0.150898:0.767374:0.150898:0.751801:0.140781:0.751801:0.000000
≤:@0.284748:0.725893:0.294865:0.725893:0.294865:0.710320:0.284748:0.710320:0.000000
≤:@0.284748:0.746624:0.294865:0.746624:0.294865:0.731051:0.284748:0.731051:0.000000
≥:@0.283595:0.767374:0.293712:0.767374:0.293712:0.751801:0.283595:0.751801:0.000000
La solución satisface el sistema de inecuaciones.:@0.096359:0.791486:0.448303:0.791486:0.448303:0.775816:0.096359:0.775816:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
La función que representa la ganancia :@0.388400:0.815205:0.698759:0.815205:0.698759:0.799535:0.388400:0.799535:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
máxima es f(x, y) = 30  + 15 . Para :@0.388400:0.831801:0.698724:0.831801:0.698724:0.816132:0.388400:0.816132:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.582425:0.831801:0.589888:0.831801:0.589888:0.815440:0.582425:0.815440:0.000000
y:@0.642075:0.831801:0.649557:0.831801:0.649557:0.815440:0.642075:0.815440:0.000000
determinar la ganancia máxima, reemplazo :@0.388400:0.848398:0.698722:0.848398:0.698722:0.832728:0.388400:0.832728:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
los vértices en esta función.:@0.388400:0.864994:0.584729:0.864994:0.584729:0.849324:0.388400:0.849324:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
La ganancia máxima es $ 450 y se produce :@0.388400:0.888713:0.698759:0.888713:0.698759:0.873043:0.388400:0.873043:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cuando se fabrican 30 pantalones marca :@0.388400:0.905310:0.698740:0.905310:0.698740:0.889640:0.388400:0.889640:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Victoria.:@0.388400:0.921906:0.446263:0.921906:0.446263:0.906236:0.388400:0.906236:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Vértice:@0.121663:0.824821:0.174132:0.824821:0.174132:0.809243:0.121663:0.809243:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f(x, y) = 30x + 15y:@0.217001:0.824821:0.346581:0.824821:0.346581:0.809243:0.217001:0.809243:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(0, 30):@0.103990:0.850294:0.143978:0.850294:0.143978:0.836049:0.103990:0.836049:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
30(0) + 15(30) = 450 :@0.214706:0.850294:0.352528:0.850294:0.352528:0.836049:0.214706:0.836049:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(0, 0):@0.103990:0.873981:0.135802:0.873981:0.135802:0.859736:0.103990:0.859736:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
30(0) + 15(0) = 0:@0.226969:0.873981:0.336597:0.873981:0.336597:0.859736:0.226969:0.859736:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(10, 0):@0.103990:0.897669:0.143978:0.897669:0.143978:0.883424:0.103990:0.883424:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
30(10) + 15(0) = 30:@0.218794:0.897669:0.344772:0.897669:0.344772:0.883424:0.218794:0.883424:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Shutterstock, 444837757.:@0.920815:0.267815:0.920815:0.192536:0.909426:0.192536:0.909426:0.267815:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.798328:0.651893:0.804062:0.651893:0.804062:0.640811:0.798328:0.640811:0.000000
x:@0.894465:0.717385:0.900056:0.717385:0.900056:0.706303:0.894465:0.706303:0.000000
0:@0.802184:0.722448:0.807131:0.722448:0.807131:0.713829:0.802184:0.713829:0.000000
60:@0.795187:0.669486:0.805080:0.669486:0.805080:0.660867:0.795187:0.660867:0.000000:0.000000
40:@0.795187:0.684889:0.805080:0.684889:0.805080:0.676270:0.795187:0.676270:0.000000:0.000000
20:@0.795187:0.700292:0.805080:0.700292:0.805080:0.691673:0.795187:0.691673:0.000000:0.000000
–20:@0.790119:0.731094:0.805080:0.731094:0.805080:0.722475:0.790119:0.722475:0.000000:0.000000:0.000000
–40:@0.790119:0.746499:0.805080:0.746499:0.805080:0.737880:0.790119:0.737880:0.000000:0.000000:0.000000
20:@0.825742:0.722448:0.835634:0.722448:0.835634:0.713829:0.825742:0.713829:0.000000:0.000000
–20:@0.781346:0.722448:0.796306:0.722448:0.796306:0.713829:0.781346:0.713829:0.000000:0.000000:0.000000
–40:@0.760820:0.722448:0.775781:0.722448:0.775781:0.713829:0.760820:0.713829:0.000000:0.000000:0.000000
–60:@0.740295:0.722448:0.755256:0.722448:0.755256:0.713829:0.740295:0.713829:0.000000:0.000000:0.000000
40:@0.846267:0.722448:0.856160:0.722448:0.856160:0.713829:0.846267:0.713829:0.000000:0.000000
60:@0.866792:0.722448:0.876685:0.722448:0.876685:0.713829:0.866792:0.713829:0.000000:0.000000
3x + y = 40:@0.728167:0.665264:0.780446:0.665264:0.780446:0.654814:0.728167:0.654814:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3x + y = 30:@0.732917:0.676679:0.785196:0.676679:0.785196:0.666229:0.732917:0.666229:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Ilustración 1:@0.842387:0.771318:0.904143:0.771318:0.904143:0.759419:0.842387:0.759419:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
La región factible :@0.732565:0.344508:0.851187:0.344508:0.851187:0.330263:0.732565:0.330263:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
puede ser::@0.732565:0.359596:0.802270:0.359596:0.802270:0.345350:0.732565:0.345350:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Acotada:@0.732565:0.381812:0.788082:0.381812:0.788082:0.367567:0.732565:0.367567:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.732565:0.470678:0.736234:0.470678:0.736234:0.456433:0.732565:0.456433:0.000000
No acotada:@0.732565:0.492895:0.809324:0.492895:0.809324:0.478649:0.732565:0.478649:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿Sabías que?:@0.765136:0.319997:0.867004:0.319997:0.867004:0.303096:0.765136:0.303096:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Y:@0.752302:0.397693:0.759312:0.397693:0.759312:0.385842:0.752302:0.385842:0.000000
X:@0.874409:0.458063:0.882019:0.458063:0.882019:0.446213:0.874409:0.446213:0.000000
Y:@0.753192:0.511965:0.759933:0.511965:0.759933:0.500569:0.753192:0.500569:0.000000
X:@0.874238:0.581167:0.881556:0.581167:0.881556:0.569771:0.874238:0.569771:0.000000
Archivo Editorial:@0.628333:0.418916:0.689949:0.418916:0.689949:0.410309:0.628333:0.410309:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Archivo Editorial:@0.304928:0.913707:0.366544:0.913707:0.366544:0.905100:0.304928:0.905100:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Ilustración 2:@0.841412:0.949749:0.903168:0.949749:0.903168:0.937850:0.841412:0.937850:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.798896:0.799357:0.804630:0.799357:0.804630:0.788275:0.798896:0.788275:0.000000
x:@0.895672:0.902182:0.901262:0.902182:0.901262:0.891100:0.895672:0.891100:0.000000
0:@0.787504:0.900704:0.792451:0.900704:0.792451:0.892084:0.787504:0.892084:0.000000
30:@0.777835:0.809989:0.787728:0.809989:0.787728:0.801370:0.777835:0.801370:0.000000:0.000000
25:@0.777835:0.824086:0.787728:0.824086:0.787728:0.815467:0.777835:0.815467:0.000000:0.000000
20:@0.777835:0.838182:0.787728:0.838182:0.787728:0.829563:0.777835:0.829563:0.000000:0.000000
15:@0.777835:0.852289:0.787728:0.852289:0.787728:0.843670:0.777835:0.843670:0.000000:0.000000
10:@0.777835:0.866659:0.787728:0.866659:0.787728:0.858040:0.777835:0.858040:0.000000:0.000000
5:@0.782781:0.881029:0.787728:0.881029:0.787728:0.872410:0.782781:0.872410:0.000000
–5:@0.778937:0.909352:0.788951:0.909352:0.788951:0.900733:0.778937:0.900733:0.000000:0.000000
–10:@0.773991:0.923685:0.788951:0.923685:0.788951:0.915066:0.773991:0.915066:0.000000:0.000000:0.000000
5:@0.810797:0.900704:0.815743:0.900704:0.815743:0.892084:0.810797:0.892084:0.000000
10 15 20:@0.828160:0.900704:0.875698:0.900704:0.875698:0.892084:0.828160:0.892084:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
–5:@0.770780:0.900704:0.780794:0.900704:0.780794:0.892084:0.770780:0.892084:0.000000:0.000000
–10:@0.749372:0.900704:0.764333:0.900704:0.764333:0.892084:0.749372:0.892084:0.000000:0.000000:0.000000
 ©:@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