151:@0.916858:0.966074:0.945034:0.966074:0.945034:0.949450:0.916858:0.949450:0.000000:0.000000:0.000000 2.:@0.108233:0.121435:0.120505:0.121435:0.120505:0.104721:0.108233:0.104721:0.000000:0.000000 Considerar el conjunto de restricciones: :@0.120506:0.121218:0.424179:0.121218:0.424179:0.104721:0.120506:0.104721:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.108233:0.173271:0.112375:0.173271:0.112375:0.156773:0.108233:0.156773:0.000000 Determinemos gráficamente el conjunto .:@0.131968:0.173271:0.436243:0.173271:0.436243:0.156773:0.131968:0.156773:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 S:@0.425609:0.173386:0.433488:0.173386:0.433488:0.156917:0.425609:0.156917:0.000000 :@0.108233:0.204949:0.112375:0.204949:0.112375:0.188452:0.108233:0.188452:0.000000 Asociada con la restricción + 3 ≤ 9, tenemos el conjunto:@0.131968:0.204949:0.551216:0.204949:0.551216:0.188452:0.131968:0.188452:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.326410:0.205065:0.333885:0.205065:0.333885:0.188596:0.326410:0.188596:0.000000 y:@0.361473:0.205065:0.369160:0.205065:0.369160:0.188596:0.361473:0.188596:0.000000 :@0.108233:0.229429:0.112375:0.229429:0.112375:0.212931:0.108233:0.212931:0.000000 L:@0.261296:0.229545:0.269137:0.229545:0.269137:0.213076:0.261296:0.213076:0.000000 1:@0.269143:0.232711:0.274096:0.232711:0.274096:0.223093:0.269143:0.223093:0.000000 = {( , ) | + 3 = 9},:@0.274097:0.229433:0.466445:0.229433:0.466445:0.212935:0.274097:0.212935:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x y:@0.304998:0.229549:0.327057:0.229549:0.327057:0.213080:0.304998:0.213080:0.000000:0.000000:0.000000 :@0.337150:0.228914:0.351802:0.228914:0.351802:0.215541:0.337150:0.215541:0.000000 R:@0.355944:0.228346:0.369249:0.228346:0.369249:0.215484:0.355944:0.215484:0.000000 2:@0.369249:0.223081:0.374202:0.223081:0.374202:0.213463:0.369249:0.213463:0.000000 x:@0.387496:0.229549:0.394970:0.229549:0.394970:0.213080:0.387496:0.213080:0.000000 y:@0.422558:0.229549:0.430245:0.229549:0.430245:0.213080:0.422558:0.213080:0.000000 :@0.108226:0.261040:0.112368:0.261040:0.112368:0.244543:0.108226:0.244543:0.000000 que representa una recta de pendiente :@0.131961:0.261040:0.411708:0.261040:0.411708:0.244543:0.131961:0.244543:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 m:@0.411708:0.261156:0.426504:0.261156:0.426504:0.244687:0.411708:0.244687:0.000000 1:@0.426519:0.264317:0.431472:0.264317:0.431472:0.254699:0.426519:0.254699:0.000000 = – y que corta al:@0.431472:0.261040:0.582184:0.261040:0.582184:0.244543:0.431472:0.244543:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 eje en el punto (9, 0) y al eje en el punto (0, 3).:@0.131975:0.285519:0.477728:0.285519:0.477728:0.269021:0.131975:0.269021:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.156018:0.285634:0.163493:0.285634:0.163493:0.269166:0.156018:0.269166:0.000000 y:@0.345262:0.285634:0.352949:0.285634:0.352949:0.269166:0.345262:0.269166:0.000000 :@0.108239:0.317951:0.112381:0.317951:0.112381:0.301453:0.108239:0.301453:0.000000 La restricción + 3 ≤ 9 representa el semiplano que se extiende :@0.131975:0.317951:0.599923:0.317957:0.599923:0.301459:0.131975:0.301453:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.228763:0.318066:0.236238:0.318066:0.236238:0.301598:0.228763:0.301598:0.000000 y:@0.262362:0.318066:0.270049:0.318066:0.270049:0.301598:0.262362:0.301598:0.000000 S:@0.469864:0.318066:0.477744:0.318066:0.477744:0.301598:0.469864:0.301598:0.000000 1:@0.477704:0.321234:0.482657:0.321234:0.482657:0.311616:0.477704:0.311616:0.000000 bajo la recta .:@0.131972:0.335308:0.238224:0.335308:0.238224:0.318810:0.131972:0.318810:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 L:@0.222671:0.335423:0.230512:0.335423:0.230512:0.318955:0.222671:0.318955:0.000000 1:@0.230517:0.338586:0.235470:0.338586:0.235470:0.328968:0.230517:0.328968:0.000000 :@0.108242:0.367740:0.112384:0.367740:0.112384:0.351242:0.108242:0.351242:0.000000 La restricción – ≤ 3 se asocia al conjunto:@0.131976:0.367740:0.443590:0.367740:0.443590:0.351242:0.131976:0.351242:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x y:@0.230229:0.367855:0.264174:0.367855:0.264174:0.351387:0.230229:0.351387:0.000000:0.000000:0.000000 :@0.108242:0.385091:0.112384:0.385091:0.112384:0.368593:0.108242:0.368593:0.000000 L:@0.131976:0.385206:0.139817:0.385206:0.139817:0.368737:0.131976:0.368737:0.000000 2:@0.139818:0.388375:0.144771:0.388375:0.144771:0.378757:0.139818:0.378757:0.000000 = {( , ) | – = 3}, que representa una recta de pen-:@0.144770:0.385097:0.568605:0.385097:0.568605:0.368599:0.144770:0.368599:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x y:@0.175671:0.385213:0.197730:0.385213:0.197730:0.368744:0.175671:0.368744:0.000000:0.000000:0.000000 :@0.207824:0.384578:0.222477:0.384578:0.222477:0.371205:0.207824:0.371205:0.000000 R:@0.226619:0.384010:0.239924:0.384010:0.239924:0.371148:0.226619:0.371148:0.000000 2:@0.239922:0.378745:0.244875:0.378745:0.244875:0.369127:0.239922:0.369127:0.000000 x y:@0.258169:0.385213:0.292114:0.385213:0.292114:0.368744:0.258169:0.368744:0.000000:0.000000:0.000000 diente :@0.131981:0.402448:0.181088:0.402448:0.181088:0.385950:0.131981:0.385950:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 m:@0.181088:0.402563:0.195884:0.402563:0.195884:0.386095:0.181088:0.386095:0.000000 2:@0.195878:0.405725:0.200831:0.405725:0.200831:0.396107:0.195878:0.396107:0.000000 = 1, y que corta al eje en el punto (3, 0) y al eje :@0.200832:0.402448:0.560842:0.402448:0.560842:0.385950:0.200832:0.385950:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.359770:0.402563:0.367245:0.402563:0.367245:0.386095:0.359770:0.386095:0.000000 y:@0.549013:0.402563:0.556700:0.402563:0.556700:0.386095:0.549013:0.386095:0.000000 en el punto (0, –3). A la restricción x – y ≤ 3 se le denota con :@0.131978:0.419798:0.585245:0.419798:0.585245:0.403301:0.131978:0.403301:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 S:@0.568278:0.419914:0.576158:0.419914:0.576158:0.403445:0.568278:0.403445:0.000000 2:@0.576149:0.423076:0.581102:0.423076:0.581102:0.413458:0.576149:0.413458:0.000000 y es el semiplano que se extiende hacia arriba de .:@0.131972:0.437149:0.494506:0.437149:0.494506:0.420651:0.131972:0.420651:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 L:@0.478955:0.437265:0.486796:0.437265:0.486796:0.420796:0.478955:0.420796:0.000000 2:@0.486799:0.440427:0.491752:0.440427:0.491752:0.430809:0.486799:0.430809:0.000000 :@0.108238:0.469581:0.112380:0.469581:0.112380:0.453083:0.108238:0.453083:0.000000 En la Figura 5.6., se muestra la recta y el semiplano , mientras :@0.131973:0.469581:0.599910:0.469587:0.599910:0.453090:0.131973:0.453083:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 L:@0.388320:0.469697:0.396161:0.469697:0.396161:0.453228:0.388320:0.453228:0.000000 1:@0.396151:0.472865:0.401105:0.472865:0.401105:0.463247:0.396151:0.463247:0.000000 S:@0.513293:0.469703:0.521172:0.469703:0.521172:0.453234:0.513293:0.453234:0.000000 1:@0.521163:0.472865:0.526116:0.472865:0.526116:0.463247:0.521163:0.463247:0.000000 que en la Figura 5.7. se muestra a la recta y el semiplano .:@0.131967:0.486938:0.561684:0.486938:0.561684:0.470441:0.131967:0.470441:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 L:@0.423543:0.487054:0.431384:0.487054:0.431384:0.470585:0.423543:0.470585:0.000000 2:@0.431392:0.490216:0.436345:0.490216:0.436345:0.480598:0.431392:0.480598:0.000000 S:@0.546098:0.487054:0.553977:0.487054:0.553977:0.470585:0.546098:0.470585:0.000000 2:@0.553977:0.490216:0.558931:0.490216:0.558931:0.480598:0.553977:0.480598:0.000000 :@0.108239:0.519370:0.112381:0.519370:0.112381:0.502873:0.108239:0.502873:0.000000 Tomando en cuenta la no negatividad de las soluciones factibles :@0.131973:0.519370:0.599882:0.519370:0.599882:0.502873:0.131973:0.502873:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y la intersección de los dos semiplanos y , se obtiene la región :@0.131973:0.536721:0.599941:0.536727:0.599941:0.520230:0.131973:0.520223:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 S:@0.409316:0.536837:0.417195:0.536837:0.417195:0.520368:0.409316:0.520368:0.000000 1:@0.417144:0.540005:0.422097:0.540005:0.422097:0.530387:0.417144:0.530387:0.000000 S:@0.438086:0.536843:0.445966:0.536843:0.445966:0.520374:0.438086:0.520374:0.000000 2:@0.445951:0.540005:0.450905:0.540005:0.450905:0.530387:0.445951:0.530387:0.000000 factible que se muestra en la Figura 5.8.:@0.131969:0.554078:0.407980:0.554078:0.407980:0.537580:0.131969:0.537580:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Competencia digital:@0.684804:0.630133:0.827156:0.630133:0.827156:0.614661:0.684804:0.614661:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Existen programas com-:@0.685042:0.658762:0.841786:0.658762:0.841786:0.643699:0.685042:0.643699:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 putacionales que te permiten :@0.638498:0.674604:0.833499:0.674604:0.833499:0.659541:0.638498:0.659541:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 graficar inecuaciones de primer :@0.638498:0.690446:0.845742:0.690446:0.845742:0.675383:0.638498:0.675383:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 grado y obtener la región facti-:@0.638498:0.706288:0.838407:0.706288:0.838407:0.691225:0.638498:0.691225:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ble. :@0.638498:0.722130:0.664618:0.722130:0.664618:0.707067:0.638498:0.707067:0.000000:0.000000:0.000000:0.000000:0.000000 Profundiza:@0.664618:0.722328:0.737966:0.722328:0.737966:0.707067:0.664618:0.707067:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 sobre este tema :@0.737966:0.722130:0.847974:0.722130:0.847974:0.707067:0.737966:0.707067:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 en el siguiente enlace::@0.638498:0.737972:0.777739:0.737972:0.777739:0.722909:0.638498:0.722909:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 lynk.ec/13m11:@0.638498:0.761273:0.736387:0.761273:0.736387:0.745959:0.638498:0.745959:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.434065:0.096869:0.441540:0.096869:0.441540:0.080401:0.434065:0.080401:0.000000 ≥ 0,:@0.441540:0.096754:0.471883:0.096754:0.471883:0.080256:0.441540:0.080256:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.434065:0.114220:0.441752:0.114220:0.441752:0.097751:0.434065:0.097751:0.000000 ≥ 0,:@0.441752:0.114104:0.472095:0.114104:0.472095:0.097607:0.441752:0.097607:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.434065:0.131571:0.441540:0.131571:0.441540:0.115102:0.434065:0.115102:0.000000 + 3 ≤ 9,:@0.441540:0.131455:0.507158:0.131455:0.507158:0.114958:0.441540:0.114958:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.469128:0.131571:0.476815:0.131571:0.476815:0.115102:0.469128:0.115102:0.000000 x y:@0.434065:0.148922:0.468011:0.148922:0.468011:0.132453:0.434065:0.132453:0.000000:0.000000:0.000000 – ≤ 3.:@0.441540:0.148806:0.498354:0.148806:0.498354:0.132308:0.441540:0.132308:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.466309:0.253367:0.474805:0.253367:0.474805:0.236869:0.466309:0.236869:0.000000 3:@0.466309:0.269706:0.474805:0.269706:0.474805:0.253208:0.466309:0.253208:0.000000 Determinamos el punto intersección de las rectas y , esto es,:@0.108226:0.755686:0.577297:0.755699:0.577297:0.739201:0.108226:0.739188:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 B:@0.283212:0.755801:0.292401:0.755801:0.292401:0.739333:0.283212:0.739333:0.000000 L:@0.477479:0.755801:0.485320:0.755801:0.485320:0.739333:0.477479:0.739333:0.000000 1:@0.485324:0.758977:0.490278:0.758977:0.490278:0.749359:0.485324:0.749359:0.000000 L:@0.506382:0.755815:0.514223:0.755815:0.514223:0.739346:0.506382:0.739346:0.000000 2:@0.514224:0.758977:0.519177:0.758977:0.519177:0.749359:0.514224:0.749359:0.000000 { } = .:@0.108229:0.773050:0.200201:0.773050:0.200201:0.756552:0.108229:0.756552:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 B:@0.114085:0.773165:0.123275:0.773165:0.123275:0.756697:0.114085:0.756697:0.000000 L:@0.148224:0.773165:0.156064:0.773165:0.156064:0.756697:0.148224:0.756697:0.000000 1:@0.156066:0.776328:0.161019:0.776328:0.161019:0.766709:0.156066:0.766709:0.000000 :@0.165161:0.772682:0.180511:0.772682:0.180511:0.758672:0.165161:0.758672:0.000000 L:@0.184653:0.773165:0.192494:0.773165:0.192494:0.756697:0.184653:0.756697:0.000000 2:@0.192494:0.776328:0.197447:0.776328:0.197447:0.766709:0.192494:0.766709:0.000000 Hallamos ( , ) , tal que:@0.108229:0.807751:0.309826:0.807751:0.309826:0.791253:0.108229:0.791253:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x y:@0.184577:0.807867:0.206636:0.807867:0.206636:0.791398:0.184577:0.791398:0.000000:0.000000:0.000000 :@0.216732:0.807232:0.231384:0.807232:0.231384:0.793859:0.216732:0.793859:0.000000 R:@0.235526:0.806664:0.248831:0.806664:0.248831:0.793802:0.235526:0.793802:0.000000 2:@0.248829:0.801399:0.253782:0.801399:0.253782:0.791781:0.248829:0.791781:0.000000 :@0.108234:0.825102:0.112376:0.825102:0.112376:0.808604:0.108234:0.808604:0.000000 cuya solución es = , = .:@0.108234:0.842453:0.327104:0.842453:0.327104:0.825955:0.108234:0.825955:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.228274:0.842568:0.235749:0.842568:0.235749:0.826100:0.228274:0.826100:0.000000 y:@0.278306:0.842568:0.285993:0.842568:0.285993:0.826100:0.278306:0.826100:0.000000 El conjunto de soluciones factibles es la región poligonal de vértices:@0.108234:0.877154:0.595793:0.877154:0.595793:0.860656:0.108234:0.860656:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 S:@0.193348:0.877270:0.201227:0.877270:0.201227:0.860801:0.193348:0.860801:0.000000 O:@0.200977:0.911971:0.212883:0.911971:0.212883:0.895503:0.200977:0.895503:0.000000 = (0, 0), = (3, 0), = , , = (0, 3).:@0.212883:0.911856:0.503037:0.911856:0.503037:0.895358:0.212883:0.895358:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A:@0.274666:0.911971:0.285937:0.911971:0.285937:0.895503:0.274666:0.895503:0.000000 B:@0.347720:0.911971:0.356910:0.911971:0.356910:0.895503:0.347720:0.895503:0.000000 C:@0.435358:0.911971:0.445395:0.911971:0.445395:0.895503:0.435358:0.895503:0.000000 t:@0.534005:0.716771:0.544313:0.716771:0.544313:0.706746:0.534005:0.706746:0.000000 :@0.544318:0.717479:0.547199:0.717479:0.547199:0.706002:0.544318:0.706002:0.000000 Figura 5.8.:@0.547199:0.717479:0.595768:0.717479:0.595768:0.706002:0.547199:0.706002:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.329765:0.800568:0.337240:0.800568:0.337240:0.784099:0.329765:0.784099:0.000000 + 3 = 9,:@0.337240:0.800453:0.401124:0.800453:0.401124:0.783955:0.337240:0.783955:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.364828:0.800568:0.372515:0.800568:0.372515:0.784099:0.364828:0.784099:0.000000 x y:@0.329765:0.817919:0.363710:0.817919:0.363710:0.801450:0.329765:0.801450:0.000000:0.000000:0.000000 – = 3,:@0.337240:0.817803:0.392318:0.817803:0.392318:0.801306:0.337240:0.801306:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 9:@0.258078:0.834864:0.266574:0.834864:0.266574:0.818366:0.258078:0.818366:0.000000 2:@0.258078:0.851202:0.266574:0.851202:0.266574:0.834705:0.258078:0.834705:0.000000 9 3:@0.383721:0.904372:0.416661:0.904372:0.416661:0.887875:0.383721:0.887875:0.000000:0.000000:0.000000 2 2:@0.383721:0.920711:0.416661:0.920711:0.416661:0.904213:0.383721:0.904213:0.000000:0.000000:0.000000 3:@0.308783:0.834864:0.317279:0.834864:0.317279:0.818366:0.308783:0.818366:0.000000 2:@0.308783:0.851202:0.317279:0.851202:0.317279:0.834705:0.308783:0.834705:0.000000 p:@0.793223:0.299424:0.804704:0.299424:0.804704:0.289399:0.793223:0.289399:0.000000 :@0.804704:0.300132:0.807585:0.300132:0.807585:0.288655:0.804704:0.288655:0.000000 Figura 5.6.:@0.807585:0.300132:0.856154:0.300132:0.856154:0.288655:0.807585:0.288655:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 p:@0.793223:0.513921:0.804704:0.513921:0.804704:0.503896:0.793223:0.503896:0.000000 :@0.804704:0.514628:0.807585:0.514628:0.807585:0.503152:0.804704:0.503152:0.000000 Figura 5.7.:@0.807585:0.514628:0.856154:0.514628:0.856154:0.503152:0.807585:0.503152:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 L:@0.699299:0.243796:0.705436:0.243796:0.705436:0.230907:0.699299:0.230907:0.000000 1:@0.705436:0.246270:0.709312:0.246270:0.709312:0.238743:0.705436:0.238743:0.000000 S:@0.658142:0.267744:0.664309:0.267744:0.664309:0.254855:0.658142:0.254855:0.000000 1:@0.664309:0.270219:0.668185:0.270219:0.668185:0.262692:0.664309:0.262692:0.000000 0:@0.661684:0.282770:0.668702:0.282770:0.668702:0.269142:0.661684:0.269142:0.000000 x:@0.834821:0.284168:0.841425:0.284168:0.841425:0.270539:0.834821:0.270539:0.000000 3:@0.708163:0.283376:0.714073:0.283376:0.714073:0.271899:0.708163:0.271899:0.000000 6:@0.746158:0.283376:0.752068:0.283376:0.752068:0.271899:0.746158:0.271899:0.000000 9:@0.784152:0.283376:0.790062:0.283376:0.790062:0.271899:0.784152:0.271899:0.000000 3:@0.660586:0.245113:0.666497:0.245113:0.666497:0.233637:0.660586:0.233637:0.000000 6:@0.660586:0.216598:0.666497:0.216598:0.666497:0.205121:0.660586:0.205121:0.000000 y:@0.658732:0.184481:0.665193:0.184481:0.665193:0.170852:0.658732:0.170852:0.000000 L:@0.769752:0.425317:0.775888:0.425317:0.775888:0.412429:0.769752:0.412429:0.000000 2:@0.775888:0.427792:0.779764:0.427792:0.779764:0.420264:0.775888:0.420264:0.000000 S:@0.712752:0.423089:0.718918:0.423089:0.718918:0.410201:0.712752:0.410201:0.000000 2:@0.718918:0.425564:0.722795:0.425564:0.722795:0.418036:0.718918:0.418036:0.000000 0:@0.658623:0.469963:0.665641:0.469963:0.665641:0.456335:0.658623:0.456335:0.000000 x:@0.831760:0.471361:0.838364:0.471361:0.838364:0.457732:0.831760:0.457732:0.000000 3:@0.705103:0.470570:0.711013:0.470570:0.711013:0.459093:0.705103:0.459093:0.000000 6:@0.743097:0.470570:0.749007:0.470570:0.749007:0.459093:0.743097:0.459093:0.000000 9:@0.781091:0.470570:0.787002:0.470570:0.787002:0.459093:0.781091:0.459093:0.000000 3:@0.657526:0.432308:0.663436:0.432308:0.663436:0.420831:0.657526:0.420831:0.000000 –3:@0.650798:0.489329:0.664012:0.489329:0.664012:0.477852:0.650798:0.477852:0.000000:0.000000 6:@0.657526:0.403792:0.663436:0.403792:0.663436:0.392316:0.657526:0.392316:0.000000 y:@0.655671:0.385504:0.662133:0.385504:0.662133:0.371876:0.655671:0.371876:0.000000 L:@0.409431:0.618194:0.415568:0.618194:0.415568:0.605305:0.409431:0.605305:0.000000 2:@0.415568:0.620668:0.419444:0.620668:0.419444:0.613141:0.415568:0.613141:0.000000 0:@0.284356:0.672522:0.291374:0.672522:0.291374:0.658894:0.284356:0.658894:0.000000 x:@0.501052:0.673920:0.507656:0.673920:0.507656:0.660291:0.501052:0.660291:0.000000 3:@0.330837:0.673129:0.336747:0.673129:0.336747:0.661652:0.330837:0.661652:0.000000 6:@0.368832:0.673129:0.374742:0.673129:0.374742:0.661652:0.368832:0.661652:0.000000 9:@0.406826:0.673129:0.412736:0.673129:0.412736:0.661652:0.406826:0.661652:0.000000 3:@0.283260:0.634867:0.289171:0.634867:0.289171:0.623390:0.283260:0.623390:0.000000 –3:@0.276533:0.691888:0.289747:0.691888:0.289747:0.680411:0.276533:0.680411:0.000000:0.000000 6:@0.283260:0.606351:0.289171:0.606351:0.289171:0.594874:0.283260:0.594874:0.000000 y:@0.281406:0.588063:0.287867:0.588063:0.287867:0.574434:0.281406:0.574434:0.000000 L:@0.242633:0.621313:0.248769:0.621313:0.248769:0.608424:0.242633:0.608424:0.000000 1:@0.248769:0.623787:0.252645:0.623787:0.252645:0.616260:0.248769:0.616260:0.000000 S:@0.308664:0.655616:0.314830:0.655616:0.314830:0.642727:0.308664:0.642727:0.000000 C:@0.301167:0.629715:0.309022:0.629715:0.309022:0.616827:0.301167:0.616827:0.000000 B:@0.366089:0.647775:0.373281:0.647775:0.373281:0.634887:0.366089:0.634887:0.000000 A:@0.340096:0.670588:0.348916:0.670588:0.348916:0.657699:0.340096:0.657699:0.000000 ©:@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