163:@0.890754:0.963104:0.932133:0.963104:0.932133:0.941283:0.890754:0.941283:0.000000:0.000000:0.000000
Matemática:@0.795130:0.956142:0.879896:0.956142:0.879896:0.943479:0.795130:0.943479:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3.º BG:@0.837761:0.967458:0.879897:0.967458:0.879897:0.954794:0.837761:0.954794:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Paso 1. :@0.102121:0.288583:0.157756:0.288583:0.157756:0.273005:0.102121:0.273005:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Determinamos las variables que intervienen en el problema. Completamos la :@0.157756:0.288583:0.675564:0.288583:0.675564:0.273684:0.157756:0.273684:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
siguiente tabla:  : cable tipo 1;  : cable tipo 2.:@0.102121:0.303671:0.400078:0.303671:0.400078:0.288772:0.102121:0.288772:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.207124:0.303671:0.213908:0.303671:0.213908:0.288797:0.207124:0.288797:0.000000
y:@0.305427:0.303671:0.312228:0.303671:0.312228:0.288797:0.305427:0.288797:0.000000
Paso 2. :@0.102121:0.431149:0.157756:0.431149:0.157756:0.415571:0.102121:0.415571:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Determinamos las restricciones del problema y la función objetivo.:@0.157756:0.431149:0.601234:0.431149:0.601234:0.416250:0.157756:0.416250:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
De cobre, como máximo se pueden utilizar hasta 300 kg.:@0.102121:0.449794:0.479111:0.449794:0.479111:0.434895:0.102121:0.434895:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
40  + 30  ≤ 300 ÷ 10; 4  + 3  ≤ 30:@0.162430:0.464882:0.389073:0.464882:0.389073:0.449983:0.162430:0.449983:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.178780:0.464882:0.185565:0.464882:0.185565:0.450008:0.178780:0.450008:0.000000
y:@0.219237:0.464882:0.226039:0.464882:0.226039:0.450008:0.219237:0.450008:0.000000
x:@0.316317:0.464882:0.323102:0.464882:0.323102:0.450008:0.316317:0.450008:0.000000
y:@0.348599:0.464882:0.355401:0.464882:0.355401:0.450008:0.348599:0.450008:0.000000
De titanio, como máximo se pueden utilizar 40 kg.:@0.102121:0.487099:0.435856:0.487099:0.435856:0.472200:0.102121:0.472200:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
6  + 2  ≤ 40 ÷ 2; 3  +   ≤ 20:@0.162430:0.502186:0.348197:0.502186:0.348197:0.487287:0.162430:0.487287:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.170605:0.502186:0.177390:0.502186:0.177390:0.487312:0.170605:0.487312:0.000000
y:@0.202887:0.502186:0.209688:0.502186:0.209688:0.487312:0.202887:0.487312:0.000000
x:@0.283617:0.502186:0.290401:0.502186:0.290401:0.487312:0.283617:0.487312:0.000000
y:@0.307723:0.502186:0.314525:0.502186:0.314525:0.487312:0.307723:0.487312:0.000000
De aluminio, como máximo se pueden utilizar 30 kg.:@0.102121:0.524403:0.451670:0.524403:0.451670:0.509504:0.102121:0.509504:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2  + 4  ≤ 30 ÷ 2;   + 2  ≤ 15:@0.162430:0.539490:0.348197:0.539490:0.348197:0.524591:0.162430:0.524591:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.170605:0.539490:0.177390:0.539490:0.177390:0.524616:0.170605:0.524616:0.000000
y:@0.202887:0.539490:0.209688:0.539490:0.209688:0.524616:0.202887:0.524616:0.000000
x:@0.275442:0.539490:0.282226:0.539490:0.282226:0.524616:0.275442:0.524616:0.000000
y:@0.307723:0.539490:0.314525:0.539490:0.314525:0.524616:0.307723:0.524616:0.000000
La función objetivo a maximizar es:  ( ,  ) = 1 200  + 1 000y:@0.102121:0.561707:0.496622:0.561707:0.496622:0.546808:0.102121:0.546808:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
F x y:@0.338714:0.561707:0.370644:0.561707:0.370644:0.546833:0.338714:0.546833:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.428775:0.561707:0.435559:0.561707:0.435559:0.546833:0.428775:0.546833:0.000000
Paso 3. :@0.102121:0.579686:0.157756:0.579686:0.157756:0.564108:0.102121:0.564108:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
La función objetivo  ( ,  ) = 1 200  + 1 000 ;:@0.157756:0.579686:0.450167:0.579686:0.450167:0.564787:0.157756:0.564787:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
F x y:@0.289914:0.579686:0.321844:0.579686:0.321844:0.564812:0.289914:0.564812:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.379975:0.579686:0.386760:0.579686:0.386760:0.564812:0.379975:0.564812:0.000000
y:@0.440451:0.579686:0.447252:0.579686:0.447252:0.564812:0.440451:0.564812:0.000000
está sujeta a estas restricciones::@0.102121:0.594774:0.311087:0.594774:0.311087:0.579875:0.102121:0.579875:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Paso 4. :@0.102121:0.679478:0.157756:0.679478:0.157756:0.663900:0.102121:0.663900:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Graficamos las restricciones del problema y determinamos los vértices de:@0.157756:0.679478:0.645762:0.679478:0.645762:0.664579:0.157756:0.664579:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.184811:0.679478:0.188480:0.679478:0.188480:0.664579:0.184811:0.664579:0.000000
la región factible.:@0.102121:0.694566:0.215868:0.694566:0.215868:0.679667:0.102121:0.679667:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Los vértices son   (0,0);   (0; 7,5);   (3, 6);   (6, 2);   (6,67; 0):@0.102121:0.713212:0.485483:0.713212:0.485483:0.698313:0.102121:0.698313:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.211129:0.713212:0.220125:0.713212:0.220125:0.698338:0.211129:0.698338:0.000000
B:@0.258522:0.713212:0.266563:0.713212:0.266563:0.698338:0.258522:0.698338:0.000000
C:@0.319718:0.713212:0.328731:0.713212:0.328731:0.698338:0.319718:0.698338:0.000000
D:@0.370796:0.713212:0.381283:0.713212:0.381283:0.698338:0.370796:0.698338:0.000000
E:@0.423348:0.713212:0.430736:0.713212:0.430736:0.698338:0.423348:0.698338:0.000000
Paso 5. :@0.102121:0.732939:0.157756:0.732939:0.157756:0.717361:0.102121:0.717361:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Para encontrar la solución, reemplazamos cada vértice en la función objetivo a :@0.157756:0.732939:0.682818:0.732939:0.682818:0.718040:0.157756:0.718040:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
maximizar. Descartamos el punto A (0, 0) porque no tendría sentido:@0.102121:0.748026:0.552084:0.748026:0.552084:0.733127:0.102121:0.733127:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
F x y:@0.162430:0.766672:0.194360:0.766672:0.194360:0.751798:0.162430:0.751798:0.000000:0.000000:0.000000:0.000000:0.000000
( ,  ) = 1 200  + 1 000:@0.169751:0.766672:0.312967:0.766672:0.312967:0.751773:0.169751:0.751773:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.252491:0.766672:0.259276:0.766672:0.259276:0.751798:0.252491:0.751798:0.000000
y:@0.312967:0.766672:0.319768:0.766672:0.319768:0.751798:0.312967:0.751798:0.000000
F:@0.162430:0.784438:0.169751:0.784438:0.169751:0.769564:0.162430:0.769564:0.000000
(0; 7,5) = 1 200(0) + 1 000(7,5) = 750:@0.169751:0.784438:0.407082:0.784438:0.407082:0.769539:0.169751:0.769539:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
F:@0.162430:0.802203:0.169751:0.802203:0.169751:0.787329:0.162430:0.787329:0.000000
(3, 6) = 1 200(3) + 1 000(6) = 9 600:@0.169751:0.802203:0.396746:0.802203:0.396746:0.787304:0.169751:0.787304:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
F:@0.162430:0.819969:0.169751:0.819969:0.169751:0.805095:0.162430:0.805095:0.000000
(6, 2) = 1 200(6) + 1 000(2) = 9 200:@0.169751:0.819969:0.396746:0.819969:0.396746:0.805070:0.169751:0.805070:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
F:@0.162430:0.837735:0.169751:0.837735:0.169751:0.822861:0.162430:0.822861:0.000000
(6,67; 0) = 1 200(6,67) + 1 000(0) = 8 004:@0.169751:0.837735:0.435276:0.837735:0.435276:0.822836:0.169751:0.822836:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
El valor máximo de la función objetivo está en el vértice   (3, 6):@0.102121:0.856380:0.521109:0.856380:0.521109:0.841481:0.102121:0.841481:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
C:@0.476614:0.856380:0.485627:0.856380:0.485627:0.841507:0.476614:0.841507:0.000000
Paso 6. :@0.102121:0.874360:0.157756:0.874360:0.157756:0.858782:0.102121:0.858782:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Interpretamos la solución del problema.:@0.157756:0.874360:0.423747:0.874360:0.423747:0.859461:0.157756:0.859461:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Como   e   representan la cantidad de alambre en kilogramos por cada 100 m de alambre, :@0.102121:0.893006:0.707561:0.893006:0.707561:0.878107:0.102121:0.878107:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.146783:0.893006:0.175832:0.893006:0.175832:0.878132:0.146783:0.878132:0.000000:0.000000:0.000000
entonces la fábrica debe producir 300 m de alambre tipo 1, y 600 m de alambre tipo 2, así :@0.102121:0.908093:0.701998:0.908093:0.701998:0.893194:0.102121:0.893194:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
obtendrá un beneficio máximo de $9 200.:@0.102121:0.923181:0.382153:0.923181:0.382153:0.908282:0.102121:0.908282:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.227863:0.923181:0.231532:0.923181:0.231532:0.908282:0.227863:0.908282:0.000000
Problemas de mezclas de productos:@0.096358:0.116962:0.355766:0.116962:0.355766:0.101597:0.096358:0.101597:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1.:@0.096359:0.141008:0.110585:0.141008:0.110585:0.124107:0.096359:0.124107:0.000000:0.000000
  Una empresa fabrica dos tipos de cables para instalaciones eléctricas, para ello :@0.110585:0.141008:0.716468:0.141008:0.716468:0.124619:0.110585:0.124619:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
dispone de 300 kg de cobre, 40 kg de titanio y 30 kg de aluminio. Para la fabri-:@0.124848:0.157604:0.712544:0.157604:0.712544:0.141215:0.124848:0.141215:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cación de 100 m de cable del primer tipo, se necesitan 40 kg de cobre, 6 kg de :@0.124848:0.174200:0.716613:0.174200:0.716613:0.157811:0.124848:0.157811:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
titanio y 2 kg de aluminio. Con este producto se obtiene un beneficio de $1 200.:@0.124848:0.190797:0.711837:0.190797:0.711837:0.174408:0.124848:0.174408:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.606265:0.190797:0.610300:0.190797:0.610300:0.174408:0.606265:0.174408:0.000000
 :@0.096359:0.214516:0.100395:0.214516:0.100395:0.198127:0.096359:0.198127:0.000000
Para la fabricación de 100 m de cables del segundo tipo, se necesitan 30 kg de :@0.124852:0.214516:0.716526:0.214516:0.716526:0.198127:0.124852:0.198127:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cobre, 2 kg de titanio y 4 kg de aluminio. Se obtiene un beneficio de $1 000. El :@0.124848:0.231112:0.716573:0.231112:0.716573:0.214723:0.124848:0.214723:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.586658:0.231112:0.590693:0.231112:0.590693:0.214723:0.586658:0.214723:0.000000
ingeniero de producción de esta fábrica requiere determinar cuántos metros de :@0.124848:0.247708:0.716593:0.247708:0.716593:0.231319:0.124848:0.231319:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cable hay que producir de cada tipo para que el beneficio sea máximo.:@0.124848:0.264305:0.643579:0.264305:0.643579:0.247916:0.124848:0.247916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.522012:0.264305:0.526047:0.264305:0.526047:0.247916:0.522012:0.247916:0.000000
1:@0.752505:0.810186:0.759380:0.810186:0.759380:0.798096:0.752505:0.798096:0.000000
2:@0.753376:0.792463:0.760251:0.792463:0.760251:0.780373:0.753376:0.780373:0.000000
3:@0.753376:0.774740:0.760251:0.774740:0.760251:0.762650:0.753376:0.762650:0.000000
4:@0.753376:0.757017:0.760251:0.757017:0.760251:0.744927:0.753376:0.744927:0.000000
5:@0.753376:0.739294:0.760251:0.739294:0.760251:0.727204:0.753376:0.727204:0.000000
6:@0.753376:0.721571:0.760251:0.721571:0.760251:0.709481:0.753376:0.709481:0.000000
7:@0.753376:0.703848:0.760251:0.703848:0.760251:0.691758:0.753376:0.691758:0.000000
8:@0.753376:0.686125:0.760251:0.686125:0.760251:0.674035:0.753376:0.674035:0.000000
2:@0.809383:0.835091:0.816258:0.835091:0.816258:0.823000:0.809383:0.823000:0.000000
1:@0.785179:0.835091:0.792054:0.835091:0.792054:0.823000:0.785179:0.823000:0.000000
4:@0.856142:0.835091:0.863017:0.835091:0.863017:0.823000:0.856142:0.823000:0.000000
3:@0.831938:0.835091:0.838813:0.835091:0.838813:0.823000:0.831938:0.823000:0.000000
6:@0.904014:0.835091:0.910889:0.835091:0.910889:0.823000:0.904014:0.823000:0.000000
5:@0.879810:0.835091:0.886685:0.835091:0.886685:0.823000:0.879810:0.823000:0.000000
7:@0.927829:0.835091:0.934704:0.835091:0.934704:0.823000:0.927829:0.823000:0.000000
0:@0.754355:0.835091:0.761230:0.835091:0.761230:0.823000:0.754355:0.823000:0.000000
y:@0.753803:0.636134:0.758975:0.636134:0.758975:0.625546:0.753803:0.625546:0.000000
x:@0.943764:0.834282:0.948935:0.834282:0.948935:0.823694:0.943764:0.823694:0.000000
9:@0.753375:0.667467:0.760250:0.667467:0.760250:0.655377:0.753375:0.655377:0.000000
A:@0.751540:0.821893:0.761661:0.821893:0.761661:0.805160:0.751540:0.805160:0.000000
B:@0.776191:0.690249:0.785238:0.690249:0.785238:0.673516:0.776191:0.673516:0.000000
C:@0.841796:0.715384:0.851935:0.715384:0.851935:0.698651:0.841796:0.698651:0.000000
D:@0.915165:0.788568:0.926963:0.788568:0.926963:0.771835:0.915165:0.771835:0.000000
E:@0.910548:0.850932:0.918859:0.850932:0.918859:0.834199:0.910548:0.834199:0.000000
©Shutterstock:@0.942261:0.271798:0.942261:0.228973:0.930350:0.228973:0.930350:0.271798:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
En las instalaciones eléctricas :@0.740996:0.311354:0.918557:0.311354:0.918557:0.297945:0.740996:0.297945:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
se usa modelamiento :@0.740996:0.323926:0.873717:0.323926:0.873717:0.310517:0.740996:0.310517:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
matemático.:@0.740996:0.336498:0.816169:0.336498:0.816169:0.323089:0.740996:0.323089:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
4  + 3  ≤ 30:@0.328509:0.597198:0.409439:0.597198:0.409439:0.582299:0.328509:0.582299:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.336684:0.597198:0.343469:0.597198:0.343469:0.582324:0.336684:0.582324:0.000000
y:@0.368966:0.597198:0.375767:0.597198:0.375767:0.582324:0.368966:0.582324:0.000000
3  +   ≤ 20:@0.328509:0.612285:0.401264:0.612285:0.401264:0.597386:0.328509:0.597386:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.336684:0.612285:0.343469:0.612285:0.343469:0.597412:0.336684:0.597412:0.000000
y:@0.360791:0.612285:0.367592:0.612285:0.367592:0.597412:0.360791:0.597412:0.000000
x:@0.328509:0.627373:0.335293:0.627373:0.335293:0.612499:0.328509:0.612499:0.000000
 + 2  ≤ 15:@0.335293:0.627373:0.401264:0.627373:0.401264:0.612474:0.335293:0.612474:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.360791:0.627373:0.367592:0.627373:0.367592:0.612499:0.360791:0.612499:0.000000
x:@0.328509:0.642461:0.335293:0.642461:0.335293:0.627587:0.328509:0.627587:0.000000
 ≥ 0:@0.335293:0.642461:0.360791:0.642461:0.360791:0.627562:0.335293:0.627562:0.000000:0.000000:0.000000:0.000000
y:@0.328509:0.657548:0.335310:0.657548:0.335310:0.642674:0.328509:0.642674:0.000000
 ≥ 0:@0.335310:0.657548:0.360807:0.657548:0.360807:0.642649:0.335310:0.642649:0.000000:0.000000:0.000000:0.000000
Cables:@0.114189:0.327688:0.162135:0.327688:0.162135:0.312324:0.114189:0.312324:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Cantidad en kg por cada 100 m:@0.212794:0.327688:0.436319:0.327688:0.436319:0.312324:0.212794:0.312324:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Cobre:@0.492860:0.327688:0.536149:0.327688:0.536149:0.312324:0.492860:0.312324:0.000000:0.000000:0.000000:0.000000:0.000000
Titanio:@0.565231:0.327688:0.615722:0.327688:0.615722:0.312324:0.565231:0.312324:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Aluminio:@0.633346:0.327688:0.699568:0.327688:0.699568:0.312324:0.633346:0.312324:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Tipo 1:@0.110855:0.352633:0.152066:0.352633:0.152066:0.337734:0.110855:0.337734:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.322338:0.352633:0.329122:0.352633:0.329122:0.337759:0.322338:0.337759:0.000000
40:@0.504118:0.352633:0.520468:0.352633:0.520468:0.337734:0.504118:0.337734:0.000000:0.000000
x:@0.520468:0.352633:0.527253:0.352633:0.527253:0.337759:0.520468:0.337759:0.000000
6:@0.583005:0.352633:0.591180:0.352633:0.591180:0.337734:0.583005:0.337734:0.000000
x:@0.591180:0.352633:0.597965:0.352633:0.597965:0.337759:0.591180:0.337759:0.000000
2:@0.658977:0.352633:0.667152:0.352633:0.667152:0.337734:0.658977:0.337734:0.000000
x:@0.667152:0.352633:0.673937:0.352633:0.673937:0.337759:0.667152:0.337759:0.000000
Tipo 2:@0.110855:0.377578:0.152066:0.377578:0.152066:0.362679:0.110855:0.362679:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.322338:0.377578:0.329139:0.377578:0.329139:0.362704:0.322338:0.362704:0.000000
30:@0.504118:0.377578:0.520468:0.377578:0.520468:0.362679:0.504118:0.362679:0.000000:0.000000
y:@0.520468:0.377578:0.527270:0.377578:0.527270:0.362704:0.520468:0.362704:0.000000
2:@0.583005:0.377578:0.591180:0.377578:0.591180:0.362679:0.583005:0.362679:0.000000
y:@0.591180:0.377578:0.597982:0.377578:0.597982:0.362704:0.591180:0.362704:0.000000
4:@0.658977:0.377578:0.667152:0.377578:0.667152:0.362679:0.658977:0.362679:0.000000
y:@0.667152:0.377578:0.673954:0.377578:0.673954:0.362704:0.667152:0.362704:0.000000
300:@0.503431:0.402522:0.527957:0.402522:0.527957:0.387623:0.503431:0.387623:0.000000:0.000000:0.000000
40:@0.582318:0.402522:0.598669:0.402522:0.598669:0.387623:0.582318:0.387623:0.000000:0.000000
30:@0.658290:0.402522:0.674641:0.402522:0.674641:0.387623:0.658290:0.387623:0.000000:0.000000
cción y expresión:@0.117254:0.090870:0.242124:0.090870:0.242124:0.075506:0.117254:0.075506:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.095657:0.091656:0.107746:0.091656:0.107746:0.074520:0.095657:0.074520:0.000000