162:@0.067867:0.963104:0.109245:0.963104:0.109245:0.941283:0.067867:0.941283:0.000000:0.000000:0.000000
Matemática:@0.120102:0.956142:0.204868:0.956142:0.204868:0.943479:0.120102:0.943479:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3.º BG:@0.120102:0.967458:0.162238:0.967458:0.162238:0.954794:0.120102:0.954794:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
isposición y compromiso:@0.306727:0.140863:0.485691:0.140863:0.485691:0.125499:0.306727:0.125499:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
D:@0.284763:0.141649:0.297589:0.141649:0.297589:0.124513:0.284763:0.124513:0.000000
Supón que tienes:@0.126765:0.192000:0.244165:0.192000:0.244165:0.177101:0.126765:0.177101:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
una fábrica de alimentos, :@0.077110:0.205830:0.247831:0.205830:0.247831:0.190931:0.077110:0.190931:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿qué factores de mercado :@0.070962:0.219661:0.247831:0.219661:0.247831:0.204762:0.070962:0.204762:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
piensas que inciden:@0.111101:0.233491:0.244165:0.233491:0.244165:0.218592:0.111101:0.218592:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
en la fabricación:@0.134822:0.247321:0.244164:0.247321:0.244164:0.232422:0.134822:0.232422:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de un producto?:@0.132762:0.261151:0.244164:0.261151:0.244164:0.246252:0.132762:0.246252:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Saberes previos:@0.108521:0.163125:0.227756:0.163125:0.227756:0.146224:0.108521:0.146224:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
El planteamiento y modelado de problemas en programación lineal es el proce-:@0.287495:0.399335:0.903622:0.399335:0.903622:0.382946:0.287495:0.382946:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
so de formular modelos matemáticos lineales que representan situaciones reales, :@0.287495:0.415932:0.907679:0.415932:0.907679:0.399543:0.287495:0.399543:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
mediante la definición de variables de decisión, una función objetivo a optimizar :@0.287495:0.432528:0.907641:0.432528:0.907641:0.416139:0.287495:0.416139:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.406612:0.432528:0.410647:0.432528:0.410647:0.416139:0.406612:0.416139:0.000000
y un conjunto de restricciones lineales que reflejan las limitaciones del problema, con :@0.287495:0.449124:0.907604:0.449124:0.907604:0.432735:0.287495:0.432735:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.618272:0.449124:0.622307:0.449124:0.622307:0.432735:0.618272:0.432735:0.000000
el fin de determinar la solución óptima dentro del conjunto factible.:@0.287495:0.465721:0.784021:0.465721:0.784021:0.449332:0.287495:0.449332:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.308835:0.465721:0.312870:0.465721:0.312870:0.449332:0.308835:0.449332:0.000000
nidad de conocimientos:@0.306727:0.371979:0.480398:0.371979:0.480398:0.356615:0.306727:0.356615:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
U:@0.284892:0.372765:0.297460:0.372765:0.297460:0.355629:0.284892:0.355629:0.000000
Pienso y progreso:@0.294883:0.313522:0.417347:0.313522:0.417347:0.298158:0.294883:0.298158:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
  ¿Cómo se puede conseguir una dieta balanceada para los refugios de animales?:@0.294883:0.330917:0.834805:0.330917:0.834805:0.316018:0.294883:0.316018:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Un refugio de animales necesita preparar dos tipos de mezclas alimenticias: Mezcla :@0.287495:0.168345:0.907694:0.168345:0.907694:0.151956:0.287495:0.151956:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Premium y Mezcla Estándar. Las condiciones son::@0.287495:0.184941:0.646057:0.184941:0.646057:0.168553:0.287495:0.168553:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Cada kg de Mezcla Premium requiere 3 kg de proteína y 1 kg de vitaminas.:@0.287495:0.208660:0.832301:0.208660:0.832301:0.192271:0.287495:0.192271:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Cada kg de Mezcla Estándar requiere 1 kg de proteína y 2 kg de vitaminas.:@0.287495:0.225257:0.828671:0.225257:0.828671:0.208868:0.287495:0.208868:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
El refugio tiene disponibles 60 kg de proteína y 40 kg de vitaminas por semana.:@0.287495:0.241853:0.866687:0.241853:0.866687:0.225464:0.287495:0.225464:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
El costo de producir 1 kg de Mezcla Premium es $8 y de Mezcla Estándar es $5.:@0.287495:0.258450:0.862578:0.258450:0.862578:0.242061:0.287495:0.242061:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿Cuántos kilogramos de cada mezcla se deben preparar para minimizar los costos?:@0.287495:0.282169:0.892340:0.282169:0.892340:0.265780:0.287495:0.265780:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Planteamiento y modelado de problemas :@0.286308:0.060073:0.904039:0.060073:0.904039:0.026520:0.286308:0.026520:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
en programación lineal:@0.286308:0.090250:0.628509:0.090250:0.628509:0.056698:0.286308:0.056698:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
	:@0.094760:0.108603:0.183816:0.108603:0.183816:0.011514:0.094760:0.011514:0.000000:0.000000
Ejemplos paso a paso:@0.285358:0.524732:0.440250:0.524732:0.440250:0.509368:0.285358:0.509368:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1.:@0.285358:0.552335:0.299584:0.552335:0.299584:0.535434:0.285358:0.535434:0.000000:0.000000
  Regresamos a nuestro problema inicial.:@0.299584:0.552335:0.600561:0.552335:0.600561:0.535946:0.299584:0.535946:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cción y expresión:@0.306727:0.498633:0.431598:0.498633:0.431598:0.483269:0.306727:0.483269:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.285132:0.499419:0.297220:0.499419:0.297220:0.482283:0.285132:0.482283:0.000000
Paso 1. :@0.292258:0.579315:0.347893:0.579315:0.347893:0.563737:0.292258:0.563737:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Elegimos las variables:@0.347893:0.579315:0.491943:0.579315:0.491943:0.564416:0.347893:0.564416:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y organizamos la información:@0.292258:0.594403:0.488712:0.594403:0.488712:0.579504:0.292258:0.579504:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
en una tabla.:@0.292258:0.609490:0.378282:0.609490:0.378282:0.594591:0.292258:0.594591:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Paso 2.:@0.292258:0.686991:0.344509:0.686991:0.344509:0.671413:0.292258:0.671413:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 Planteamos la función objetivo y las restricciones del problema.:@0.344509:0.686991:0.770047:0.686991:0.770047:0.672092:0.344509:0.672092:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
El costo de producir 1 kg de Mezcla Premium es $8 y de Mezcla Estándar es $5:@0.292258:0.705636:0.812145:0.705636:0.812145:0.690737:0.292258:0.690737:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
F( ,  ) = 8  + 5  :@0.292258:0.725162:0.397296:0.725162:0.397296:0.710263:0.292258:0.710263:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.304437:0.725162:0.324607:0.725162:0.324607:0.710288:0.304437:0.710288:0.000000:0.000000:0.000000
x:@0.354544:0.725162:0.361328:0.725162:0.361328:0.710288:0.354544:0.710288:0.000000
y:@0.386825:0.725162:0.393627:0.725162:0.393627:0.710288:0.386825:0.710288:0.000000
Las restricciones son: :@0.531817:0.725162:0.674814:0.725162:0.674814:0.710263:0.531817:0.710263:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3:@0.685743:0.724422:0.693837:0.724422:0.693837:0.709672:0.685743:0.709672:0.000000
60:@0.742480:0.724422:0.758575:0.724422:0.758575:0.709672:0.742480:0.709672:0.000000:0.000000
2:@0.709631:0.743093:0.717724:0.743093:0.717724:0.728343:0.709631:0.728343:0.000000
40:@0.742751:0.743093:0.758858:0.743093:0.758858:0.728343:0.742751:0.728343:0.000000:0.000000
0:@0.710579:0.761763:0.718673:0.761763:0.718673:0.747013:0.710579:0.747013:0.000000
0:@0.710812:0.780434:0.718905:0.780434:0.718905:0.765684:0.710812:0.765684:0.000000
x:@0.694558:0.724422:0.701275:0.724422:0.701275:0.709696:0.694558:0.709696:0.000000
y:@0.718689:0.724422:0.725423:0.724422:0.725423:0.709696:0.718689:0.709696:0.000000
x:@0.687012:0.743093:0.693729:0.743093:0.693729:0.728367:0.687012:0.728367:0.000000
y:@0.718673:0.743093:0.725406:0.743093:0.725406:0.728367:0.718673:0.728367:0.000000
x:@0.687012:0.761763:0.693729:0.761763:0.693729:0.747038:0.687012:0.747038:0.000000
y:@0.687244:0.780434:0.693978:0.780434:0.693978:0.765709:0.687244:0.765709:0.000000
+≤:@0.705339:0.724048:0.739039:0.724048:0.739039:0.708800:0.705339:0.708800:0.000000:0.000000
+:@0.697805:0.742719:0.706910:0.742719:0.706910:0.727471:0.697805:0.727471:0.000000
≤:@0.729947:0.742719:0.739052:0.742719:0.739052:0.727471:0.729947:0.727471:0.000000
≥:@0.698276:0.761390:0.707381:0.761390:0.707381:0.746142:0.698276:0.746142:0.000000
≥:@0.698508:0.780061:0.707613:0.780061:0.707613:0.764813:0.698508:0.764813:0.000000
:@0.677595:0.725181:0.685788:0.725181:0.685788:0.709933:0.677595:0.709933:0.000000
:@0.677595:0.754183:0.685788:0.754183:0.685788:0.738935:0.677595:0.738935:0.000000
:@0.677595:0.737031:0.685788:0.737031:0.685788:0.721783:0.677595:0.721783:0.000000
:@0.677595:0.744885:0.685788:0.744885:0.685788:0.729637:0.677595:0.729637:0.000000
:@0.677595:0.783223:0.685788:0.783223:0.685788:0.767975:0.677595:0.767975:0.000000
:@0.677595:0.766033:0.685788:0.766033:0.685788:0.750785:0.677595:0.750785:0.000000
:@0.677595:0.777883:0.685788:0.777883:0.685788:0.762635:0.677595:0.762635:0.000000
Paso 3.:@0.292258:0.803740:0.344509:0.803740:0.344509:0.788162:0.292258:0.788162:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 Graficamos las restricciones.:@0.344509:0.803740:0.534293:0.803740:0.534293:0.788841:0.344509:0.788841:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.375233:0.803740:0.378902:0.803740:0.378902:0.788841:0.375233:0.788841:0.000000
Paso 4.:@0.292258:0.823341:0.344509:0.823341:0.344509:0.807763:0.292258:0.807763:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 Identificamos los vértices de la región factible.:@0.344509:0.823341:0.654522:0.823341:0.654522:0.808442:0.344509:0.808442:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.390660:0.823341:0.394329:0.823341:0.394329:0.808442:0.390660:0.808442:0.000000
A:@0.292258:0.838429:0.301254:0.838429:0.301254:0.823555:0.292258:0.823555:0.000000
( 20, 0):@0.301254:0.838429:0.344911:0.838429:0.344911:0.823530:0.301254:0.823530:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
B:@0.292258:0.853516:0.300299:0.853516:0.300299:0.838642:0.292258:0.838642:0.000000
(16, 12):@0.300299:0.853516:0.348462:0.853516:0.348462:0.838617:0.300299:0.838617:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
C:@0.292258:0.868604:0.301271:0.868604:0.301271:0.853730:0.292258:0.853730:0.000000
(0, 20):@0.301271:0.868604:0.341259:0.868604:0.341259:0.853705:0.301271:0.853705:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Paso 5.:@0.292258:0.887489:0.344509:0.887489:0.344509:0.871911:0.292258:0.871911:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 Respondemos la pregunta.  :@0.344509:0.887489:0.534997:0.887489:0.534997:0.872590:0.344509:0.872590:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
El punto factible con menor costo es preparar 0 kg de la Mezcla Premium y 20 kg de:@0.292258:0.906134:0.851410:0.906134:0.851410:0.891235:0.292258:0.891235:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
la Mezcla Estándar, con un costo de $100.:@0.292258:0.921222:0.567982:0.921222:0.567982:0.906323:0.292258:0.906323:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Mezclas (kg):@0.555055:0.586078:0.643941:0.586078:0.643941:0.570714:0.555055:0.570714:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Proteínas (kg) Vitaminas (kg):@0.675471:0.586078:0.886315:0.586078:0.886315:0.570714:0.675471:0.570714:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Mezcla Premiun ( ):@0.533009:0.611023:0.658584:0.611023:0.658584:0.596124:0.533009:0.596124:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.647360:0.611023:0.654145:0.611023:0.654145:0.596149:0.647360:0.596149:0.000000
3 kg:@0.711221:0.611023:0.739448:0.611023:0.739448:0.596124:0.711221:0.596124:0.000000:0.000000:0.000000:0.000000
1 kg:@0.820446:0.611023:0.848674:0.611023:0.848674:0.596124:0.820446:0.596124:0.000000:0.000000:0.000000:0.000000
Mezcla Estándar  ( ):@0.533009:0.635968:0.663711:0.635968:0.663711:0.621069:0.533009:0.621069:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.652470:0.635968:0.659271:0.635968:0.659271:0.621094:0.652470:0.621094:0.000000
1 kg:@0.711221:0.635968:0.739448:0.635968:0.739448:0.621069:0.711221:0.621069:0.000000:0.000000:0.000000:0.000000
2 kg:@0.820446:0.635968:0.848674:0.635968:0.848674:0.621069:0.820446:0.621069:0.000000:0.000000:0.000000:0.000000
Total disponible:@0.533009:0.660913:0.639034:0.660913:0.639034:0.646014:0.533009:0.646014:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
60 kg:@0.707133:0.660913:0.743534:0.660913:0.743534:0.646014:0.707133:0.646014:0.000000:0.000000:0.000000:0.000000:0.000000
40 kg :@0.816359:0.660913:0.856429:0.660913:0.856429:0.646014:0.816359:0.646014:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
20:@0.050349:0.712198:0.064099:0.712198:0.064099:0.700108:0.050349:0.700108:0.000000:0.000000
10:@0.050349:0.747242:0.064099:0.747242:0.064099:0.735151:0.050349:0.735151:0.000000:0.000000
10:@0.109907:0.789879:0.123657:0.789879:0.123657:0.777789:0.109907:0.777789:0.000000:0.000000
20:@0.156666:0.789879:0.170417:0.789879:0.170417:0.777789:0.156666:0.777789:0.000000:0.000000
30:@0.204538:0.789879:0.218288:0.789879:0.218288:0.777789:0.204538:0.777789:0.000000:0.000000
0:@0.057479:0.789879:0.064354:0.789879:0.064354:0.777789:0.057479:0.777789:0.000000
y:@0.056931:0.678541:0.062102:0.678541:0.062102:0.667954:0.056931:0.667954:0.000000
x:@0.246891:0.789083:0.252063:0.789083:0.252063:0.778496:0.246891:0.778496:0.000000
(0, 20):@0.072764:0.707414:0.106617:0.707414:0.106617:0.695324:0.072764:0.695324:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(16, 12):@0.145858:0.736201:0.186586:0.736201:0.186586:0.724111:0.145858:0.724111:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(20, 0):@0.166148:0.776194:0.200001:0.776194:0.200001:0.764103:0.166148:0.764103:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
20:@0.156666:0.789879:0.170416:0.789879:0.170416:0.777789:0.156666:0.777789:0.000000:0.000000
20:@0.050349:0.712198:0.064099:0.712198:0.064099:0.700108:0.050349:0.700108:0.000000:0.000000
(16, 12):@0.145857:0.736201:0.186586:0.736201:0.186586:0.724111:0.145857:0.724111:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(16, 12):@0.145857:0.736201:0.186586:0.736201:0.186586:0.724111:0.145857:0.724111:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
©Shutterstock:@0.068421:0.355714:0.068421:0.312889:0.056510:0.312889:0.056510:0.355714:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
La programación lineal ayuda :@0.073803:0.488132:0.254003:0.488132:0.254003:0.474723:0.073803:0.474723:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a generar una buena dieta :@0.073803:0.500704:0.235475:0.500704:0.235475:0.487295:0.073803:0.487295:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
para las mascotas :@0.073803:0.513276:0.182524:0.513276:0.182524:0.499866:0.073803:0.499866:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Vértices:@0.058247:0.843577:0.115842:0.843577:0.115842:0.828213:0.058247:0.828213:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
F(x, y) = 8x + 5y:@0.138223:0.843577:0.244819:0.843577:0.244819:0.828213:0.138223:0.828213:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(20, 0):@0.068248:0.868522:0.108236:0.868522:0.108236:0.853623:0.068248:0.853623:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
F(20, 0) = 160:@0.146733:0.868522:0.236308:0.868522:0.236308:0.853623:0.146733:0.853623:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(16, 12):@0.064161:0.893467:0.112324:0.893467:0.112324:0.878568:0.064161:0.878568:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
F(16, 12) = 188:@0.142646:0.893467:0.240396:0.893467:0.240396:0.878568:0.142646:0.878568:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(0, 20):@0.068248:0.918412:0.108236:0.918412:0.108236:0.903513:0.068248:0.903513:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
F(0, 20) = 100:@0.146733:0.918412:0.236308:0.918412:0.236308:0.903513:0.146733:0.903513:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
M.5.2.26.:@0.298180:0.943204:0.353208:0.943204:0.353208:0.930741:0.298180:0.930741:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
  :@0.353207:0.943204:0.360055:0.943204:0.360055:0.930912:0.353207:0.930912:0.000000:0.000000
Realizar un proceso de solución gráfica y analítica del problema de programación lineal graficando :@0.361355:0.943204:0.906631:0.943204:0.906631:0.931284:0.361355:0.931284:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.560092:0.943204:0.563027:0.943204:0.563027:0.931284:0.560092:0.931284:0.000000
 :@0.866787:0.943204:0.869722:0.943204:0.869722:0.931284:0.866787:0.931284:0.000000
las inecuaciones lineales, determinando los puntos extremos del conjunto de soluciones factibles, y encontrar la :@0.298180:0.954519:0.906643:0.954519:0.906643:0.942600:0.298180:0.942600:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
solución óptima. (Desagregada)  :@0.298180:0.965835:0.473637:0.965835:0.473637:0.953916:0.298180:0.953916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000