163:@0.937671:0.974518:0.968375:0.974518:0.968375:0.956333:0.937671:0.956333:0.000000:0.000000:0.000000
Pensamiento espacial, numérico y variacional:@0.522009:0.043661:0.926913:0.043661:0.926913:0.024916:0.522009:0.024916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Utilidad marginal = :@0.073089:0.144304:0.216572:0.144304:0.216572:0.127870:0.073089:0.127870:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∆x:@0.220630:0.147778:0.231637:0.147778:0.231637:0.136592:0.220630:0.136592:0.000000:0.000000
→:@0.231598:0.147217:0.242333:0.147217:0.242333:0.137179:0.231598:0.137179:0.000000
0:@0.242275:0.147778:0.248400:0.147778:0.248400:0.136573:0.242275:0.136573:0.000000
lím:@0.222946:0.140233:0.245624:0.140233:0.245624:0.123799:0.222946:0.123799:0.000000:0.000000:0.000000
 :@0.252582:0.144310:0.256613:0.144310:0.256613:0.127876:0.252582:0.127876:0.000000
∆U:@0.259816:0.136836:0.279548:0.136836:0.279548:0.120430:0.259816:0.120430:0.000000:0.000000
∆x:@0.261620:0.153228:0.277763:0.153228:0.277763:0.136822:0.261620:0.136822:0.000000:0.000000
 = :@0.282770:0.144311:0.301656:0.144311:0.301656:0.127877:0.282770:0.127877:0.000000:0.000000:0.000000
dU:@0.302112:0.137728:0.322342:0.137728:0.322342:0.121321:0.302112:0.121321:0.000000:0.000000
dx:@0.303898:0.154120:0.320538:0.154120:0.320538:0.137714:0.303898:0.137714:0.000000:0.000000
 =  ' ( ).:@0.322821:0.144301:0.383178:0.144301:0.383178:0.127867:0.322821:0.127867:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
U  x:@0.341614:0.144301:0.375244:0.144301:0.375244:0.127895:0.341614:0.127895:0.000000:0.000000:0.000000:0.000000
El costo marginal y la utilidad marginal se interpretan como el costo o la utilidad de :@0.073089:0.178805:0.710457:0.178805:0.710457:0.162371:0.073089:0.162371:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
producir y vender una unidad adicional, dado que, en general, las unidades son números :@0.073089:0.195447:0.710229:0.195447:0.710229:0.179013:0.073089:0.179013:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
enteros.:@0.073089:0.212089:0.130739:0.212089:0.130739:0.195655:0.073089:0.195655:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Costo marginal =   ( ) ≈  ( + 1) –  ( ).:@0.244185:0.239451:0.535240:0.239451:0.535240:0.223017:0.244185:0.223017:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
C ' n:@0.372833:0.239451:0.406794:0.239451:0.406794:0.223045:0.372833:0.223045:0.000000:0.000000:0.000000:0.000000:0.000000
C n :@0.430301:0.239451:0.457672:0.239451:0.457672:0.223045:0.430301:0.223045:0.000000:0.000000:0.000000:0.000000
C n:@0.503175:0.239451:0.527307:0.239451:0.527307:0.223045:0.503175:0.223045:0.000000:0.000000:0.000000
Habría dos maneras de encontrar los costos y las utilidades marginales: derivar las :@0.073071:0.266813:0.710641:0.266813:0.710641:0.250379:0.073071:0.250379:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
funciones de costo y utilidad o calcular los costos y utilidades de producir y vender  + 1 :@0.073071:0.283455:0.710348:0.283455:0.710348:0.267021:0.073071:0.267021:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x :@0.672209:0.283455:0.682903:0.283455:0.682903:0.267048:0.672209:0.267048:0.000000:0.000000
unidades y hacer la diferencia de los costos y utilidades de producir y vender   unidades.:@0.073071:0.300096:0.706356:0.300096:0.706356:0.283663:0.073071:0.283663:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.625325:0.300096:0.632780:0.300096:0.632780:0.283690:0.625325:0.283690:0.000000
Problema::@0.073053:0.327458:0.149967:0.327458:0.149967:0.310789:0.073053:0.310789:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 costo marginal y utilidad marginal.:@0.149866:0.327458:0.403253:0.327458:0.403253:0.311025:0.149866:0.311025:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Una empresa fabrica y vende cierto producto. El costo total (en dólares) para producir   :@0.073053:0.354820:0.710330:0.354820:0.710330:0.338386:0.073053:0.338386:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.698844:0.354820:0.706299:0.354820:0.706299:0.338414:0.698844:0.338414:0.000000
unidades del producto está dado por::@0.073053:0.371462:0.346794:0.371462:0.346794:0.355028:0.073053:0.355028:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
C x:@0.301781:0.398824:0.323870:0.398824:0.323870:0.382418:0.301781:0.382418:0.000000:0.000000:0.000000
( ) = 500 + 30  – 0,05:@0.311611:0.398824:0.465035:0.398824:0.465035:0.382390:0.311611:0.382390:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.410678:0.398824:0.418133:0.398824:0.418133:0.382418:0.410678:0.382418:0.000000
х:@0.464906:0.398824:0.472361:0.398824:0.472361:0.382418:0.464906:0.382418:0.000000
2:@0.472368:0.392775:0.477605:0.392775:0.477605:0.383194:0.472368:0.383194:0.000000
Además, la :@0.073089:0.426202:0.155485:0.426202:0.155485:0.409769:0.073089:0.409769:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
utilidad total :@0.155351:0.426202:0.256346:0.426202:0.256346:0.409533:0.155351:0.409533:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(en dólares) por vender x unidades está dada por::@0.256204:0.426202:0.614251:0.426202:0.614251:0.409769:0.256204:0.409769:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
U x:@0.323998:0.453564:0.347228:0.453564:0.347228:0.437158:0.323998:0.437158:0.000000:0.000000:0.000000
( ) = 80  – 0,02:@0.334969:0.453564:0.442909:0.453564:0.442909:0.437131:0.334969:0.437131:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.388552:0.453564:0.396007:0.453564:0.396007:0.437158:0.388552:0.437158:0.000000
x:@0.442780:0.453564:0.450235:0.453564:0.450235:0.437158:0.442780:0.437158:0.000000
2:@0.450190:0.447502:0.455427:0.447502:0.455427:0.437921:0.450190:0.437921:0.000000
a.  Encontremos el costo marginal  ´( ) y la utilidad marginal  ´( )**:@0.104633:0.480929:0.602562:0.480929:0.602562:0.464495:0.104633:0.464495:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
C x:@0.364041:0.480929:0.391560:0.480929:0.391560:0.464523:0.364041:0.464523:0.000000:0.000000:0.000000
U x:@0.554851:0.480929:0.583511:0.480929:0.583511:0.464523:0.554851:0.464523:0.000000:0.000000:0.000000
b.  Calculemos el costo marginal y la utilidad marginal cuando se producen y :@0.104633:0.501145:0.710458:0.501145:0.710458:0.484711:0.104633:0.484711:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
venden 100 unidades.:@0.134760:0.517787:0.294815:0.517787:0.294815:0.501353:0.134760:0.501353:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
c.  Interpretemos los resultados: ¿conviene producir más unidades en este punto?:@0.104633:0.538002:0.705628:0.538002:0.705628:0.521568:0.104633:0.521568:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Paso 1::@0.073096:0.565363:0.125387:0.565363:0.125387:0.548694:0.073096:0.548694:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 encontremos el costo marginal y la utilidad marginal.:@0.125281:0.565363:0.512761:0.565363:0.512761:0.548930:0.125281:0.548930:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
• :@0.073089:0.592728:0.082108:0.592728:0.082108:0.576058:0.073089:0.576058:0.000000:0.000000
El costo marginal es la derivada del costo total con respecto a  .:@0.103288:0.592728:0.581563:0.592728:0.581563:0.576058:0.103288:0.576058:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.569709:0.592728:0.577827:0.592728:0.577827:0.576044:0.569709:0.576044:0.000000
C  x:@0.275672:0.620700:0.308161:0.620700:0.308161:0.604294:0.275672:0.604294:0.000000:0.000000:0.000000:0.000000
' ( )  = :@0.288759:0.620700:0.335735:0.620700:0.335735:0.604266:0.288759:0.604266:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
d:@0.341668:0.614123:0.350927:0.614123:0.350927:0.597717:0.341668:0.597717:0.000000
dx:@0.337968:0.630515:0.354608:0.630515:0.354608:0.614109:0.337968:0.614109:0.000000:0.000000
 (500 + 30  – 0,05 ).:@0.356891:0.620696:0.503767:0.620699:0.503767:0.604265:0.356891:0.604262:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.428937:0.620696:0.436392:0.620696:0.436392:0.604290:0.428937:0.604290:0.000000
x:@0.483164:0.620696:0.490619:0.620696:0.490619:0.604290:0.483164:0.604290:0.000000
2:@0.490569:0.614635:0.495806:0.614635:0.495806:0.605054:0.490569:0.605054:0.000000
Derivando::@0.103207:0.648061:0.182435:0.648061:0.182435:0.631627:0.103207:0.631627:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
C  x:@0.326984:0.675423:0.359473:0.675423:0.359473:0.659017:0.326984:0.659017:0.000000:0.000000:0.000000:0.000000
' ( ). = 30 – 0,1 .:@0.340072:0.675423:0.452448:0.675423:0.452448:0.658989:0.340072:0.658989:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.441864:0.675423:0.449319:0.675423:0.449319:0.659017:0.441864:0.659017:0.000000
• :@0.073089:0.702788:0.082108:0.702788:0.082108:0.686119:0.073089:0.686119:0.000000:0.000000
La utilidad marginal es la derivada de la utilidad total con respecto a :@0.103288:0.702788:0.620786:0.702788:0.620786:0.686119:0.103288:0.686119:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x.:@0.620440:0.702788:0.632367:0.702788:0.632367:0.686105:0.620440:0.686105:0.000000:0.000000
U  x:@0.299822:0.730761:0.333452:0.730761:0.333452:0.714355:0.299822:0.714355:0.000000:0.000000:0.000000:0.000000
' ( ) = :@0.314051:0.730761:0.357069:0.730761:0.357069:0.714327:0.314051:0.714327:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
d:@0.363012:0.724182:0.372271:0.724182:0.372271:0.707776:0.363012:0.707776:0.000000
dx:@0.359312:0.740574:0.375952:0.740574:0.375952:0.724168:0.359312:0.724168:0.000000:0.000000
 (80  – 0,02 ).:@0.378235:0.730756:0.479614:0.730758:0.479614:0.714324:0.378235:0.714322:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.404778:0.730756:0.412233:0.730756:0.412233:0.714349:0.404778:0.714349:0.000000
x:@0.459006:0.730756:0.466461:0.730756:0.466461:0.714349:0.459006:0.714349:0.000000
2:@0.466416:0.724694:0.471652:0.724694:0.471652:0.715113:0.466416:0.715113:0.000000
Derivando::@0.103204:0.758120:0.182432:0.758120:0.182432:0.741686:0.103204:0.741686:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
U  x:@0.327956:0.785482:0.361586:0.785482:0.361586:0.769076:0.327956:0.769076:0.000000:0.000000:0.000000:0.000000
' ( ) = 80 – 0,4 .:@0.342185:0.785482:0.451450:0.785482:0.451450:0.769048:0.342185:0.769048:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.440866:0.785482:0.448321:0.785482:0.448321:0.769076:0.440866:0.769076:0.000000
Paso 2::@0.073071:0.812844:0.125362:0.812844:0.125362:0.796174:0.073071:0.796174:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 calculemos el costo marginal y la utilidad marginal para   = 100.:@0.125256:0.812844:0.590278:0.812844:0.590278:0.796410:0.125256:0.796410:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.534154:0.812844:0.541609:0.812844:0.541609:0.796438:0.534154:0.796438:0.000000
Sustituyendo   = 100 en las ecuaciones del costo marginal y la utilidad marginal::@0.103185:0.840206:0.683548:0.840206:0.683548:0.823772:0.103185:0.823772:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.202916:0.840206:0.210371:0.840206:0.210371:0.823800:0.202916:0.823800:0.000000
• :@0.073089:0.867574:0.082108:0.867574:0.082108:0.850905:0.073089:0.850905:0.000000:0.000000
Costo marginal::@0.103288:0.867574:0.221923:0.867574:0.221923:0.850905:0.103288:0.850905:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
C :@0.250417:0.892440:0.263560:0.892440:0.263560:0.876034:0.250417:0.876034:0.000000:0.000000
' (100) = 30 – 0,1(100) = 30 – 10 = 20.:@0.263505:0.892440:0.529232:0.892440:0.529232:0.876006:0.263505:0.876006:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
El costo marginal para producir la unidad número 101 es 20 dólares.:@0.103214:0.919802:0.594189:0.919802:0.594189:0.903368:0.103214:0.903368:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Interdisciplinariedad :@0.740294:0.174451:0.906668:0.174451:0.906668:0.157504:0.740294:0.157504:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Matemáticas y :@0.740294:0.191092:0.849287:0.191092:0.849287:0.174659:0.740294:0.174659:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
finanzas:@0.740294:0.207734:0.799179:0.207734:0.799179:0.191300:0.740294:0.191300:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Cuando el número de :@0.740730:0.243979:0.889265:0.243979:0.889265:0.229040:0.740730:0.229040:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
unidades producidas y :@0.740730:0.259108:0.894039:0.259108:0.894039:0.244168:0.740730:0.244168:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
vendidas aumenta de :@0.740730:0.274237:0.887848:0.274237:0.887848:0.259297:0.740730:0.259297:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.740730:0.289366:0.747508:0.289366:0.747508:0.274452:0.740730:0.274452:0.000000
1:@0.747447:0.289427:0.751970:0.289427:0.751970:0.281153:0.747447:0.281153:0.000000
 a   , las derivadas de :@0.751930:0.289366:0.892739:0.289366:0.892739:0.274426:0.751930:0.274426:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.766640:0.289366:0.773417:0.289366:0.773417:0.274452:0.766640:0.274452:0.000000
2:@0.773353:0.289427:0.777876:0.289427:0.777876:0.281153:0.773353:0.281153:0.000000
las funciones de costo :@0.740730:0.304495:0.890592:0.304495:0.890592:0.289555:0.740730:0.289555:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y utilidad nos permiten :@0.740730:0.319624:0.897547:0.319624:0.897547:0.304684:0.740730:0.304684:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
entender cómo cambian :@0.740730:0.334753:0.908815:0.334753:0.908815:0.319813:0.740730:0.319813:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
el costo y la utilidad por :@0.740730:0.349882:0.901269:0.349882:0.901269:0.334942:0.740730:0.334942:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cada unidad adicional :@0.740730:0.365011:0.889476:0.365011:0.889476:0.350071:0.740730:0.350071:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
producida. La derivada :@0.740730:0.380140:0.894476:0.380140:0.894476:0.365200:0.740730:0.365200:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de la función de costo :@0.740730:0.395269:0.890877:0.395269:0.890877:0.380329:0.740730:0.380329:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
muestra cómo varía el :@0.740730:0.410398:0.890641:0.410398:0.890641:0.395458:0.740730:0.395458:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
costo de producir una :@0.740730:0.425527:0.890065:0.425527:0.890065:0.410587:0.740730:0.410587:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
unidad más, mientras que :@0.740730:0.440656:0.915574:0.440656:0.915574:0.425716:0.740730:0.425716:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
la derivada de la función :@0.740730:0.455785:0.905643:0.455785:0.905643:0.440845:0.740730:0.440845:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de utilidad muestra cómo :@0.740730:0.470913:0.915097:0.470913:0.915097:0.455974:0.740730:0.455974:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cambia la utilidad por :@0.740730:0.486042:0.887704:0.486042:0.887704:0.471103:0.740730:0.471103:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cada unidad adicional :@0.740730:0.501171:0.889476:0.501171:0.889476:0.486232:0.740730:0.486232:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
vendida. Estos cambios :@0.740730:0.516300:0.897949:0.516300:0.897949:0.501360:0.740730:0.501360:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
se pueden aproximar :@0.740730:0.531429:0.884561:0.531429:0.884561:0.516489:0.740730:0.516489:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
observando las derivadas :@0.740730:0.546558:0.911503:0.546558:0.911503:0.531618:0.740730:0.531618:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
en el punto inicial, lo que :@0.740730:0.561687:0.910097:0.561687:0.910097:0.546747:0.740730:0.546747:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ayuda a la compañía a :@0.740730:0.576816:0.891462:0.576816:0.891462:0.561876:0.740730:0.561876:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
tomar decisiones sobre la :@0.740730:0.591945:0.912524:0.591945:0.912524:0.577005:0.740730:0.577005:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
producción para maximizar :@0.740730:0.607074:0.924780:0.607074:0.924780:0.592134:0.740730:0.592134:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
la utilidad y controlar los :@0.740730:0.622203:0.905151:0.622203:0.905151:0.607263:0.740730:0.607263:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
costos.:@0.740730:0.637332:0.785865:0.637332:0.785865:0.622392:0.740730:0.622392:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
MUESTRA EDITORIAL:@0.248902:0.947499:0.888171:0.113285:0.743922:0.050540:0.104653:0.884754:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 Muestra editorial solo para fines didácticos – Prohibida su venta:@0.095585:0.659700:0.095585:0.341447:0.077558:0.341447:0.077558:0.659700:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000