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Función Objetivo Variables de decisión y parámetros Restricciones.

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Presentación del tema: "Función Objetivo Variables de decisión y parámetros Restricciones."— Transcripción de la presentación:

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3 Función Objetivo Variables de decisión y parámetros Restricciones

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5 La óptica Central desea determinar cuanto debe producir para que sea óptimamente aprovechada (es decir, obtener el > beneficio). Ella posee 74 modelos de monturas. 74 Monturas Tornillos15000 unid. Carey 4700 gr. Lentejas de silicona1000 lent. Cada montura posee 6 tornillos, 5 gr. cobre 2 lentejas de silicona se posee 478 monturas en inventario final de periodo anterior. Su producción debe ser menor o igual a este. Por el comportamiento de mercado se sabe que la demanda de monturas al mes es de 1000 unidades.

6 De acuerdo al estudio de mercado se determino que del modelo Amadeus se debe producir una cantidad mayor a 40, del modelo Barón se debe producir a lo más 30 unidades

7 Los tiempos y requerimientos se mostraron en el siguiente cuadro. Var.Tiempo Dpta Tornillos Inst. carey Coloc. Siliconas MarcaCantidadCosto Unit Precio Unit. Utilidad X1X1 252310Amadeus3140.7553.7913.04 X2X2 18208Andrea Biagiotti4813.2215.472.25 X3X3 18208Angel Eye112153 X4X4 10155Baglioni177.259.522.27 X5X5 18208Barbinzon C/flex1011.00154 X6X6 23m2510Baron3338.2543.8575.607 X7X7 23 m2510Belutti140.0049.989.98 X8X8 10 m125Best17.00103 X9X9 15 m166Biaggio1311.00154 X 10 12135Bibi19.00123 X 11 18208Broadway110.00155 X 12 10125Camel26.3092.7 X 13 10125Cameroon25.208.333.12 X 14 16177Carusso117.75159.25 X 15 11135Cecilie19.95122.05

8 X 16 10125Clare collection27.00103 X 17 11135Clio19.2012.53.3 X 18 202310Couple Rim120.0129.759.74 X 19 282510Crispol147.10535.9 X 20 10125Cross48.083 X 21 10125Cta34.084 X 22 10125Christiam Dior14.1083.9 X 23 10125Dasic165.308.333.03 X 24 24125Dilen523.403511.6 X 25 112510Dirary17.0103 X 26 10135Donald duck15.708.332.63 X 27 10125Duck head15.108.333.23 X 28 10125Escape16.0104 X 29 12135Europtics46.0104 X 30 12135Flemingo45.208.333.13 X 31 9104Flinistones p niños323.103511.9 X 32 242510Frost57.108.331.23 X 33 10125Ferry Weber130.2049.9819.78 X 34 282510Gianni211.2015.173.97 X 35 16178Giovanni2613.10151.9 X 36 17188Giovanni Ochialli14.4072.6

9 X 37 8104Giro13.5084.5 X 38 10125Goya lens34.409.525.12 X 39 11135Gratfitti112.10152.9 X 40 17188Hermes18.0102 X 41 11135Historie de Voir125.108.333.23 X 42 10125Hollayday149.40155.6 X 43 16177Hollywood18.10125.9 X 44 13155Jr. Optical27.30135.7 X 45 14166Jazmin o Jazmine105.108.333.23 X 46 9104Kenzo85.108.333.23 X 47 10125Kirk35.108.332.32 X 48 10125Lectos Alicia17.50102.50 X 49 8104Lector Nitro42.2063.80 X 50 202310Logros213.70184.3 X 51 9104Maniatan45.108.333.23 X 52 9104Maru15.108.333.23 X 53 10125Melissa24.1083.9 X 54 8104Monc Blanc63.2062.8

10 X 55 192110Myke2514.2017.693.49 X 56 11135Napoli26.70103.3 X 57 12145Panorama16.70103.3 X 58 8104Pascali14.1061.9 X 59 9104Passport Ochiali44.5083.5 X 60 11135Primicia15.30104.7 X 61 11135Primmera45.30104.7 X 62 12145Profesor35.30104.7 X 63 9104Reiz35.108.333.23 X 64 13156Revelato16.7012.675.97 X 65 10125Rexon204.208.334.13 X 66 10125Roden184.208.334.13 X 67 17208Rover411.3016.665.36 X 68 894s/m63.2073.8 X 69 794Salón kids23.106.543.8 X 70 894Stom153.2073.8 X 71 9104Sun13.2073.7 X 72 894Sziois63.20725.6 X 73 15177Tribal2310.3014 X 74 302510u. Pacific580.40106 Total disponible 980010710950062

11 Amadeus Andrea Biagiotti Angel Eye Baglioni Barbinzon C/flex Baron Belutti Best Biaggio Bibi Broadway Camel Cameroon Carusso Cecilie Clare collection Clio Couple Rim Crispol Cross Cta Christiam Dior Dasic Dilen Dirary Donald duck Duck head Escape Europtics Flemingo Flinistones p niños Frost Ferry Weber Gianni Giovanni Giovanni Ochialli Giro Goya lens Gratfitti Hermes Historie de Voir Hollayday Hollywood Jr. Optical Jazmin o Jazmine Kenzo Kirk Lectos Alicia Lector Nitro Logros Maniatan Maru Melissa Monc Blanc Myke Napoli Panorama Pascali Passport Ochiali Primicia

12 Primmera Profesor Reiz Revelato Rexon Roden Rover s/m Salón kids Stom Sun Sziois Tribal u. Pacific

13 Max Z = 13.04X1 + 2.25 X2 + 3 X3+ 2.27 X4+ 4 X5+ 5.607 X6+ 9.98 X7+ 3 X8+ 4 X9+ 3 X10+ 5 X11+ 2.7 X12+ 3.12 X13+ 9.25 X14+ 2.05 X15+ 3 X16+ 3.3 X17+ 9.74 X18+ 5.9 X19+ 3 X20+4 X21+ 39X22+ 3.03 X23+ 11.6 X24+ 3 X25+ 2.63 X26+ 3.23 X27+ 4 X28+ 4 X29+ 3.13 X30+ 11.9 X31+ 1.23 X32+ 19.78 X33+ 3.97 X34+ 1.9 X35+ 2.6 X36+ 4.5 X37+ 5.12 X38+ 2.9 X39+ 2 X40+ 3.23 X41+ 5.6 X42+ 3.9 X43+ 5.7 X44+ 3.23 X45+ 3.23 X46+ 3.23 X47+ 2.50 X48+ 3.80 X49+ 4.3 X50+ 3.23 X51+ 3.23 X52+ 3.9 X53+ 2.8 X54+ 3.49 X55+ 3.3 X56+ 3.3 X57+ 1.9 X58+ 3.5 X59+ 4.7 X60+ 4.7 X61+ 4.7 X62+ 3.23 X63+ 5.97 X64+ 4.13 X65+ 4.13 X66+ 5.36 X67+ 3.8 X68+ 3.44 X69+ 3.8 X70+ 3.8 X71+ 3.8 X72+ 3.7 X73+ 25.6 X74. Función objetivo: Maximizar la utilidad. Max Z = Maximizar la utilidad

14 6X1 + 6X2 + 6X3 + 6X4 + 6X5 + 6X6 + 6X7 + 6X8+ 6X9+ 6X10 + 6X11 + 6X12 + 6X13 + 6 X14 + 6X15n + 6X16 + 6X17 + 6X18 + 6X19 + 6X20 + 6X21+ 6X22 + 6X23+ 6X24 + 6X25 + 6 X26 + 6X27 + 6X28 + 6X29 + 6X30 + 6X31+ 6X32 + 6X33 + 6X34 + 6X35 + 6X36 + 6 X37 + 6X38 + 6X39 + 6X40+ 6X41 + 6X42 + 6X43 + 6X44 + 6X45 + 6X46 + 6X47 + 6X48 + 6X49 + 6X50 + 6X51 + 6X52 + 6X53 + 6X54 + 6X55 + 6X56 + 6X57 + 6X58 + 6X59 + 6 X60 + 6X61 + 6X62 + 6X63 + 6X64 + 6X65 + 6X66 + 6X67 + 6X68 + 6X69 + 6X70 + 6X71 +6 X72 + 6X73 + 6X74 1600 unidades

15 5X1 + 5X2 + 5X3 + 5X4 + 5X5 + 5X6 + 5X7 + 5X8+ 5X9+ 5X10 + 5X11 + 5X12 + 5X13 + 5X14 + 5X15n + 5X16 + 5X17 + 5X18 + 5X19 + 5X20 + 5X21+ 5X22 + 5X23+ 5X24 + 5X25 + 5X26 + 5X27 + 5X28 + 5X29 + 5X30 + 5X31+ 5X32 + 5X33 + 5X34 + 5X35 + 5X36 + 5 X37 + 5X38 + 5X39 + 5X40+ 5X41 + 5X42 + 5X43 + 5X44 + 5X45 + 5X46 + 5X47 + 5X48 + 5X49 + 5X50 + 5X51 + 5X52 + 5X53 + 5X54 + 5X55 + 5X56 + 5X57 + 5X58 + 5X59 + 5X60 + 5X61 + 5X62 + 5X63 + 5X64 + 5X65 + 5X66 + 5X67 + 5X68 + 5X69 + 5X70 + 5X71 +5 X72 + 5X73 + 5X74 4700 Gr.

16 2X1 + 2X2 + 2X3 + 2X4 + 2X5 + 2X6 + 2X7 + 2X8+ 2X9+ 2X10 + 2X11 + 2X12 + 2X13 + 2X14 + 2X15n + 2X16 + 2X17 + 2X18 + 2X19 + 2X20 + 2X21+ 2X22 + 2X23+ 2X24 + 2X25 + 2X26 + 2X27 + 2X28 + 2X29 + 2X30 + 2X31+ 2X32 + 2X33 + 2X34 + 2X35 + 2X36 +2 X37 + 2X38 + 2X39 + 2X40 + 2X41 + 2X42 + 2X43 + 2X44 + 2X45 + 2X46 + 2X47 + 2X48 + 2X49 + 2X50 + 2X51 + 2X52 + 2X53 + 2X54 + 2X55 + 2X56 + 2X57 + 2X58 + 2X59 + 2X60 + 2X61 + 2X62 + 2X63 + 2X64 + 2X65 + 2X66 + 2X67 + 2X68 + 2X69 + 2X70 + 2X71 + 2X72 + 2X73 + 2X74 1000 unidades.

17 X1 + X2 + X3 + X4 + X5 + X6 + X7 + X8+ X9+ X10 + X11 + X12 + X13 + X14 + X15n + X16 + X17 + X18 + X19 + X20 + X21+ X22 + X23+ X24 + X25 + X26 + X27 + X28 + X29 + X30 + X31+ X32 + X33 + X34 + X35 + X36 + X37 + X38 + X39 + X40 + X41 + X42 + X43 + X44 + X45 + X46 + X47 + X48 + X49 + X50 + X51 + X52 + X53 + X54 + X55 + X56 + X57 + X58 + X59 + X60 + X61 + X62 + X63 + X64 + X65 + X66 + X67 + X68 + X69 + X70 + X71 + X72 + X73 + X74 474 monturas.

18 X1 + X2 + X3 + X4 + X5 + X6 + X7 + X8+ X9+ X10 + X11 + X12 + X13 + X14 + X15n + X16 + X17 + X18 + X19 + X20 + X21+ X22 + X23+ X24 + X25 + X26 + X27 + X28 + X29 + X30 + X31+ X32 + X33 + X34 + X35 + X36 + X37 + X38 + X39 + X40 + X41 + X42 + X43 + X44 + X45 + X46 + X47 + X48 + X49 + X50 + X51 + X52 + X53 + X54 + X55 + X56 + X57 + X58 + X59 + X60 + X61 + X62 + X63 + X64 + X65 + X66 + X67 + X68 + X69 + X70 + X71 + X72 + X73 + X74 1000 monturas.

19 X1 40 X6 30

20 25X1 + 18X2 + 18X3 + 10X4 + 18X5 + 23X6 + 23X7 + 10X8+ 15X9+ 12X10 + 18X11 + 10X12 + 10X13 + 16X14 + 11X15n + 10X16 + 11X17 + 20X18 + 28X19 + 10X20 + 10X21+ 10X22 + 10X23+ 10X24 + 24X25 + 11X26 + 10X27 + 10X28 + 12X29 + 12X30 + 9X31+ 24X32 + 10X33 + 28X34 + 16X35 + 17X36 + 8X37 + 10X38 + 11X39 + 17X40 + 11X41 + 10X42 + 13X43 + 14X44 + 9X45 + 10X46 + 10X47 + 10X48 + 8X49 + 20X50 + 9X51 + 9X52 + 10X53 + 8X54 + 19X55 + 11X56 + 12X57 + 8X58 + 9X59 + 10X60 + 11X61 + 12X62 + 9X63 + 13X64 + 10X65 + 10X66 + 17X67 + 8X68 + 7X69 + 8X70 + 9X71 + 8X72 + 15X73 + 30X74 9800.

21 23X1 + 20X2 + 20X3 + 15X4 + 20X5 + 25X6 + 25X7 + 12X8+ 16X9+ 3X10 + 20X11 + 12X12 + 12X13 + 17X14 + 13X15n + 12X16 + 13X17 + 33X18 + 25X19 + 12X20 + 12X21+ 12X22 + 12X23+ 12X24 + 25X25 + 13X26 + 12X27 + 12X28 + 13X29 + 13X30 + 10X31+ 25X32 + 12X33 + 25X34 + 17X35 + 18X36 + 10X37 + 12X38 + 13X39 + 18X40 + 13X41 + 12X42 + 17X43 + 15X44 + 16X45 + 10X46 + 12X47 + 12X48 + 10X49 + 23X50 + 10X51 + 10X52 + 12X53 + 10X54 + 21X55 + 13X56 + 14X57 + 10X58 + 10X59 + 13X60 + 13X61 + 14X62 + 10X63 + 15X64 + 12X65 + 12X66 + 20X67 + 9X68 + 9X69 + 9X70 + 10X71 + 9X72 + 17X73 + 25X74 10710.

22 10X1 + 8X2 + 8X3 + 5X4 + 8X5 + 10X6 + 10X7 + 5X8+ 6X9+ 7X10 + 8X11 + 5X12 + 5X13 + 7X14 + 5X15n + 5X16 + 5X17 + 10X18 + 10X19 + 5X20 + 5X21+ 5X22 + 5X23+ 5X24 + 10X25 + 5X26 + 5X27 + 5X28 + 5X29 + 5X30 + 4X31+ 10X32 + 5X33 + 10X34 + 8X35 + 8X36 + 4X37 + 5X38 + 5X39 + 8X40 + 5X41 + 5X42 + 7X43 + 5X44 + 6X45 + 4X46 + 5X47 + 5X48 + 4X49 + 10X50 + 4X51 + 4X52 + 5X53 + 4X54 + 10X55 + 5X56 + 5X57 + 4X58 + 4X59 + 5X60 + 5X61 + 5X62 + 4X63 + 6X64 + 5X65 + 5X66 + 8X67 + 4X68 + 4X69 + 4X70 + 4X71 + 4X72 + 7X73 + 10X74 9500.

23 X1 + X2 + X3 + X4 + X5 + X6 + X7 + X8+ X9+ X10 + X11 + X12 + X13 + X14 + X15n + X16 + X17 + X18 + X19 + X20 + X21+ X22 + X23+ X24 + X25 + X26 + X27 + X28 + X29 + X30 + X31+ X32 + X33 + X34 + X35 + X36 + X37 + X38 + X39 + X40 + X41 + X42 + X43 + X44 + X45 + X46 + X47 + X48 + X49 + X50 + X51 + X52 + X53 + X54 + X55 + X56 + X57 + X58 + X59 + X60 + X61 + X62 + X63 + X64 + X65 + X66 + X67 + X68 + X69 + X70 + X71 + X72 + X73 + X74 0.

24 Objective Functio n(Max.) =1.019.482,00 Left Hand Right HandSlackShadow Allowabl e Constrai ntSide Directio nSide or SurplusPrice Min. RHS Max. RHS 1C12.844,00<=16.000,0013.156,0002.844,00M 2C22.370,00<=4.700,002.330,0002.370,00M 3C3948<=1.000,00520948M 4C4474<=47401.978,0070500 5C5474<=1.000,005260474M 6C640>=400-6740311,3333 7C730<=3003.629,000343,0769 8C85.730,00<=9.800,004.070,0005.730,00M 9C96.518,00<=10.710,004.192,0006.518,00M 1010C102.720,00<=9.500,006.780,0002.720,00M Resultados obtenidos por el

25 13.156,00 unidades de tornillos, 2.330,00 unidades de Carey, 52 lentejas de Silicona. 526 monturas en función de la demanda, 4.070,00 minutos en el departamento de tornillo, 4.192,00 minutos en el departamento de colocación de Carey 6.780,00 minutos en el departamento de colocación de Silicona. La solución óptima es de s/.1.019.482,00 Sobran

26 MARCA DE MONTURASUNIDADES A PRODUCIR Amadeus 40 Andrea Biagiotti 0 Angel Eye 0 Baglioni 0 Barbinzon C/flex 0 Baron 30 Belutti 0 Best 0 Biaggio 0 Bibi 0 Broadway 0 Camel 0 Cameroon 0 Carusso 0 Cecilie 0 Clare collection 0 Clio 0 Couple Rim 0

27 Crispol 0 Cross 0 Cta 0 Christiam Dior 0 Dasic 0 Dilen 0 Dirary 0 Donald duck 0 Duck head 0 Escape 0 Europtics 0 Flemingo 0 Flinistones p niños 0 Frost 0 Ferry Weber 404 Gianni 0 Giovanni 0 Giovanni Ochialli 0 Giro 0

28 Goya lens 0 Gratfitti 0 Hermes 0 Historie de Voir 0 Hollayday 0 Hollywood 0 Jr. Optical 0 Jazmin o Jazmine 0 Kenzo 0 Kirk 0 Lectos Alicia 0 Lector Nitro 0 Logros 0 Maniatan 0 Maru 0 Melissa 0 Monc Blanc 0 Myke 0 Napoli 0 Panorama 0

29 Pascali 0 Passport Ochiali 0 Primicia 0 Primmera 0 Profesor 0 Reiz 0 Revelato 0 Rexon 0 Roden 0 Rover 0 s/m 0 Salón kids 0 Stom 0 Sun 0 Sziois 0 Tribal 0 u. Pacific 0


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