{"id":7377,"date":"2019-11-27T13:17:52","date_gmt":"2019-11-27T12:17:52","guid":{"rendered":"http:\/\/smart--grid.net\/?page_id=7377"},"modified":"2024-02-11T19:00:58","modified_gmt":"2024-02-11T18:00:58","slug":"lp-cas-particuliers","status":"publish","type":"page","link":"https:\/\/complex-systems-ai.com\/es\/programacion-lineal\/lp-casos-especificos-ejercicios-soluciones\/","title":{"rendered":"3 ejercicios corregidos para casos especiales en LP"},"content":{"rendered":"<div data-elementor-type=\"wp-page\" data-elementor-id=\"7377\" class=\"elementor elementor-7377\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-42294c0 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"42294c0\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-72b814c\" data-id=\"72b814c\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-8f54bc8 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"8f54bc8\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/complex-systems-ai.com\/es\/programacion-lineal\/\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Programaci\u00f3n lineal<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-10e061d\" data-id=\"10e061d\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-77f02c0 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"77f02c0\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/complex-systems-ai.com\/es\/\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Pagina de inicio<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-58bb868\" data-id=\"58bb868\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-70a15e5 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"70a15e5\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/fr.wikipedia.org\/wiki\/Algorithme_du_simplexe\" target=\"_blank\" rel=\"noopener\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Wiki<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-054a238 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"054a238\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-d70eb3c\" data-id=\"d70eb3c\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-e8ef4aa elementor-widget elementor-widget-heading\" data-id=\"e8ef4aa\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_82_2 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Contenido<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Tabla de contenido alternativo\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Palanca<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewbox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewbox=\"0 0 24 24\" version=\"1.2\" baseprofile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/complex-systems-ai.com\/es\/programacion-lineal\/lp-casos-especificos-ejercicios-soluciones\/#Exercices-Corriges-de-Cas-Particuliers-Grand-M-en-Programmation-Lineaire\" >Ejercicios corregidos para casos especiales (Big M) en programaci\u00f3n lineal<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/complex-systems-ai.com\/es\/programacion-lineal\/lp-casos-especificos-ejercicios-soluciones\/#Tutoriel\" >Tutorial<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/complex-systems-ai.com\/es\/programacion-lineal\/lp-casos-especificos-ejercicios-soluciones\/#Exercice-1\" >Ejercicio 1<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/complex-systems-ai.com\/es\/programacion-lineal\/lp-casos-especificos-ejercicios-soluciones\/#Exercice-2\" >Ejercicio 2<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/complex-systems-ai.com\/es\/programacion-lineal\/lp-casos-especificos-ejercicios-soluciones\/#Exercice-3\" >Ejercicio 3<\/a><\/li><\/ul><\/nav><\/div>\n<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"Exercices-Corriges-de-Cas-Particuliers-Grand-M-en-Programmation-Lineaire\"><\/span>Ejercicios corregidos para casos especiales (Big M) en programaci\u00f3n lineal<span class=\"ez-toc-section-end\"><\/span><\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-9405ae1 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"9405ae1\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-4078d74\" data-id=\"4078d74\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-b7b6059 elementor-widget elementor-widget-text-editor\" data-id=\"b7b6059\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Este tutorial ofrece ejercicios corregidos en casos particulares (degeneraci\u00f3n, M grande, simplex de dos fases).<\/p>\n<p><img decoding=\"async\" class=\"aligncenter wp-image-11096 size-full\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/09\/cropped-Capture.png\" alt=\"casos particulares\" width=\"97\" height=\"97\" title=\"\"><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-f429ff2 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"f429ff2\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-ec6ca00\" data-id=\"ec6ca00\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-7f5b421 elementor-widget elementor-widget-heading\" data-id=\"7f5b421\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"Tutoriel\"><\/span>Tutorial<span class=\"ez-toc-section-end\"><\/span><\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-35e8fb3 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"35e8fb3\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-9adfecf\" data-id=\"9adfecf\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-c2dfee0 elementor-widget elementor-widget-text-editor\" data-id=\"c2dfee0\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Un corredor necesita, para sus clientes, 108 MWh de electricidad para la ciudad 1 y 96 MWh de electricidad para la ciudad 2. Sin embargo, las leyes de Kirchhoff no permiten que un distribuidor apunte a una sola ciudad para el tr\u00e1nsito de energ\u00eda. Dos distribuidores atienden estas ciudades: el distribuidor A puede enviar 12 MWh a la ciudad 1 y 8 MWh a la ciudad 2 por lote comprado; El distribuidor B puede enviar 9 MWh a la ciudad 1 y 12 MWh a la ciudad 2 por lote comprado. Todos los lotes tienen el mismo precio. \u00bfCu\u00e1ntos lotes debe comprar el corredor para satisfacer la demanda de energ\u00eda de las dos ciudades? Resuelva por el m\u00e9todo gr\u00e1fico y por el simplex.<\/p>\n<p><!-- \/wp:paragraph --><!-- wp:heading {\"level\":4} --><!-- \/wp:heading --><!-- wp:paragraph --><\/p>\n<p>El programa lineal es el siguiente: X1 para el primer lote y X2 para el segundo lote<\/p>\n<p><!-- \/wp:paragraph --><!-- wp:image {\"id\":7368,\"sizeSlug\":\"large\"} --><\/p>\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" class=\"alignnone wp-image-7368 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire44.png\" alt=\"casos especiales programaci\u00f3n lineal forma primaria ejercicios corregidos\" width=\"224\" height=\"109\" title=\"\"><\/figure>\n<p><!-- \/wp:image --><!-- wp:paragraph --><\/p>\n<p>Lo que da por resoluci\u00f3n gr\u00e1fica:<\/p>\n<p><!-- \/wp:paragraph --><!-- wp:image {\"id\":7369,\"sizeSlug\":\"large\"} --><\/p>\n<figure class=\"wp-block-image size-large\"><img fetchpriority=\"high\" decoding=\"async\" class=\"alignnone wp-image-7369 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire45.png\" alt=\"ejercicios corregidos de forma primal de programacion lineal\" width=\"865\" height=\"684\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire45.png 865w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire45-300x237.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire45-768x607.png 768w\" sizes=\"(max-width: 865px) 100vw, 865px\" \/><\/figure>\n<p><!-- \/wp:image --><!-- wp:paragraph --><\/p>\n<p>El gradiente es (-1, -1) porque es un m\u00ednimo (min f (x) = - max -f (x)). En el campo de la definici\u00f3n en verde, el punto C es el \u00fanico extremo que es un \u00f3ptimo global. Resolver el sistema anterior en forma de igualdad da las coordenadas (6, 4) con Z = 10.<\/p>\n<p><!-- \/wp:paragraph --><!-- wp:paragraph --><\/p>\n<p>Para la resoluci\u00f3n del simplex es necesario sobre todo reducir a la forma est\u00e1ndar.<\/p>\n<p><!-- \/wp:paragraph --><!-- wp:image {\"id\":7375,\"sizeSlug\":\"large\"} --><\/p>\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-7375 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire46.png\" alt=\"programaci\u00f3n lineal s\u00edmplex de dos fases m\u00e9todo degenerado de la gran M\" width=\"762\" height=\"146\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire46.png 762w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire46-300x57.png 300w\" sizes=\"(max-width: 762px) 100vw, 762px\" \/><\/figure>\n<p><!-- \/wp:image --><!-- wp:paragraph --><\/p>\n<p>Es necesario resolver el simplex en dos fases para eliminar las variables artificiales:<\/p>\n<p><!-- \/wp:paragraph --><!-- wp:image {\"id\":7385,\"sizeSlug\":\"large\"} --><\/p>\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-7385 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire48.png\" alt=\"programaci\u00f3n lineal s\u00edmplex de dos fases m\u00e9todo degenerado de la gran M\" width=\"444\" height=\"169\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire48.png 444w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire48-300x114.png 300w\" sizes=\"(max-width: 444px) 100vw, 444px\" \/><\/figure>\n<p><!-- \/wp:image --><!-- wp:paragraph --><\/p>\n<p>Y el resultado de la primera fase. Notamos que Z = 0, por lo que hay una soluci\u00f3n al problema:<\/p>\n<p><!-- \/wp:paragraph --><!-- wp:image {\"id\":7388,\"sizeSlug\":\"large\"} --><\/p>\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-7388 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire49.png\" alt=\"programaci\u00f3n lineal s\u00edmplex de dos fases m\u00e9todo degenerado de la gran M\" width=\"485\" height=\"169\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire49.png 485w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire49-300x105.png 300w\" sizes=\"(max-width: 485px) 100vw, 485px\" \/><\/figure>\n<p><!-- \/wp:image --><!-- wp:paragraph --><\/p>\n<p>Para la segunda fase, la fila Z se vuelve a calcular despu\u00e9s de eliminar las columnas de variables artificiales. Para hacer esto, tomamos los buenos coeficientes de la funci\u00f3n objetivo (-1, -1, 0, 0):<\/p>\n<p><!-- \/wp:paragraph --><!-- wp:paragraph --><\/p>\n<p>- (0) + (-1 * 6) + (-1 * 4) = -10 para la columna b (P0)<br \/>- (- 1) + (-1 * 1) + (-1 * 0) = 0 para la columna P1<br \/>- (- 1) + (-1 * 0) + (-1 * 1) = 0 para la columna P2<br \/>- (0) + (-1 * -1 \/ 6) + (-1 * 1\/9) = 1\/18 para la columna P3 <br \/>- (0) + (-1 * 1\/8) + (-1 * -1 \/ 6) = 1\/24 para la columna P4<\/p>\n<p><!-- \/wp:paragraph --><!-- wp:paragraph --><\/p>\n<p>Lo que da el siguiente simplex:<\/p>\n<p><!-- \/wp:paragraph --><!-- wp:image {\"id\":7390,\"sizeSlug\":\"large\"} --><\/p>\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-7390 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire50.png\" alt=\"programaci\u00f3n lineal s\u00edmplex de dos fases m\u00e9todo degenerado de la gran M\" width=\"396\" height=\"170\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire50.png 396w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire50-300x129.png 300w\" sizes=\"(max-width: 396px) 100vw, 396px\" \/><\/figure>\n<p><!-- \/wp:image --><!-- wp:paragraph --><\/p>\n<p>Todos los coeficientes excepto la columna b son positivos, por lo tanto, el simplex ya tiene la soluci\u00f3n \u00f3ptima que es Z = 10 con el vector (6, 4, 0, 0).<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-c322702 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"c322702\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-e22a8a6\" data-id=\"e22a8a6\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-8fbee2e elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"8fbee2e\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"divider.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-divider\">\n\t\t\t<span class=\"elementor-divider-separator\">\n\t\t\t\t\t\t<\/span>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-70ada31 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"70ada31\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-8552450\" data-id=\"8552450\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-41bbb6b elementor-widget elementor-widget-heading\" data-id=\"41bbb6b\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"Exercice-1\"><\/span>Ejercicio 1<span class=\"ez-toc-section-end\"><\/span><\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-bf15981 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"bf15981\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-61aa7e5\" data-id=\"61aa7e5\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-c115d07 elementor-widget elementor-widget-text-editor\" data-id=\"c115d07\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Un revendedor de electricidad prometi\u00f3 a sus clientes que al menos 25% de su electricidad ser\u00eda de origen renovable. Calcul\u00f3 que para el pr\u00f3ximo a\u00f1o tendr\u00e1 un mercado de como m\u00e1ximo 18 TWh. Tambi\u00e9n ha preseleccionado a tres proveedores a los que comprar\u00e1 su electricidad al por mayor. Aqu\u00ed est\u00e1n las cantidades (en TWh), la tarifa de electricidad renovable y el margen generado (en miles de euros \/ TWh) que estos tres productores pueden aportar. \u00bfDe qu\u00e9 productores y en qu\u00e9 cantidad este revendedor debe comprar su electricidad para obtener el mejor beneficio posible? Resuelva el problema lineal con el m\u00e9todo M grande usando Excel.<\/p>\n<p><!-- \/wp:paragraph --><!-- wp:image {\"id\":7306,\"sizeSlug\":\"large\"} --><\/p>\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-7306 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire27.png\" alt=\"programaci\u00f3n lineal s\u00edmplex de dos fases m\u00e9todo degenerado de la gran M\" width=\"562\" height=\"143\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire27.png 562w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire27-300x76.png 300w\" sizes=\"(max-width: 562px) 100vw, 562px\" \/><\/figure>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-3a3dfbd elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"3a3dfbd\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-07333c5\" data-id=\"07333c5\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-186893c elementor-widget elementor-widget-toggle\" data-id=\"186893c\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"toggle.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-2551\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-2551\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon elementor-toggle-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-closed\"><i class=\"fas fa-caret-right\"><\/i><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-opened\"><i class=\"elementor-toggle-icon-opened fas fa-caret-up\"><\/i><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-toggle-title\" tabindex=\"0\">Soluci\u00f3n<\/a>\n\t\t\t\t\t<\/div>\n\n\t\t\t\t\t<div id=\"elementor-tab-content-2551\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-2551\"><p>Despu\u00e9s del formato est\u00e1ndar, el problema es el siguiente, hay m\u00e1s restricciones que variables, por lo que podemos resolver el primario:<\/p>\n<p><!-- \/wp:paragraph --><!-- wp:image {\"id\":7396,\"sizeSlug\":\"large\"} --><\/p>\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-7396 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire51.png\" alt=\"programaci\u00f3n lineal s\u00edmplex de dos fases m\u00e9todo degenerado de la gran M\" width=\"602\" height=\"509\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire51.png 602w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire51-300x254.png 300w\" sizes=\"(max-width: 602px) 100vw, 602px\" \/><\/figure>\n<p><!-- \/wp:image --><!-- wp:paragraph --><\/p>\n<p>El problema se resuelve en dos fases porque hay una variable artificial. Aqu\u00ed est\u00e1 la tabla de la primera fase:<\/p>\n<p><!-- \/wp:paragraph --><!-- wp:image {\"id\":7397,\"sizeSlug\":\"large\"} --><\/p>\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-7397 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire52.png\" alt=\"programaci\u00f3n lineal s\u00edmplex de dos fases m\u00e9todo degenerado de la gran M\" width=\"548\" height=\"250\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire52.png 548w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire52-300x137.png 300w\" sizes=\"(max-width: 548px) 100vw, 548px\" \/><\/figure>\n<p><!-- \/wp:image --><!-- wp:paragraph --><\/p>\n<p>Y la soluci\u00f3n de la primera fase, notamos que Z = 0 por lo que hay una soluci\u00f3n al problema:<\/p>\n<p><!-- \/wp:paragraph --><!-- wp:image {\"id\":7398,\"sizeSlug\":\"large\"} --><\/p>\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-7398 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lienaire53.png\" alt=\"programaci\u00f3n lineal s\u00edmplex de dos fases m\u00e9todo degenerado de la gran M\" width=\"605\" height=\"250\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lienaire53.png 605w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lienaire53-300x124.png 300w\" sizes=\"(max-width: 605px) 100vw, 605px\" \/><\/figure>\n<p><!-- \/wp:image --><!-- wp:paragraph --><\/p>\n<p>Despu\u00e9s de recalcular los coeficientes de Z, la segunda fase comienza con la siguiente tabla:<\/p>\n<p><!-- \/wp:paragraph --><!-- wp:image {\"id\":7399,\"sizeSlug\":\"large\"} --><\/p>\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-7399 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire54.png\" alt=\"programaci\u00f3n lineal s\u00edmplex de dos fases m\u00e9todo degenerado de la gran M\" width=\"567\" height=\"252\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire54.png 567w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire54-300x133.png 300w\" sizes=\"(max-width: 567px) 100vw, 567px\" \/><\/figure>\n<p><!-- \/wp:image --><!-- wp:paragraph --><\/p>\n<p>Y termina con la siguiente tabla:<\/p>\n<p><!-- \/wp:paragraph --><!-- wp:image {\"id\":7400,\"sizeSlug\":\"large\"} --><\/p>\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-7400 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire55.png\" alt=\"programaci\u00f3n lineal s\u00edmplex de dos fases m\u00e9todo degenerado de la gran M\" width=\"606\" height=\"250\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire55.png 606w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire55-300x124.png 300w\" sizes=\"(max-width: 606px) 100vw, 606px\" \/><\/figure><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-09a3d82 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"09a3d82\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-8dda0c9\" data-id=\"8dda0c9\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-b649e80 elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"b649e80\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"divider.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-divider\">\n\t\t\t<span class=\"elementor-divider-separator\">\n\t\t\t\t\t\t<\/span>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-68e3858 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"68e3858\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-70ccd20\" data-id=\"70ccd20\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-90714ed elementor-widget elementor-widget-heading\" data-id=\"90714ed\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"Exercice-2\"><\/span>Ejercicio 2<span class=\"ez-toc-section-end\"><\/span><\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-0666fd3 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"0666fd3\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-273d7a5\" data-id=\"273d7a5\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-fab7f25 elementor-widget elementor-widget-text-editor\" data-id=\"fab7f25\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Resuelva el siguiente programa lineal (por Excel):<\/p>\n<p><!-- \/wp:paragraph --><!-- wp:image {\"id\":7482,\"sizeSlug\":\"large\"} --><\/p>\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-7482 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire87.png\" alt=\"programaci\u00f3n lineal s\u00edmplex de dos fases m\u00e9todo degenerado de la gran M\" width=\"321\" height=\"142\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire87.png 321w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire87-300x133.png 300w\" sizes=\"(max-width: 321px) 100vw, 321px\" \/><\/figure>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-1fab040 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"1fab040\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-82936cf\" data-id=\"82936cf\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-c000f54 elementor-widget elementor-widget-toggle\" data-id=\"c000f54\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"toggle.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-2011\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-2011\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon elementor-toggle-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-closed\"><i class=\"fas fa-caret-right\"><\/i><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-opened\"><i class=\"elementor-toggle-icon-opened fas fa-caret-up\"><\/i><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-toggle-title\" tabindex=\"0\">Soluci\u00f3n<\/a>\n\t\t\t\t\t<\/div>\n\n\t\t\t\t\t<div id=\"elementor-tab-content-2011\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-2011\"><p>Se nota sobre todo que hay m\u00e1s variables que restricciones, por lo que es necesario resolver el programa lineal pasando por el simplex y las variaciones complementarias. El dual en forma can\u00f3nica y luego est\u00e1ndar es el siguiente:<\/p>\n<p><!-- \/wp:paragraph --><!-- wp:image {\"id\":7484,\"sizeSlug\":\"large\"} --><\/p>\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-7484 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire88-1.png\" alt=\"programaci\u00f3n lineal s\u00edmplex de dos fases m\u00e9todo degenerado de la gran M\" width=\"566\" height=\"517\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire88-1.png 566w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire88-1-300x274.png 300w\" sizes=\"(max-width: 566px) 100vw, 566px\" \/><\/figure>\n<p><!-- \/wp:image --><!-- wp:paragraph --><\/p>\n<p>Por lo tanto, debemos resolver el problema de la M grande para eliminar las variables artificiales. El simplex a resolver es el siguiente:<\/p>\n<p><!-- \/wp:paragraph --><!-- wp:image {\"id\":7485,\"sizeSlug\":\"large\"} --><\/p>\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-7485 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire89.png\" alt=\"programaci\u00f3n lineal s\u00edmplex de dos fases m\u00e9todo degenerado de la gran M\" width=\"522\" height=\"224\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire89.png 522w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire89-300x129.png 300w\" sizes=\"(max-width: 522px) 100vw, 522px\" \/><\/figure>\n<p><!-- \/wp:image --><!-- wp:paragraph --><\/p>\n<p>Lo que resulta en:<\/p>\n<p><!-- \/wp:paragraph --><!-- wp:image {\"id\":7487,\"sizeSlug\":\"large\"} --><\/p>\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-7487 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire90.png\" alt=\"programaci\u00f3n lineal s\u00edmplex de dos fases m\u00e9todo degenerado de la gran M\" width=\"646\" height=\"224\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire90.png 646w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire90-300x104.png 300w\" sizes=\"(max-width: 646px) 100vw, 646px\" \/><\/figure>\n<p><!-- \/wp:image --><!-- wp:paragraph --><\/p>\n<p>Eliminando las variables artificiales y volviendo al programa dual tenemos la siguiente tabla:<\/p>\n<p><!-- \/wp:paragraph --><!-- wp:image {\"id\":7489,\"sizeSlug\":\"large\"} --><\/p>\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-7489 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire91.png\" alt=\"programaci\u00f3n lineal s\u00edmplex de dos fases m\u00e9todo degenerado de la gran M\" width=\"506\" height=\"223\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire91.png 506w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire91-300x132.png 300w\" sizes=\"(max-width: 506px) 100vw, 506px\" \/><\/figure>\n<p><!-- \/wp:image --><!-- wp:paragraph --><\/p>\n<p>La soluci\u00f3n \u00f3ptima tiene para el vector (3\/7, 2\/7) con Z = 65\/7. Repasemos las diferencias complementarias para encontrar una soluci\u00f3n al primario.<\/p>\n<p><!-- \/wp:paragraph --><!-- wp:paragraph --><\/p>\n<p>Las dos variables no son cero, por lo tanto, las restricciones de la primaria est\u00e1n saturadas. Las restricciones 2 y 3 del dual est\u00e1n insaturadas, por lo que la segunda y la tercera variable del primario son cero. Por tanto, debe resolverse el siguiente problema:<\/p>\n<p><!-- \/wp:paragraph --><!-- wp:list --><\/p>\n<ul>\n<li>X1 + 5 X4 = 15<\/li>\n<li>2 X1 - 4 X4 = 10<\/li>\n<\/ul>\n<p><!-- \/wp:list --><!-- wp:paragraph --><\/p>\n<p>El vector soluci\u00f3n del primario es (55\/7, 0, 0, 10\/7) y Z = 65\/7. Hay una fuerte dualidad, por lo que es una soluci\u00f3n \u00f3ptima de lo primordial.<\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-92be164 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"92be164\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-4cb5ff2\" data-id=\"4cb5ff2\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-7708842 elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"7708842\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"divider.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-divider\">\n\t\t\t<span class=\"elementor-divider-separator\">\n\t\t\t\t\t\t<\/span>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-19a06a9 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"19a06a9\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-6f3a20a\" data-id=\"6f3a20a\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-5817d18 elementor-widget elementor-widget-heading\" data-id=\"5817d18\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"Exercice-3\"><\/span>Ejercicio 3<span class=\"ez-toc-section-end\"><\/span><\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-e2ad90d elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"e2ad90d\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-8a50d77\" data-id=\"8a50d77\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-e3cf8c9 elementor-widget elementor-widget-text-editor\" data-id=\"e3cf8c9\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Cuando un eco-distrito produce m\u00e1s energ\u00eda de la que consume, vende el excedente de energ\u00eda al vecindario y a la red. Por lo tanto, el ecodistrito busca maximizar sus ganancias en base a ofertas del mercado local. Las ofertas del mercado son las siguientes:<\/p>\n<p><!-- \/wp:paragraph --><!-- wp:table {\"hasFixedLayout\":true} --><\/p>\n<figure class=\"wp-block-table\">\n<table class=\"has-fixed-layout\">\n<tbody>\n<tr>\n<td>Oferta n \u00b0<\/td>\n<td>1<\/td>\n<td>2<\/td>\n<td>3<\/td>\n<td>4<\/td>\n<td>5<\/td>\n<td>6<\/td>\n<\/tr>\n<tr>\n<td>Lucro<\/td>\n<td>10<\/td>\n<td>8<\/td>\n<td>15<\/td>\n<td>4<\/td>\n<td>1<\/td>\n<td>5<\/td>\n<\/tr>\n<tr>\n<td>Energ\u00eda (en kWh)<\/td>\n<td>5<\/td>\n<td>10<\/td>\n<td>10<\/td>\n<td>5<\/td>\n<td>1<\/td>\n<td>7<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/figure>\n<p><!-- \/wp:table --><!-- wp:paragraph --><\/p>\n<p>El problema se formula de la siguiente manera: el eco-distrito busca obtener el m\u00e1ximo beneficio por una venta de energ\u00eda de 25 kWh. El eco-distrito debe vender todo el excedente energ\u00e9tico.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-fe78576 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"fe78576\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-3fe9ecd\" data-id=\"3fe9ecd\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-8694f14 elementor-widget elementor-widget-toggle\" data-id=\"8694f14\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"toggle.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-1411\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-1411\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon elementor-toggle-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-closed\"><i class=\"fas fa-caret-right\"><\/i><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-opened\"><i class=\"elementor-toggle-icon-opened fas fa-caret-up\"><\/i><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-toggle-title\" tabindex=\"0\">Soluci\u00f3n<\/a>\n\t\t\t\t\t<\/div>\n\n\t\t\t\t\t<div id=\"elementor-tab-content-1411\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-1411\"><p>Para solucionar este problema, considere que cada oferta est\u00e1 representada por una variable (en porcentaje de aceptaci\u00f3n de la oferta) que estar\u00e1 entre 0 y 1.<\/p>\n<p><!-- \/wp:paragraph --><!-- wp:paragraph --><\/p>\n<p>El problema se formula de la siguiente manera:<\/p>\n<p><!-- \/wp:paragraph --><!-- wp:image {\"id\":7495,\"sizeSlug\":\"large\"} --><\/p>\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-7495 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire92.png\" alt=\"programaci\u00f3n lineal s\u00edmplex de dos fases m\u00e9todo degenerado de la gran M\" width=\"432\" height=\"236\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire92.png 432w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire92-300x164.png 300w\" sizes=\"(max-width: 432px) 100vw, 432px\" \/><\/figure>\n<p><!-- \/wp:image --><!-- wp:paragraph --><\/p>\n<p>Lo que da como forma est\u00e1ndar:<\/p>\n<p><!-- \/wp:paragraph --><!-- wp:image {\"id\":7496,\"sizeSlug\":\"large\"} --><\/p>\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-7496 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire93.png\" alt=\"programaci\u00f3n lineal s\u00edmplex de dos fases m\u00e9todo degenerado de la gran M\" width=\"765\" height=\"236\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire93.png 765w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire93-300x93.png 300w\" sizes=\"(max-width: 765px) 100vw, 765px\" \/><\/figure>\n<p><!-- \/wp:image --><!-- wp:paragraph --><\/p>\n<p>Comencemos resolviendo la gran M:<\/p>\n<p><!-- \/wp:paragraph --><!-- wp:image {\"id\":7497,\"sizeSlug\":\"large\"} --><\/p>\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-7497 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire94.png\" alt=\"programaci\u00f3n lineal s\u00edmplex de dos fases m\u00e9todo degenerado de la gran M\" width=\"708\" height=\"314\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire94.png 708w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire94-300x133.png 300w\" sizes=\"(max-width: 708px) 100vw, 708px\" \/><\/figure>\n<p><!-- \/wp:image --><!-- wp:paragraph --><\/p>\n<p>Despu\u00e9s de resolver la M grande y volver a la forma est\u00e1ndar:<\/p>\n<p><!-- \/wp:paragraph --><!-- wp:image {\"id\":7499,\"sizeSlug\":\"large\"} --><\/p>\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-7499 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire95.png\" alt=\"programaci\u00f3n lineal s\u00edmplex de dos fases m\u00e9todo degenerado de la gran M\" width=\"753\" height=\"306\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire95.png 753w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire95-300x122.png 300w\" sizes=\"(max-width: 753px) 100vw, 753px\" \/><\/figure>\n<p><!-- \/wp:image --><!-- wp:paragraph --><\/p>\n<p>Observamos que el valor Z para la variable 1, 2, 3, 4, 5 est\u00e1 en cero, por lo que hay un n\u00famero infinito de soluciones. La soluci\u00f3n obtenida aqu\u00ed es Z = 166\/5 con el vector (1, 9\/10, 1, 0, 1, 0).<\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>","protected":false},"excerpt":{"rendered":"<p>P\u00e1gina de inicio de programaci\u00f3n lineal Wiki Ejercicios corregidos para casos especiales (Big M) en programaci\u00f3n lineal Este tutorial ofrece ejercicios corregidos para casos especiales... <\/p>","protected":false},"author":1,"featured_media":0,"parent":486,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-7377","page","type-page","status-publish","hentry"],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/pages\/7377","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/comments?post=7377"}],"version-history":[{"count":9,"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/pages\/7377\/revisions"}],"predecessor-version":[{"id":20337,"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/pages\/7377\/revisions\/20337"}],"up":[{"embeddable":true,"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/pages\/486"}],"wp:attachment":[{"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/media?parent=7377"}],"curies":[{"name":"gracias","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}