{"id":7367,"date":"2019-11-14T16:57:42","date_gmt":"2019-11-14T15:57:42","guid":{"rendered":"http:\/\/smart--grid.net\/?page_id=7367"},"modified":"2024-02-11T16:52:04","modified_gmt":"2024-02-11T15:52:04","slug":"forme-primale-exo","status":"publish","type":"page","link":"https:\/\/complex-systems-ai.com\/es\/programacion-lineal\/lp-primal-form-ejercicios-soluciones\/","title":{"rendered":"6 ejercicios corregidos sobre Forma Primal de programaci\u00f3n lineal"},"content":{"rendered":"<div data-elementor-type=\"wp-page\" data-elementor-id=\"7367\" class=\"elementor elementor-7367\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-174ce8e elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"174ce8e\" 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-bcea258\" data-id=\"bcea258\" 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-c247c14 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"c247c14\" 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-80ebb80\" data-id=\"80ebb80\" 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-3fecaea elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"3fecaea\" 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-124d476\" data-id=\"124d476\" 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-5da3038 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"5da3038\" 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-2725c20 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"2725c20\" 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-91b5713\" data-id=\"91b5713\" 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-2667ee5 elementor-widget elementor-widget-heading\" data-id=\"2667ee5\" 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_88 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-primal-form-ejercicios-soluciones\/#Exercices-corriges-de-programmation-lineaire-forme-primale\" >Ejercicios de programaci\u00f3n lineal corregidos (forma primaria)<\/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-primal-form-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-primal-form-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-primal-form-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-primal-form-ejercicios-soluciones\/#Exercice-3\" >Ejercicio 3<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/complex-systems-ai.com\/es\/programacion-lineal\/lp-primal-form-ejercicios-soluciones\/#Exercice-4\" >Ejercicio 4<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/complex-systems-ai.com\/es\/programacion-lineal\/lp-primal-form-ejercicios-soluciones\/#Exercice-5\" >Ejercicio 5<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/complex-systems-ai.com\/es\/programacion-lineal\/lp-primal-form-ejercicios-soluciones\/#Exercice-6\" >Ejercicio 6<\/a><\/li><\/ul><\/nav><\/div>\n<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"Exercices-corriges-de-programmation-lineaire-forme-primale\"><\/span>Ejercicios de programaci\u00f3n lineal corregidos (forma primaria)<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-8b10dce elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"8b10dce\" 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-1fda209\" data-id=\"1fda209\" 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-b136a86 elementor-widget elementor-widget-text-editor\" data-id=\"b136a86\" 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 varios ejercicios corregidos sobre modelado en forma b\u00e1sica de programaci\u00f3n lineal.<\/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=\"forma primaria de programaci\u00f3n lineal\" 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-ec4d68b elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"ec4d68b\" 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-aeddf7d\" data-id=\"aeddf7d\" 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-18dbb12 elementor-widget elementor-widget-heading\" data-id=\"18dbb12\" 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-2037f27 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"2037f27\" 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-a79cb70\" data-id=\"a79cb70\" 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-a4326b8 elementor-widget elementor-widget-text-editor\" data-id=\"a4326b8\" 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 fabricante de herramientas de fresado fabrica dos tipos de cortadores: A y B. Los cortadores tipo A se venden a 300 cada uno y se fabrican con 1 unidad de acero, 2 unidades de carburo removible y 1 unidad de diamante sint\u00e9tico. Los cortadores tipo B se venden a 200 cada uno y est\u00e1n hechos con 2 unidades de acero, 1 unidad de carburo removible y 1 unidad de diamante sint\u00e9tico.\u00a0<\/p>\n<p>Las existencias son 5 unidades de acero, 5 unidades de carburo y 2 unidades de diamante. El fabricante quiere construir al menos 5 cortadores tipo A y 5 cortadores tipo B. El costo de mantenimiento de la f\u00e1brica es de 2500. \u00bfC\u00f3mo debe distribuir el fabricante su producci\u00f3n para maximizar sus ganancias, es rentable?<\/p>\n<p><!-- \/wp:paragraph --><\/p>\n<p><!-- wp:heading {\"level\":4} --><\/p>\n<p><!-- \/wp:heading --><\/p>\n<p><!-- wp:paragraph --><\/p>\n<p>Primero, se debe realizar el programa lineal:<\/p>\n<p><!-- \/wp:paragraph --><\/p>\n<p><!-- wp:list --><\/p>\n<ul>\n<li>Funci\u00f3n objetivo: z = 300A + 200B-2500<\/li>\n<li>Restricciones:\n<ul>\n<li>A + 2B \u2264 5<\/li>\n<li>2A + B \u2264 5<\/li>\n<li>A + B \u2264 2<\/li>\n<li>A \u2265 5<\/li>\n<li>B \u2265 5<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p><!-- \/wp:list --><\/p>\n<p><!-- wp:paragraph --><\/p>\n<p>El programa no est\u00e1 en forma can\u00f3nica, debe renderizarse en esta forma antes de resolverlo.<\/p>\n<p><!-- \/wp:paragraph --><\/p>\n<p><!-- wp:paragraph --><\/p>\n<p>Sea x<sub>1<\/sub> = A-5 y x<sub>2<\/sub> = B-5. El programa lineal se convierte en el siguiente:<\/p>\n<p><!-- \/wp:paragraph --><\/p>\n<p><!-- wp:image {\"id\":7295,\"sizeSlug\":\"large\"} --><\/p>\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" class=\"alignnone wp-image-7295 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/10\/lineaire23.png\" alt=\"ejercicios corregidos de forma primal de programacion lineal\" width=\"241\" height=\"139\" title=\"\"><\/figure>\n<p><!-- \/wp:image --><\/p>\n<p><!-- wp:paragraph --><\/p>\n<p>El programa lineal tiene 2 variables, por lo que es posible resolverlo gr\u00e1ficamente. Las restricciones dan el dominio de las siguientes soluciones:<\/p>\n<p><!-- \/wp:paragraph --><\/p>\n<p><!-- wp:image {\"id\":7296,\"sizeSlug\":\"large\"} --><\/p>\n<figure class=\"wp-block-image size-large\"><img fetchpriority=\"high\" decoding=\"async\" class=\"alignnone wp-image-7296 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/10\/lineaire24.png\" alt=\"ejercicios corregidos de forma primal de programacion lineal\" width=\"313\" height=\"214\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/10\/lineaire24.png 313w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/10\/lineaire24-300x205.png 300w\" sizes=\"(max-width: 313px) 100vw, 313px\" \/><\/figure>\n<p><!-- \/wp:image --><\/p>\n<p><!-- wp:paragraph --><\/p>\n<p>El gradiente de la funci\u00f3n objetivo es (3,2), que da como punto final la intersecci\u00f3n de la segunda y tercera restricci\u00f3n. Por tanto, debemos resolver el sistema:<\/p>\n<p><!-- \/wp:paragraph --><\/p>\n<p><!-- wp:image {\"id\":7300,\"sizeSlug\":\"large\"} --><\/p>\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-7300 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/10\/lineaire25-1.png\" alt=\"ejercicios corregidos de forma primal de programacion lineal\" width=\"216\" height=\"97\" title=\"\"><\/figure>\n<p><!-- \/wp:image --><\/p>\n<p><!-- wp:paragraph --><\/p>\n<p>Que tiene por soluci\u00f3n el vector (10, 2). Esto da en el problema inicial el vector (15, 7) y para la funci\u00f3n objetivo igual a 900. La operaci\u00f3n es positiva y por lo tanto rentable para la f\u00e1brica.<\/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-240cea0 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"240cea0\" 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-9acfca7\" data-id=\"9acfca7\" 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-a6cfb80 elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"a6cfb80\" 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-45deb9e elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"45deb9e\" 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-22cae59\" data-id=\"22cae59\" 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-eb86472 elementor-widget elementor-widget-heading\" data-id=\"eb86472\" 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-db83b55 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"db83b55\" 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-6089a84\" data-id=\"6089a84\" 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-6f46155 elementor-widget elementor-widget-text-editor\" data-id=\"6f46155\" 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? Resuelve por m\u00e9todo gr\u00e1fico.<\/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-9a8d15c elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"9a8d15c\" 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-fed16ee\" data-id=\"fed16ee\" 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-cbe2e59 elementor-widget elementor-widget-toggle\" data-id=\"cbe2e59\" 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-2131\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-2131\" 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-2131\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-2131\"><p>El programa lineal es el siguiente: X1 para el primer lote y X2 para el segundo lote<\/p>\n<p><!-- \/wp:paragraph --><\/p>\n<p><!-- wp:image {\"id\":7368,\"sizeSlug\":\"large\"} --><\/p>\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-7368 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire44.png\" alt=\"ejercicios corregidos de forma primal de programacion lineal\" width=\"224\" height=\"109\" title=\"\"><\/figure>\n<p><!-- \/wp:image --><\/p>\n<p><!-- wp:paragraph --><\/p>\n<p>Lo que da por resoluci\u00f3n gr\u00e1fica:<\/p>\n<p><!-- \/wp:paragraph --><\/p>\n<p><!-- wp:image {\"id\":7369,\"sizeSlug\":\"large\"} --><\/p>\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" 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 --><\/p>\n<p><!-- 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><\/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-6230c97 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"6230c97\" 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-9071ae8\" data-id=\"9071ae8\" 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-33e6b40 elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"33e6b40\" 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-ff01de7 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"ff01de7\" 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-68fdbec\" data-id=\"68fdbec\" 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-7998bdb elementor-widget elementor-widget-heading\" data-id=\"7998bdb\" 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-228ae00 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"228ae00\" 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-33c9989\" data-id=\"33c9989\" 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-7d9a915 elementor-widget elementor-widget-text-editor\" data-id=\"7d9a915\" 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>Resolver por el m\u00e9todo gr\u00e1fico y luego por el simplex los siguientes problemas:<\/p>\n<p><!-- \/wp:paragraph --><\/p>\n<p><!-- wp:list {\"ordered\":true} --><\/p>\n<ol>\n<li>Una empresa que fabrica dos tipos de productos busca maximizar su beneficio. Aqu\u00ed est\u00e1 su hoja de ruta.<\/li>\n<\/ol>\n<p><!-- \/wp:list --><\/p>\n<p><!-- wp:image {\"id\":7418,\"sizeSlug\":\"large\"} --><\/p>\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-7418 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire66.png\" alt=\"ejercicios corregidos de forma primal de programacion lineal\" width=\"375\" height=\"233\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire66.png 375w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire66-300x186.png 300w\" sizes=\"(max-width: 375px) 100vw, 375px\" \/><\/figure>\n<p><!-- \/wp:image --><\/p>\n<p><!-- wp:list {\"ordered\":true,\"start\":2} --><\/p>\n<ol start=\"2\">\n<li>As\u00ed mismo con el siguiente programa lineal:<\/li>\n<\/ol>\n<p><!-- \/wp:list --><\/p>\n<p><!-- wp:image {\"id\":7424,\"sizeSlug\":\"large\"} --><\/p>\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-7424 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire70.png\" alt=\"ejercicios corregidos de forma primal de programacion lineal\" width=\"286\" height=\"96\" title=\"\"><\/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-7118ddf elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"7118ddf\" 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-ae8f505\" data-id=\"ae8f505\" 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-f82145a elementor-widget elementor-widget-toggle\" data-id=\"f82145a\" 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-2601\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-2601\" 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-2601\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-2601\"><p>La metodolog\u00eda es siempre la misma para la parte de resoluci\u00f3n gr\u00e1fica. Aqu\u00ed est\u00e1n las correcciones de los s\u00edmplex con el estado inicial y el estado final de la tabla para el primer ejemplo.<\/p>\n<p><!-- \/wp:paragraph --><\/p>\n<p><!-- wp:paragraph --><\/p>\n<p>Problema 0:<\/p>\n<p><!-- \/wp:paragraph --><\/p>\n<p><!-- wp:image {\"id\":7422,\"sizeSlug\":\"large\"} --><\/p>\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-7422 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire68.png\" alt=\"ejercicios corregidos de forma primal de programacion lineal\" width=\"362\" height=\"166\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire68.png 362w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire68-300x138.png 300w\" sizes=\"(max-width: 362px) 100vw, 362px\" \/><\/figure>\n<p><!-- \/wp:image --><\/p>\n<p><!-- wp:paragraph --><\/p>\n<p>Y para la soluci\u00f3n:<\/p>\n<p><!-- \/wp:paragraph --><\/p>\n<p><!-- wp:image {\"id\":7423,\"sizeSlug\":\"large\"} --><\/p>\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-7423 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire69.png\" alt=\"ejercicios corregidos de forma primal de programacion lineal\" width=\"391\" height=\"166\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire69.png 391w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire69-300x127.png 300w\" sizes=\"(max-width: 391px) 100vw, 391px\" \/><\/figure>\n<p><!-- \/wp:image --><\/p>\n<p><!-- wp:paragraph --><\/p>\n<p>La funci\u00f3n objetivo tiene para el valor Z = 1875 con P1 y P2 en base (por lo tanto, no cero) teniendo respectivamente para el valor (25,15) como se estipula en la columna b representada por P0.<\/p>\n<p><!-- \/wp:paragraph --><\/p>\n<p><!-- wp:paragraph --><\/p>\n<p>El segundo programa lineal tiene como soluci\u00f3n Z = 8.2 con el vector de variables b\u00e1sicas (3.2, 1.8).<\/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-277b5a0 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"277b5a0\" 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-fc9aba6\" data-id=\"fc9aba6\" 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-927d564 elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"927d564\" 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-15234aa elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"15234aa\" 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-d19da62\" data-id=\"d19da62\" 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-d7bddf6 elementor-widget elementor-widget-heading\" data-id=\"d7bddf6\" 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-558ea71 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"558ea71\" 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-b602d5d\" data-id=\"b602d5d\" 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-7d290c4 elementor-widget elementor-widget-text-editor\" data-id=\"7d290c4\" 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>BIM optimiza la construcci\u00f3n, rehabilitaci\u00f3n y mantenimiento de edificios. Entre los elementos a optimizar est\u00e1n los trabajadores. En general, hay 4 tipos de trabajadores seg\u00fan su fin de semana. Los salarios de los trabajadores dependen de estos d\u00edas de licencia:<\/p>\n<p><!-- \/wp:paragraph --><\/p>\n<p><!-- wp:image {\"id\":7307,\"sizeSlug\":\"large\"} --><\/p>\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-7307 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire28.png\" alt=\"ejercicios corregidos de forma primal de programacion lineal\" width=\"562\" height=\"115\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire28.png 562w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire28-300x61.png 300w\" sizes=\"(max-width: 562px) 100vw, 562px\" \/><\/figure>\n<p><!-- \/wp:image --><\/p>\n<p><!-- wp:paragraph --><\/p>\n<p>Las demandas diarias de los trabajadores son las siguientes:<\/p>\n<p><!-- \/wp:paragraph --><\/p>\n<p><!-- wp:image {\"id\":7311,\"sizeSlug\":\"large\"} --><\/p>\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-7311 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire29.png\" alt=\"ejercicios corregidos de forma primal de programacion lineal\" width=\"577\" height=\"63\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire29.png 577w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire29-300x33.png 300w\" sizes=\"(max-width: 577px) 100vw, 577px\" \/><\/figure>\n<p><!-- \/wp:image --><\/p>\n<p><!-- wp:paragraph --><\/p>\n<p>\u00bfCu\u00e1ntas personas de cada categor\u00eda deben emplearse para satisfacer la demanda y minimizar el costo de personal? Da la forma can\u00f3nica del problema y resu\u00e9lvelo usando Solver Excel.<\/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-f95ddfc elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"f95ddfc\" 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-6714618\" data-id=\"6714618\" 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-d3500f2 elementor-widget elementor-widget-toggle\" data-id=\"d3500f2\" 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-2211\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-2211\" 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-2211\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-2211\"><p>El programa lineal es el siguiente:<\/p>\n<p><!-- \/wp:paragraph --><\/p>\n<p><!-- wp:image {\"id\":7402,\"sizeSlug\":\"large\"} --><\/p>\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-7402 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire56.png\" alt=\"ejercicios corregidos de forma primal de programacion lineal\" width=\"387\" height=\"254\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire56.png 387w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire56-300x197.png 300w\" sizes=\"(max-width: 387px) 100vw, 387px\" \/><\/figure>\n<p><!-- \/wp:image --><\/p>\n<p><!-- wp:paragraph --><\/p>\n<p>La resoluci\u00f3n de Excel es la siguiente:<\/p>\n<p><!-- \/wp:paragraph --><\/p>\n<p><!-- wp:image {\"id\":7404,\"sizeSlug\":\"large\"} --><\/p>\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-7404 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire57.png\" alt=\"ejercicios corregidos de forma primal de programacion lineal\" width=\"596\" height=\"355\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire57.png 596w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire57-300x179.png 300w\" sizes=\"(max-width: 596px) 100vw, 596px\" \/><\/figure>\n<p><!-- \/wp:image --><\/p>\n<p><!-- wp:paragraph --><\/p>\n<p>El resultado es el siguiente:<\/p>\n<p><!-- \/wp:paragraph --><\/p>\n<p><!-- wp:image {\"id\":7405,\"width\":863,\"height\":414,\"sizeSlug\":\"large\"} --><\/p>\n<figure class=\"wp-block-image size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-7405 size-large\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire58-1024x491.png\" alt=\"ejercicios corregidos de forma primal de programacion lineal\" width=\"1024\" height=\"491\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire58-1024x491.png 1024w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire58-300x144.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire58-768x368.png 768w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire58.png 1163w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<p><!-- \/wp:image --><\/p>\n<p><!-- wp:paragraph --><\/p>\n<p>Tenga en cuenta que la soluci\u00f3n \u00f3ptima no es \u00fanica. La soluci\u00f3n da n\u00fameros enteros, lo cual es pr\u00e1ctico dado el problema (parece obvio que se necesitan individuos &quot;enteros&quot;).<\/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-981a0df elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"981a0df\" 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-c05d706\" data-id=\"c05d706\" 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-64a1ced elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"64a1ced\" 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-721ee4b elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"721ee4b\" 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-a104b33\" data-id=\"a104b33\" 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-3233dbf elementor-widget elementor-widget-heading\" data-id=\"3233dbf\" 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-4\"><\/span>Ejercicio 4<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-df248f2 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"df248f2\" 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-6ffa939\" data-id=\"6ffa939\" 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-261a3c5 elementor-widget elementor-widget-text-editor\" data-id=\"261a3c5\" 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>Una empresa fabrica tres tipos de productos, A, B y C. Cada producto requiere materias primas y mano de obra, as\u00ed como espacio de almacenamiento. Aqu\u00ed est\u00e1n las necesidades de materia prima, mano de obra y almacenamiento para una unidad de cada uno de los 3 tipos de productos:<\/p>\n<p><!-- \/wp:paragraph --><\/p>\n<p><!-- wp:list --><\/p>\n<ul>\n<li>Producto A: 4 kg de materias primas, 2 horas de mano de obra, 1 unidad de volumen.<\/li>\n<li>Producto B: 2 kg de materias primas, 1\/2 hora de trabajo 1 unidad de volumen.<\/li>\n<li>Producto C: 1 kg de materia prima, 3 horas de mano de obra, 1 unidad de volumen.<\/li>\n<\/ul>\n<p><!-- \/wp:list --><\/p>\n<p><!-- wp:paragraph --><\/p>\n<p>Cada producto aporta 6 euros si es de tipo A, 2 euros si es de tipo B y 4 euros si es de tipo C. Los recursos disponibles son 6000 kg de materias primas, 4000 horas de mano de obra. 2.500 unidades de volumen de almacenamiento.<\/p>\n<p><!-- \/wp:paragraph --><\/p>\n<p><!-- wp:paragraph --><\/p>\n<p>Modele el programa lineal y resu\u00e9lvalo a mano usando el simplex.<\/p>\n<p><!-- \/wp:paragraph --><\/p>\n<p><!-- wp:paragraph --><\/p>\n<p>Un competidor, que carece de materias primas, ofrece comprar 300 kg a esta empresa, a un precio de 1,5 euros el kg. \u00bfCree que la empresa deber\u00eda aceptar esta propuesta? (Suponga que lo acepta si le resulta rentable, resuelva el problema a mano con el simplex).<\/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-75ee89f elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"75ee89f\" 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-fdcb62e\" data-id=\"fdcb62e\" 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-12a3b27 elementor-widget elementor-widget-toggle\" data-id=\"12a3b27\" 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-1951\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-1951\" 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-1951\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-1951\"><p>El problema en forma est\u00e1ndar es el siguiente:<\/p>\n<p><!-- \/wp:paragraph --><\/p>\n<p><!-- wp:image {\"id\":7411,\"sizeSlug\":\"large\"} --><\/p>\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-7411 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire61.png\" alt=\"ejercicios corregidos de forma primal de programacion lineal\" width=\"411\" height=\"155\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire61.png 411w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire61-300x113.png 300w\" sizes=\"(max-width: 411px) 100vw, 411px\" \/><\/figure>\n<p><!-- \/wp:image --><\/p>\n<p><!-- wp:paragraph --><\/p>\n<p>Con la soluci\u00f3n simplex:<\/p>\n<p><!-- \/wp:paragraph --><\/p>\n<p><!-- wp:image {\"id\":7412,\"sizeSlug\":\"large\"} --><\/p>\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-7412 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire62.png\" alt=\"ejercicios corregidos de forma primal de programacion lineal\" width=\"466\" height=\"193\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire62.png 466w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire62-300x124.png 300w\" sizes=\"(max-width: 466px) 100vw, 466px\" \/><\/figure>\n<p><!-- \/wp:image --><\/p>\n<p><!-- wp:paragraph --><\/p>\n<p>El problema de redenci\u00f3n tiene adicionalmente en la funci\u00f3n objetivo 450. La primera variable tiene para el elemento b = 5700. En este caso, la soluci\u00f3n \u00f3ptima es (1310, 0, 460) con Z = 10150, por lo que la proposici\u00f3n es rentable.<\/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-00fe71d elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"00fe71d\" 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-00549e4\" data-id=\"00549e4\" 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-cf75d46 elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"cf75d46\" 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-d5bf124 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"d5bf124\" 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-33292fb\" data-id=\"33292fb\" 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-b03d62d elementor-widget elementor-widget-heading\" data-id=\"b03d62d\" 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-5\"><\/span>Ejercicio 5<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-a6be04a elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"a6be04a\" 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-3cea7db\" data-id=\"3cea7db\" 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-a87a16a elementor-widget elementor-widget-text-editor\" data-id=\"a87a16a\" 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>Una empresa fabrica tres tipos de bater\u00edas: tipo seco 1 (PS1), tipo seco 2 (PS2) y combustible (PC). El proceso de fabricaci\u00f3n tiene tres etapas: montaje, prueba de calidad, tratamiento de aislamiento. Solo las bater\u00edas que pasan la prueba de calidad se someten al tratamiento de aislamiento. Las bater\u00edas que no superan la prueba de calidad se desechan. Durante el pr\u00f3ximo mes, la empresa dispondr\u00e1 de 9.000 horas de tiempo de m\u00e1quina para el montaje, 1.200 horas para las pruebas de calidad y 8.500 horas para el procesamiento del aislamiento. La siguiente tabla resume la informaci\u00f3n relevante del proceso de fabricaci\u00f3n:<\/p>\n<p><!-- \/wp:paragraph --><\/p>\n<p><!-- wp:image {\"id\":7312,\"sizeSlug\":\"large\"} --><\/p>\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-7312 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire30.png\" alt=\"ejercicios corregidos de forma primal de programacion lineal\" width=\"602\" height=\"141\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire30.png 602w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire30-300x70.png 300w\" sizes=\"(max-width: 602px) 100vw, 602px\" \/><\/figure>\n<p><!-- \/wp:image --><\/p>\n<p><!-- wp:paragraph --><\/p>\n<p>\u00bfCu\u00e1l es la cantidad \u00f3ptima de bater\u00edas de cada tipo para fabricar el pr\u00f3ximo mes si la empresa est\u00e1 segura de vender toda su producci\u00f3n?<\/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-d58f0b0 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"d58f0b0\" 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-e687ed9\" data-id=\"e687ed9\" 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-c2bc6b7 elementor-widget elementor-widget-toggle\" data-id=\"c2bc6b7\" 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-2041\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-2041\" 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-2041\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-2041\"><p>Sean X1, X2, X3 las tres variables que representan el n\u00famero de pilas v\u00e1lidas de cada tipo y X4, X5, X6 las tres variables que representan el n\u00famero de pilas inv\u00e1lidas de cada tipo.<\/p>\n<p><!-- \/wp:paragraph --><\/p>\n<p><!-- wp:paragraph --><\/p>\n<p>El programa lineal en forma can\u00f3nica es el siguiente:<\/p>\n<p><!-- \/wp:paragraph --><\/p>\n<p><!-- wp:image {\"id\":7408,\"sizeSlug\":\"large\"} --><\/p>\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-7408 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire59.png\" alt=\"ejercicios corregidos de forma primal de programacion lineal\" width=\"479\" height=\"215\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire59.png 479w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire59-300x135.png 300w\" sizes=\"(max-width: 479px) 100vw, 479px\" \/><\/figure>\n<p><!-- \/wp:image --><\/p>\n<p><!-- wp:image {\"id\":7409,\"width\":952,\"height\":324,\"sizeSlug\":\"large\"} --><\/p>\n<figure class=\"wp-block-image size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-7409 size-large\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire60-1024x349.png\" alt=\"ejercicios corregidos de forma primal de programacion lineal\" width=\"1024\" height=\"349\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire60-1024x349.png 1024w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire60-300x102.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire60-768x262.png 768w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire60-1200x409.png 1200w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire60.png 1301w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<p><!-- \/wp:image --><\/p>\n<p><!-- wp:paragraph --><\/p>\n<p>Esto da como soluci\u00f3n (419417.476, 0, 741176.471) para bater\u00edas v\u00e1lidas y para la funci\u00f3n objetivo Z = 1278957.05. Como la soluci\u00f3n no da un resultado entero, es posible truncar la parte flotante (\u00a1cuidado, ya no ser\u00e1 una soluci\u00f3n \u00f3ptima!).<\/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-13744c0 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"13744c0\" 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-61aaa8e\" data-id=\"61aaa8e\" 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-c13d079 elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"c13d079\" 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-e9ebb66 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"e9ebb66\" 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-ca29287\" data-id=\"ca29287\" 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-d1e90c7 elementor-widget elementor-widget-heading\" data-id=\"d1e90c7\" 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-6\"><\/span>Ejercicio 6<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-4e7f597 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"4e7f597\" 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-0bc5ccc\" data-id=\"0bc5ccc\" 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-718e4f1 elementor-widget elementor-widget-text-editor\" data-id=\"718e4f1\" 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>En una red el\u00e9ctrica, la cantidad de energ\u00eda que puede pasar de las centrales el\u00e9ctricas a las ciudades est\u00e1 limitada por las capacidades de las l\u00edneas de muy alta tensi\u00f3n. El problema se describe de la siguiente manera:<\/p>\n<p><!-- \/wp:paragraph --><\/p>\n<p><!-- wp:list --><\/p>\n<ul>\n<li>Las fuentes, representadas por v\u00e9rtices, producen una cantidad de energ\u00eda<\/li>\n<li>Los pozos, representados por v\u00e9rtices, reciben una cantidad de energ\u00eda<\/li>\n<li>L\u00edneas, representadas por aristas entre un par de v\u00e9rtices, por donde pasa la energ\u00eda.<\/li>\n<\/ul>\n<p><!-- \/wp:list --><\/p>\n<p><!-- wp:image {\"id\":7322,\"sizeSlug\":\"large\"} --><\/p>\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-7322 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/dinicalgorithm.png\" alt=\"ejercicios corregidos de forma primal de programacion lineal\" width=\"499\" height=\"240\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/dinicalgorithm.png 499w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/dinicalgorithm-300x144.png 300w\" sizes=\"(max-width: 499px) 100vw, 499px\" \/><\/figure>\n<p><!-- \/wp:image --><\/p>\n<p><!-- wp:paragraph --><\/p>\n<p>Este gr\u00e1fico dice lo siguiente:<\/p>\n<p><!-- \/wp:paragraph --><\/p>\n<p><!-- wp:list --><\/p>\n<ul>\n<li>S es una fuente ficticia, que describe la producci\u00f3n de las fuentes de energ\u00eda representadas por el v\u00e9rtice 1 y el v\u00e9rtice 2.<\/li>\n<li>T es un pozo ficticio, que describe la recepci\u00f3n de energ\u00eda de las ciudades representadas por el v\u00e9rtice 3 y el v\u00e9rtice 4.<\/li>\n<li>Las l\u00edneas est\u00e1n orientadas, es decir que la energ\u00eda solo pasa en una direcci\u00f3n. Por ejemplo, el enlace (1, 3) puede circular hasta 4 unidades de energ\u00eda entre el v\u00e9rtice 1 y el v\u00e9rtice 3.<\/li>\n<li>Los v\u00ednculos entre S y las fuentes describen la producci\u00f3n de energ\u00eda de la fuente. Por ejemplo, el enlace (S, 1) dice que la fuente 1 puede producir hasta 10 unidades de energ\u00eda.<\/li>\n<li>Los v\u00ednculos entre los pozos y T describen la demanda de energ\u00eda del pozo. Por ejemplo, el enlace (3, T) dice que la ciudad 3 requiere 10 unidades de energ\u00eda.<\/li>\n<\/ul>\n<p><!-- \/wp:list --><\/p>\n<p><!-- wp:paragraph --><\/p>\n<p>La funci\u00f3n objetivo de este tipo de problemas es:<\/p>\n<p><!-- \/wp:paragraph --><\/p>\n<p><!-- wp:list --><\/p>\n<ul>\n<li>maximizar la cantidad de energ\u00eda que se puede hacer pasar de S a T. La soluci\u00f3n proporcionar\u00e1 la cantidad de energ\u00eda que pasa por cada l\u00ednea. Para calcular este flujo, se agrega un arco entre el pozo ficticio y la fuente ficticia no restringida. La soluci\u00f3n \u00f3ptima es igual al flujo que pasa por este arco.<\/li>\n<\/ul>\n<p><!-- \/wp:list --><\/p>\n<p><!-- wp:paragraph --><\/p>\n<p>Este problema est\u00e1 sujeto a dos tipos de restricciones:<\/p>\n<p><!-- \/wp:paragraph --><\/p>\n<p><!-- wp:list --><\/p>\n<ul>\n<li>la suma de las energ\u00edas que entran en un v\u00e9rtice menos la suma de las energ\u00edas que salen del mismo v\u00e9rtice es cero. Es decir que no hay p\u00e9rdidas de energ\u00eda en la red.<\/li>\n<li>la energ\u00eda que pasa a trav\u00e9s de una l\u00ednea no puede ser mayor que la capacidad de la l\u00ednea.<\/li>\n<li>la energ\u00eda que pasa por una l\u00ednea es positiva o nula.<\/li>\n<\/ul>\n<p><!-- \/wp:list --><\/p>\n<p><!-- wp:paragraph --><\/p>\n<p>Por tanto, las variables son:<\/p>\n<p><!-- \/wp:paragraph --><\/p>\n<p><!-- wp:list --><\/p>\n<ul>\n<li>para cada fila, una variable describe la cantidad de energ\u00eda que la atraviesa.<\/li>\n<\/ul>\n<p><!-- \/wp:list --><\/p>\n<p><!-- wp:paragraph --><\/p>\n<p>Formule el problema lineal para el gr\u00e1fico anterior y resu\u00e9lvalo a trav\u00e9s de Excel.<\/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-5acc14d elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"5acc14d\" 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-5314929\" data-id=\"5314929\" 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-38d5c36 elementor-widget elementor-widget-toggle\" data-id=\"38d5c36\" 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-5951\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-5951\" 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-5951\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-5951\"><p>El problema lineal est\u00e1 escrito en Excel de la siguiente manera:<\/p>\n<p><!-- \/wp:paragraph --><\/p>\n<p><!-- wp:image {\"id\":7416,\"width\":823,\"height\":402,\"sizeSlug\":\"large\"} --><\/p>\n<figure class=\"wp-block-image size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-7416 size-large\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire64-1024x501.png\" alt=\"ejercicios corregidos de forma primal de programacion lineal\" width=\"1024\" height=\"501\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire64-1024x501.png 1024w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire64-300x147.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire64-768x376.png 768w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire64.png 1092w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<p><!-- \/wp:image --><\/p>\n<p><!-- wp:paragraph --><\/p>\n<p>Lo que da como resultado:<\/p>\n<p><!-- \/wp:paragraph --><\/p>\n<p><!-- wp:image {\"id\":7417,\"width\":826,\"height\":412,\"sizeSlug\":\"large\"} --><\/p>\n<figure class=\"wp-block-image size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-7417 size-large\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire65-1024x511.png\" alt=\"ejercicios corregidos de forma primal de programacion lineal\" width=\"1024\" height=\"511\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire65-1024x511.png 1024w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire65-300x150.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire65-768x383.png 768w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire65.png 1072w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/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<\/div>","protected":false},"excerpt":{"rendered":"<p>Programaci\u00f3n lineal P\u00e1gina de inicio Wiki Ejercicios de programaci\u00f3n lineal corregidos (forma primaria) Este tutorial ofrece varios ejercicios corregidos sobre modelado en forma primaria... <\/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-7367","page","type-page","status-publish","hentry"],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/pages\/7367","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=7367"}],"version-history":[{"count":6,"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/pages\/7367\/revisions"}],"predecessor-version":[{"id":20317,"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/pages\/7367\/revisions\/20317"}],"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=7367"}],"curies":[{"name":"gracias","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}