{"id":7237,"date":"2019-10-25T12:28:41","date_gmt":"2019-10-25T11:28:41","guid":{"rendered":"http:\/\/smart--grid.net\/?page_id=7237"},"modified":"2022-12-03T23:03:32","modified_gmt":"2022-12-03T22:03:32","slug":"lp-solutions-et-domaine-realisables","status":"publish","type":"page","link":"https:\/\/complex-systems-ai.com\/es\/programacion-lineal\/lp-soluciones-y-dominio-realizable\/","title":{"rendered":"LP: Soluciones y \u00e1rea factible"},"content":{"rendered":"<div data-elementor-type=\"wp-page\" data-elementor-id=\"7237\" class=\"elementor elementor-7237\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-767d6b3 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"767d6b3\" 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-3081152\" data-id=\"3081152\" 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-af9db5b elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"af9db5b\" 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-e5fc4f3\" data-id=\"e5fc4f3\" 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-50e77d0 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"50e77d0\" 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-9b5f693\" data-id=\"9b5f693\" 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-dca0073 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"dca0073\" 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\/Optimisation_lin%C3%A9aire\" 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-321d7a80 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"321d7a80\" 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-119c2c77\" data-id=\"119c2c77\" 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-5577bc84 elementor-widget elementor-widget-text-editor\" data-id=\"5577bc84\" 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\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_85 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-soluciones-y-dominio-realizable\/#Domaine-realisable\" >Dominio alcanzable<\/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-soluciones-y-dominio-realizable\/#Domaine-realisable-ou-domaine-de-definition\" >Dominio alcanzable (o dominio de definici\u00f3n)<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"Domaine-realisable\"><\/span>Dominio alcanzable<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p class=\"wp-block-paragraph\">Una soluci\u00f3n de uno <a href=\"https:\/\/complex-systems-ai.com\/es\/ayuda-con-la-decision\/modelado-lineal\/\">problema lineal<\/a> Se dice que es factible si se cumplen todas las restricciones. El dominio factible contiene todas las soluciones factibles del problema. La soluci\u00f3n \u00f3ptima es la soluci\u00f3n o soluciones factibles \u201cmejores\u201d.<\/p>\n\n<p class=\"wp-block-paragraph\">Para saber si una soluci\u00f3n es factible, basta con probar si se cumplen todas las restricciones, que se puede hacer a mano o en forma de matriz.<\/p>\n\n<p class=\"wp-block-paragraph\"><strong><em>A mano :<\/em><\/strong><\/p>\n\n<figure class=\"wp-block-image size-medium\"><img fetchpriority=\"high\" decoding=\"async\" class=\"alignnone wp-image-7242 size-medium\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/10\/optimisationlineaire-300x213.png\" alt=\"programaci\u00f3n lineal dominio de definici\u00f3n dominio realizable\" width=\"300\" height=\"213\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/10\/optimisationlineaire-300x213.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/10\/optimisationlineaire.png 534w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/figure>\n\n<p class=\"wp-block-paragraph\">Comprobemos si la soluci\u00f3n (3, 1) es factible.<\/p>\n\n<p class=\"wp-block-paragraph\">La primera ecuaci\u00f3n da 3 * 1\/3 + 1 = 2, la restricci\u00f3n se cumple.<br \/>La segunda desigualdad da -2 * 3 + 5 * 1 = -1 \u2264 7, la restricci\u00f3n se cumple.<br \/>La tercera desigualdad da 3 + 1 = 4 \u2264 4, la restricci\u00f3n est\u00e1 satisfecha, decimos que est\u00e1 saturada.<br \/>Se satisfacen ambas restricciones de tipo.<\/p>\n\n<p class=\"wp-block-paragraph\">La soluci\u00f3n es alcanzable. El valor de la funci\u00f3n objetivo es z = 3 - 1 = 2.<\/p>\n\n<p class=\"wp-block-paragraph\"><em><strong>Desde un punto de vista matricial: <\/strong><\/em>debemos multiplicar la matriz de la <a href=\"https:\/\/complex-systems-ai.com\/es\/programacion-lineal\/\">programa lineal<\/a> por el vector soluci\u00f3n y compare el resultado con los miembros correctos del programa lineal<\/p>\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" class=\"alignnone wp-image-7244 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/10\/lineaire5.png\" alt=\"programaci\u00f3n lineal dominio de definici\u00f3n dominio realizable\" width=\"238\" height=\"90\" title=\"\"><\/figure>\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Domaine-realisable-ou-domaine-de-definition\"><\/span>Dominio alcanzable (o dominio de definici\u00f3n)<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n<p class=\"wp-block-paragraph\">Cada restricci\u00f3n se puede comparar con una ecuaci\u00f3n que divide el plano en dos. Por ejemplo, la ecuaci\u00f3n a<sub>I<\/sub>* X<sub>1<\/sub> + b<sub>I<\/sub>* X<sub>2<\/sub> = c<sub>I<\/sub> divide el plano en dos semiplanos P<sub>1<\/sub> y P<sub>2<\/sub> ecuaci\u00f3n:<\/p>\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" class=\"aligncenter wp-image-7246 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/10\/lineaire6.png\" alt=\"programaci\u00f3n lineal dominio de definici\u00f3n dominio realizable\" width=\"402\" height=\"201\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/10\/lineaire6.png 402w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/10\/lineaire6-300x150.png 300w\" sizes=\"(max-width: 402px) 100vw, 402px\" \/><\/figure>\n\n<p class=\"wp-block-paragraph\">La restricci\u00f3n menor o igual determinar\u00e1 un semiplano, la restricci\u00f3n mayor o igual determinar\u00e1 el otro semiplano. Para saber en qu\u00e9 semiplano se encuentran las soluciones factibles de las restricciones, basta con probar un ejemplo simple y determinar si es factible o no.<\/p>\n\n<p class=\"wp-block-paragraph\">Por ejemplo para la restricci\u00f3n: x<sub>1<\/sub> + x<sub>2<\/sub> \u2264 4, la soluci\u00f3n (0,0) es factible, por lo que el origen est\u00e1 en el semiplano factible.<\/p>\n\n<p class=\"wp-block-paragraph\">La intersecci\u00f3n de todos los semiplanos factibles constituye el dominio factible. Este \u00faltimo puede ser acotado o ilimitado.<\/p>\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-7248 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/10\/lineaire7.png\" alt=\"programaci\u00f3n lineal dominio de definici\u00f3n dominio realizable\" width=\"557\" height=\"205\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/10\/lineaire7.png 557w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/10\/lineaire7-300x110.png 300w\" sizes=\"(max-width: 557px) 100vw, 557px\" \/><\/figure>\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<\/div>","protected":false},"excerpt":{"rendered":"<p>Programaci\u00f3n lineal P\u00e1gina principal Wiki Dominio factible Se dice que la soluci\u00f3n de un problema lineal es factible si se satisfacen todas las restricciones. El dominio factible contiene... <\/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-7237","page","type-page","status-publish","hentry"],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/pages\/7237","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=7237"}],"version-history":[{"count":4,"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/pages\/7237\/revisions"}],"predecessor-version":[{"id":17904,"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/pages\/7237\/revisions\/17904"}],"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=7237"}],"curies":[{"name":"gracias","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}