{"id":2110,"date":"2016-02-10T16:10:29","date_gmt":"2016-02-10T15:10:29","guid":{"rendered":"http:\/\/smart--grid.net\/?page_id=2110"},"modified":"2022-12-03T22:58:55","modified_gmt":"2022-12-03T21:58:55","slug":"resolution-graphique","status":"publish","type":"page","link":"https:\/\/complex-systems-ai.com\/es\/programacion-lineal\/resolucion-graficos\/","title":{"rendered":"LP: resoluci\u00f3n gr\u00e1fica"},"content":{"rendered":"<div data-elementor-type=\"wp-page\" data-elementor-id=\"2110\" class=\"elementor elementor-2110\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-d0e44e7 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"d0e44e7\" 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-b2027a8\" data-id=\"b2027a8\" 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-ae249dd elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"ae249dd\" 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-b246b1f\" data-id=\"b246b1f\" 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-ffd3150 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"ffd3150\" 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-a501d2c\" data-id=\"a501d2c\" 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-65184d2 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"65184d2\" 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-5e3c6c02 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"5e3c6c02\" 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-2e4d69e1\" data-id=\"2e4d69e1\" 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-458d2283 elementor-widget elementor-widget-text-editor\" data-id=\"458d2283\" 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_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\/resolucion-graficos\/#Resolution-graphique\" >Resoluci\u00f3n de gr\u00e1ficos<\/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\/resolucion-graficos\/#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-3\" href=\"https:\/\/complex-systems-ai.com\/es\/programacion-lineal\/resolucion-graficos\/#Tracer-la-fonction-objectif\" >Grafica la funci\u00f3n objetivo<\/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\/resolucion-graficos\/#Solutions-optimales\" >Soluciones \u00f3ptimas<\/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\/resolucion-graficos\/#Les-quatre-possibilites-de-solution-optimale\" >Las cuatro posibilidades de soluci\u00f3n \u00f3ptima<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"Resolution-graphique\"><\/span>Resoluci\u00f3n de gr\u00e1ficos<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Es posible resolver los problemas con dos variables (o dos restricciones para un problema dual) directamente mediante una resoluci\u00f3n gr\u00e1fica. El proceso de resoluci\u00f3n se desarrolla en tres etapas:<\/p>\n\n<ol class=\"wp-block-list\">\n<li>Dominio alcanzable<\/li>\n<li>Grafica la funci\u00f3n objetivo<\/li>\n<li>Determine la soluci\u00f3n \u00f3ptima<\/li>\n<\/ol>\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Domaine-realisable\"><\/span>Dominio alcanzable<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n<div style=\"padding: 3px; border: 2px dotted #a5a5a5; background-color: #f6f9fa;\">Para esto, representamos cada restricci\u00f3n en el <a href=\"https:\/\/complex-systems-ai.com\/es\/teoria-de-grafos\/\">grafico<\/a>, sombreando o coloreando el lado que no satisface la restricci\u00f3n.<\/div>\n\n<div style=\"padding: 5px; background-color: #ffdcd3; border: 2px solid #ff7964; -moz-border-radius: 9px; -khtml-border-radius: 9px; -webkit-border-radius: 9px; border-radius: 9px;\">As\u00ed, destacamos una <a href=\"https:\/\/complex-systems-ai.com\/es\/programacion-lineal\/lp-soluciones-y-dominio-realizable\/\">campo de definici\u00f3n<\/a> o dominio factible, cualquier punto en el dominio de definici\u00f3n satisface todas las restricciones del <a href=\"https:\/\/complex-systems-ai.com\/es\/ayuda-con-la-decision\/modelo-matematico\/\">modelo matem\u00e1tico<\/a>.<\/div>\n\n<p>Vamos a tomarlo <a href=\"https:\/\/complex-systems-ai.com\/es\/programacion-lineal\/\">programa lineal<\/a> Pr\u00f3ximo :<\/p>\n\n<figure class=\"wp-block-image\"><img fetchpriority=\"high\" decoding=\"async\" class=\"alignnone wp-image-7253 size-medium\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/10\/lineaire8-1-300x264.png\" alt=\"Programaci\u00f3n lineal de dominio realizable de resoluci\u00f3n gr\u00e1fica\" width=\"300\" height=\"264\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/10\/lineaire8-1-300x264.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/10\/lineaire8-1.png 524w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/figure>\n\n<p>Dibujemos el dominio de la definici\u00f3n:<\/p>\n\n<p>Agregar la primera restricci\u00f3n y el tipo de variables<\/p>\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" class=\"alignnone wp-image-7254 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/10\/lineaire9.png\" alt=\"Programaci\u00f3n lineal de dominio realizable de resoluci\u00f3n gr\u00e1fica\" width=\"797\" height=\"644\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/10\/lineaire9.png 797w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/10\/lineaire9-300x242.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/10\/lineaire9-768x621.png 768w\" sizes=\"(max-width: 797px) 100vw, 797px\" \/><\/figure>\n\n<p>Adici\u00f3n de la segunda restricci\u00f3n<\/p>\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" class=\"alignnone wp-image-7255 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/10\/lineaire10.png\" alt=\"Programaci\u00f3n lineal de dominio realizable de resoluci\u00f3n gr\u00e1fica\" width=\"808\" height=\"654\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/10\/lineaire10.png 808w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/10\/lineaire10-300x243.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/10\/lineaire10-768x622.png 768w\" sizes=\"(max-width: 808px) 100vw, 808px\" \/><\/figure>\n\n<p>Adici\u00f3n de la tercera restricci\u00f3n<\/p>\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-7256 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/10\/lineaire11.png\" alt=\"Programaci\u00f3n lineal de dominio realizable de resoluci\u00f3n gr\u00e1fica\" width=\"806\" height=\"645\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/10\/lineaire11.png 806w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/10\/lineaire11-300x240.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/10\/lineaire11-768x615.png 768w\" sizes=\"(max-width: 806px) 100vw, 806px\" \/><\/figure>\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Tracer-la-fonction-objectif\"><\/span>Grafica la funci\u00f3n objetivo<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n<p>Para resolver el problema, representamos la funci\u00f3n objetivo en el punto (100,0) luego en varios puntos (siguiendo el gradiente de la funci\u00f3n objetivo) hasta que la funci\u00f3n objetivo tenga solo un punto o una faceta del campo de definici\u00f3n.<\/p>\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-7257 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/10\/lineaire12.png\" alt=\"Programaci\u00f3n lineal de dominio realizable de resoluci\u00f3n gr\u00e1fica\" width=\"812\" height=\"651\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/10\/lineaire12.png 812w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/10\/lineaire12-300x241.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/10\/lineaire12-768x616.png 768w\" sizes=\"(max-width: 812px) 100vw, 812px\" \/><\/figure>\n\n<p>El gradiente de la funci\u00f3n objetivo es (350,300). Por lo tanto, el valor z aumenta cuando la funci\u00f3n objetivo se mueve en la misma direcci\u00f3n que el vector (350,300), por lo tanto, se mueve hacia la esquina noreste. Podemos ver claramente en la siguiente figura que el valor de z ha aumentado tomando otra l\u00ednea de la funci\u00f3n objetivo.<\/p>\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-7258 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/10\/lineaire13.png\" alt=\"Programaci\u00f3n lineal de dominio realizable de resoluci\u00f3n gr\u00e1fica\" width=\"863\" height=\"639\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/10\/lineaire13.png 863w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/10\/lineaire13-300x222.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/10\/lineaire13-768x569.png 768w\" sizes=\"(max-width: 863px) 100vw, 863px\" \/><\/figure>\n\n<p>Luego obtenemos las soluciones globales \u00f3ptimas. Si trazamos la funci\u00f3n objetivo nuevamente siguiendo el gradiente, la l\u00ednea estar\u00e1 fuera del dominio de definici\u00f3n.<\/p>\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Solutions-optimales\"><\/span>Soluciones \u00f3ptimas<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n<p>Las soluciones \u00f3ptimas son los \u00faltimos puntos antes de que la l\u00ednea de la funci\u00f3n objetivo abandone el dominio de definici\u00f3n.<\/p>\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-7259 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/10\/lineaire14.png\" alt=\"Programaci\u00f3n lineal de dominio realizable de resoluci\u00f3n gr\u00e1fica\" width=\"891\" height=\"649\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/10\/lineaire14.png 891w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/10\/lineaire14-300x219.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/10\/lineaire14-768x559.png 768w\" sizes=\"(max-width: 891px) 100vw, 891px\" \/><\/figure>\n\n<p>La soluci\u00f3n \u00f3ptima se encuentra en la intersecci\u00f3n de la primera y la segunda restricci\u00f3n, por lo que satisface ambas restricciones. El vector soluci\u00f3n es la soluci\u00f3n del sistema:<\/p>\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-7260 size-medium\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/10\/lineaire15-300x69.png\" alt=\"Programaci\u00f3n lineal de dominio realizable de resoluci\u00f3n gr\u00e1fica\" width=\"300\" height=\"69\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/10\/lineaire15-300x69.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/10\/lineaire15.png 466w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/figure>\n\n<p>La soluci\u00f3n de este sistema es (122,78) que da z = 66100.<\/p>\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Les-quatre-possibilites-de-solution-optimale\"><\/span>Las cuatro posibilidades de soluci\u00f3n \u00f3ptima<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n<p>Hay cuatro posibilidades:<\/p>\n\n<ul class=\"wp-block-list\">\n<li style=\"text-align: justify;\">o existe una soluci\u00f3n \u00fanica (un punto);<\/li>\n<li style=\"text-align: justify;\">ya sea una infinidad de soluciones (una faceta);<\/li>\n<li style=\"text-align: justify;\">o la soluci\u00f3n no est\u00e1 acotada, la l\u00ednea de la funci\u00f3n objetivo siempre estar\u00e1 en el dominio de definici\u00f3n siguiendo el gradiente;<\/li>\n<li style=\"text-align: justify;\">o no hay soluci\u00f3n, por ejemplo si el dominio est\u00e1 vac\u00edo.<\/li>\n<\/ul>\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>P\u00e1gina de inicio de Wiki de Programaci\u00f3n Lineal Resoluci\u00f3n Gr\u00e1fica Es posible resolver problemas con dos variables (o dos restricciones para un problema dual) directamente... <\/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-2110","page","type-page","status-publish","hentry"],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/pages\/2110","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=2110"}],"version-history":[{"count":4,"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/pages\/2110\/revisions"}],"predecessor-version":[{"id":17906,"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/pages\/2110\/revisions\/17906"}],"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=2110"}],"curies":[{"name":"gracias","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}