{"id":7347,"date":"2019-11-13T14:41:00","date_gmt":"2019-11-13T13:41:00","guid":{"rendered":"http:\/\/smart--grid.net\/?page_id=7347"},"modified":"2024-02-11T20:47:59","modified_gmt":"2024-02-11T19:47:59","slug":"modelisation-lineaire-ex","status":"publish","type":"page","link":"https:\/\/complex-systems-ai.com\/es\/ayuda-con-la-decision\/soluciones-ejercicios-de-modelado-lineal\/","title":{"rendered":"6 Ejercicios Corregidos Modelado Lineal"},"content":{"rendered":"<div data-elementor-type=\"wp-page\" data-elementor-id=\"7347\" class=\"elementor elementor-7347\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-5363c42 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"5363c42\" 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-f007154\" data-id=\"f007154\" 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-66637e1 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"66637e1\" 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\/ayuda-con-la-decision\/\">\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\">Ayuda con la decisi\u00f3n<\/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-449df46\" data-id=\"449df46\" 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-52cb346 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"52cb346\" 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-49c9240\" data-id=\"49c9240\" 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-9a0caf5 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"9a0caf5\" 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\/Mod%C3%A8le_math%C3%A9matique\" 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-f29edd1 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"f29edd1\" 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-6e1631e\" data-id=\"6e1631e\" 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-334bae5 elementor-widget elementor-widget-heading\" data-id=\"334bae5\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_82_2 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Contenido<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Tabla de contenido alternativo\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Palanca<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewbox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewbox=\"0 0 24 24\" version=\"1.2\" baseprofile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/complex-systems-ai.com\/es\/ayuda-con-la-decision\/soluciones-ejercicios-de-modelado-lineal\/#Exercices-Corriges-sur-la-modelisation-lineaire-a-partir-denonce\" >Ejercicios corregidos de modelado lineal a partir de enunciados.<\/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\/ayuda-con-la-decision\/soluciones-ejercicios-de-modelado-lineal\/#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-3\" href=\"https:\/\/complex-systems-ai.com\/es\/ayuda-con-la-decision\/soluciones-ejercicios-de-modelado-lineal\/#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-4\" href=\"https:\/\/complex-systems-ai.com\/es\/ayuda-con-la-decision\/soluciones-ejercicios-de-modelado-lineal\/#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-5\" href=\"https:\/\/complex-systems-ai.com\/es\/ayuda-con-la-decision\/soluciones-ejercicios-de-modelado-lineal\/#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-6\" href=\"https:\/\/complex-systems-ai.com\/es\/ayuda-con-la-decision\/soluciones-ejercicios-de-modelado-lineal\/#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-7\" href=\"https:\/\/complex-systems-ai.com\/es\/ayuda-con-la-decision\/soluciones-ejercicios-de-modelado-lineal\/#Exercice-6\" >Ejercicio 6<\/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\/ayuda-con-la-decision\/soluciones-ejercicios-de-modelado-lineal\/#Exercice-7\" >Ejercicio 7<\/a><\/li><\/ul><\/nav><\/div>\n<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"Exercices-Corriges-sur-la-modelisation-lineaire-a-partir-denonce\"><\/span>Ejercicios corregidos de modelado lineal a partir de enunciados.<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-7f834b4 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"7f834b4\" 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-0cec216\" data-id=\"0cec216\" 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-371a7c1 elementor-widget elementor-widget-text-editor\" data-id=\"371a7c1\" 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>Ejercicios corregidos anteriores de <a href=\"https:\/\/complex-systems-ai.com\/es\/ayuda-con-la-decision\/modelado-lineal\/\">modelado lineal<\/a>.<\/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=\"modelado 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-039cc63 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"039cc63\" 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-34e95b3\" data-id=\"34e95b3\" 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-7d48274 elementor-widget elementor-widget-heading\" data-id=\"7d48274\" 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-e2e4676 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"e2e4676\" 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-0606959\" data-id=\"0606959\" 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-2816055 elementor-widget elementor-widget-text-editor\" data-id=\"2816055\" 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 dos productos A y B, utilizando una m\u00e1quina my dos materias primas py q. Tenemos 8 horas de m, 10 kg de py 36 kg de q todos los d\u00edas. Suponemos que:<\/p>\n<ul>\n<li>la producci\u00f3n de una unidad de A requiere 2 kg de py 9 kg de q, y utiliza la m\u00e1quina m durante 1 hora;<\/li>\n<li>la producci\u00f3n de una unidad de B requiere 2 kg de py 4 kg de q, y utiliza la m\u00e1quina m durante 2 horas;<\/li>\n<li>los beneficios obtenidos son 50 \u20ac por unidad de A y 60 \u20ac por unidad de B<\/li>\n<\/ul>\n<p>El objetivo de la empresa es maximizar el beneficio que podr\u00e1 obtener, por d\u00eda, de estos 2 productos haciendo el mejor uso de sus recursos.<\/p>\n<ol>\n<li>Escribe una tabla para resumir la informaci\u00f3n.<\/li>\n<li>Definir las variables<\/li>\n<li>Definir las restricciones<\/li>\n<li>Definir la funci\u00f3n objetivo<\/li>\n<\/ol>\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-6d049ff elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"6d049ff\" 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-5a3d81f\" data-id=\"5a3d81f\" 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-e646e4e elementor-widget elementor-widget-toggle\" data-id=\"e646e4e\" 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-2411\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-2411\" 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-2411\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-2411\"><ol>\n<li>La siguiente tabla resume los datos relacionados con este problema de producci\u00f3n:<\/li>\n<\/ol>\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" width=\"334\" height=\"137\" class=\"wp-image-7218\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/10\/lineaire1.png\" alt=\"\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/10\/lineaire1.png 334w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/10\/lineaire1-300x123.png 300w\" sizes=\"(max-width: 334px) 100vw, 334px\" \/><\/figure>\n<p>2. Aqu\u00ed se desconocen dos datos: la cantidad de producto A a producir y la cantidad de producto B a producir. Vamos a nombrarlos respectivamente x<sub>1<\/sub> y x<sub>2<\/sub>. Tenemos dos variables en nuestros problemas de decisi\u00f3n.<\/p>\n<p>3. Comprender c\u00f3mo se restringen las variables de decisi\u00f3n. Para ello, es necesario utilizar los datos en las especificaciones.<\/p>\n<ul>\n<li>Restricci\u00f3n de la m\u00e1quina m (primera l\u00ednea): El tiempo de uso de la m\u00e1quina m para fabricar los productos A y B no puede exceder las 8 horas disponibles: m\u22648.\n<ul>\n<li>La m\u00e1quina produce una unidad de A en 1 hora<\/li>\n<li>La m\u00e1quina produce una unidad de B en 2 horas.<\/li>\n<li>Reformulemos la restricci\u00f3n por: la cantidad de A y B producida no excede las 8h<\/li>\n<li>X<sub>1<\/sub> + 2 * x<sub>2<\/sub> \u22648<\/li>\n<\/ul>\n<\/li>\n<li>Restricci\u00f3n de material p: La cantidad de material p no puede exceder los 10 kg\n<ul>\n<li>Una unidad de A consume 2 kg de p<\/li>\n<li>Una unidad de B consume 2 kg de p<\/li>\n<li>Formulaci\u00f3n de la restricci\u00f3n: la cantidad de producto utilizada por A y B no supera los 10 kg<\/li>\n<li>2 * x<sub>1<\/sub> + 2 * x<sub>2<\/sub> \u2264 10<\/li>\n<\/ul>\n<\/li>\n<li>Restricci\u00f3n del material q: de manera similar concluimos que la cantidad de producto utilizada por A (9 kg por unidad) y por B (4 kg por unidad) no excede los 36 kg\n<ul>\n<li>9 * x<sub>1<\/sub> + 4 * x<sub>2<\/sub> \u2264 36<\/li>\n<\/ul>\n<\/li>\n<li>Restricci\u00f3n de la positividad: se observa que el texto no brinda informaci\u00f3n directa sobre las variables de decisi\u00f3n. Sin embargo, es l\u00f3gico que estos sean positivos o cero, parece poco probable que produzca -1 unidad de A.\n<ul>\n<li>X<sub>1<\/sub> , X<sub>2<\/sub> \u2265 0<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>4. La funci\u00f3n objetivo es, como su nombre indica, el objetivo del industrial: maximizar su beneficio. Sabemos que vender una unidad de A gana $ 50 y vender una unidad de B gana $ 60. Sea z la ganancia total, entonces la funci\u00f3n objetivo es max z = 50 * x<sub>1<\/sub> + 60 * x<sub>2<\/sub> .<\/p>\n<p>los <a href=\"https:\/\/complex-systems-ai.com\/es\/ayuda-con-la-decision\/modelo-matematico\/\">modelo matem\u00e1tico<\/a> lineal, se\u00f1alado (P), se puede resumir de la siguiente manera:<\/p>\n<figure class=\"wp-block-image size-large\"><img fetchpriority=\"high\" decoding=\"async\" width=\"371\" height=\"141\" class=\"wp-image-7221\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/10\/lineaire2.png\" alt=\"\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/10\/lineaire2.png 371w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/10\/lineaire2-300x114.png 300w\" sizes=\"(max-width: 371px) 100vw, 371px\" \/><\/figure><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-0252c98 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"0252c98\" 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-0f6ccfa\" data-id=\"0f6ccfa\" 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-cdccb41 elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"cdccb41\" 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-f94419f elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"f94419f\" 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-3e3cb81\" data-id=\"3e3cb81\" 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-54d7c74 elementor-widget elementor-widget-heading\" data-id=\"54d7c74\" 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-8c08955 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"8c08955\" 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-a9b744a\" data-id=\"a9b744a\" 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-e136912 elementor-widget elementor-widget-text-editor\" data-id=\"e136912\" 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 de fabricaci\u00f3n de chasis planea producir dos nuevos modelos utilizando las capacidades de sus tres talleres. Estos son respectivamente un marco de aluminio y un marco de madera.<\/p>\n<p>El primer producto requiere ir al primer taller para realizar el marco de aluminio y al tercer taller donde se monta el vidrio en el marco. Mientras que el segundo producto requiere el paso en el segundo taller para fabricar el marco de madera y en el tercer taller donde se monta el vidrio en el marco. Las utilidades unitarias, los tiempos de fabricaci\u00f3n de cada uno de los productos en cada uno de los talleres as\u00ed como las capacidades semanales de estos talleres se dan en la siguiente tabla:<\/p>\n<p><!-- \/wp:paragraph --><\/p>\n<p><!-- wp:image {\"id\":7224,\"sizeSlug\":\"large\"} --><\/p>\n<figure><img decoding=\"async\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/10\/lineaire4.png\" alt=\"\" title=\"\"><\/figure>\n<p><!-- \/wp:image --><\/p>\n<p><!-- wp:paragraph --><\/p>\n<p>Formule el problema lineal.<\/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-f0e8e1f elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"f0e8e1f\" 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-854fad3\" data-id=\"854fad3\" 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-d86d93b elementor-widget elementor-widget-toggle\" data-id=\"d86d93b\" 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-2261\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-2261\" 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-2261\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-2261\"><p>Las restricciones est\u00e1n en las primeras tres l\u00edneas, mientras que la funci\u00f3n objetivo est\u00e1 en la \u00faltima l\u00ednea. Lo que da: X1 para el producto 1 y X2 para el producto 2<\/p>\n<p><!-- \/wp:paragraph --><\/p>\n<p><!-- wp:image {\"id\":7350,\"sizeSlug\":\"large\"} --><\/p>\n<figure><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire38.png?w=264\" alt=\"ejercicios corregidos de modelado lineal\" width=\"264\" height=\"150\" title=\"\"><\/figure><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-2dc3194 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"2dc3194\" 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-323a4fa\" data-id=\"323a4fa\" 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-fee0f81 elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"fee0f81\" 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-919e503 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"919e503\" 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-5abe999\" data-id=\"5abe999\" 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-72db959 elementor-widget elementor-widget-heading\" data-id=\"72db959\" 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-cd888a7 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"cd888a7\" 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-4f0fa00\" data-id=\"4f0fa00\" 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-00c0306 elementor-widget elementor-widget-text-editor\" data-id=\"00c0306\" 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 productor de electricidad quiere que estas dos centrales nucleares P y Q suministren una cantidad de energ\u00eda a las ciudades A, B y C. Las cantidades m\u00ednimas de energ\u00eda que deben satisfacerse son 16 para A, 12 para B y 18 para C.<\/p>\n<p>Cuando un reactor de P produce, env\u00eda 2 unidades a A, 1 unidad a B y 1 unidad a C; y cuesta 20 \u20ac por d\u00eda. Cuando un reactor de Q produce, env\u00eda 1 unidad a A, 1 unidad a B y 3 unidades a C; y cuesta 40 \u20ac. El productor est\u00e1 buscando la combinaci\u00f3n m\u00e1s barata de reactores P y Q que cumpla con el requisito de consumo m\u00ednimo para las ciudades A, B, C. Los datos se resumen en la siguiente tabla:<\/p>\n<p><!-- \/wp:paragraph --><\/p>\n<p><!-- wp:image {\"id\":7223,\"sizeSlug\":\"large\"} --><\/p>\n<figure><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/10\/lineaire-3.png?w=383\" alt=\"ejercicios corregidos de modelado lineal\" width=\"383\" height=\"138\" title=\"\"><\/figure>\n<p><!-- \/wp:image --><\/p>\n<p><!-- wp:paragraph --><\/p>\n<p>Formule el problema lineal.<\/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-518f166 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"518f166\" 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-9405b34\" data-id=\"9405b34\" 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-e57d2d3 elementor-widget elementor-widget-toggle\" data-id=\"e57d2d3\" 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-2401\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-2401\" 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-2401\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-2401\"><p>Las restricciones est\u00e1n en las primeras tres l\u00edneas, mientras que la funci\u00f3n objetivo est\u00e1 en la \u00faltima l\u00ednea. Lo que da: X1 para el productor P, X2 para el productor Q<\/p>\n<p><!-- \/wp:paragraph --><\/p>\n<p><!-- wp:image {\"id\":7352,\"sizeSlug\":\"large\"} --><\/p>\n<figure><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire39.png?w=238\" alt=\"ejercicios corregidos de modelado lineal\" width=\"238\" height=\"159\" title=\"\"><\/figure><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-b71ad88 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"b71ad88\" 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-7818b13\" data-id=\"7818b13\" 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-4385564 elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"4385564\" 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-5bf2bbe elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"5bf2bbe\" 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-4459f1e\" data-id=\"4459f1e\" 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-c417f9b elementor-widget elementor-widget-heading\" data-id=\"c417f9b\" 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-841e92c elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"841e92c\" 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-0dd2755\" data-id=\"0dd2755\" 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-303271d elementor-widget elementor-widget-text-editor\" data-id=\"303271d\" 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>Los siguientes ejercicios no son independientes, las restricciones se acumulan o cambian de una parte a otra.<\/p>\n<p><!-- \/wp:paragraph --><\/p>\n<p><!-- wp:heading {\"level\":4} --><\/p>\n<p><span style=\"color: var( --e-global-color-text ); font-family: var( --e-global-typography-text-font-family ), Sans-serif; font-weight: var( --e-global-typography-text-font-weight ); font-size: 1.125rem;\">Una f\u00e1brica de autom\u00f3viles recibe 100 toneladas de aluminio y 80 toneladas de acero cada semana. La f\u00e1brica produce tres tipos de veh\u00edculos de construcci\u00f3n: transporte, obra estructural, gr\u00faa; vendidos respectivamente 250k \u20ac, 300k \u20ac y 400k \u20ac.<\/span><\/p>\n<p><!-- \/wp:paragraph --><\/p>\n<p><!-- wp:paragraph --><\/p>\n<p>La producci\u00f3n de transporte requiere 5 toneladas de aluminio y 3 toneladas de acero; la Obra Estructural necesita 3 toneladas de aluminio y 5 toneladas de acero; la Grulla requiere 5 toneladas de cada uno. Formule el problema lineal para maximizar las ganancias de la planta.<\/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-06e81d8 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"06e81d8\" 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-8e4196f\" data-id=\"8e4196f\" 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-88d0ee5 elementor-widget elementor-widget-toggle\" data-id=\"88d0ee5\" 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-1431\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-1431\" 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-1431\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-1431\"><p>los <a href=\"https:\/\/complex-systems-ai.com\/es\/programacion-lineal\/\">programa lineal<\/a> es el siguiente: X1 para el Transporte, X2 para la Shell y X3 para la Gr\u00faa<\/p>\n<p><!-- \/wp:paragraph --><\/p>\n<p><!-- wp:image {\"id\":7354,\"sizeSlug\":\"large\"} --><\/p>\n<figure><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire40.png?w=318\" alt=\"ejercicios corregidos de modelado lineal\" width=\"318\" height=\"145\" title=\"\"><\/figure><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-2ff7eb4 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"2ff7eb4\" 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-e2cabb2\" data-id=\"e2cabb2\" 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-fe01a4b elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"fe01a4b\" 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-54d33fc elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"54d33fc\" 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-00101c3\" data-id=\"00101c3\" 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-ee40f7e elementor-widget elementor-widget-heading\" data-id=\"ee40f7e\" 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-eb217d6 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"eb217d6\" 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-9d33db8\" data-id=\"9d33db8\" 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-27d1a9d elementor-widget elementor-widget-text-editor\" data-id=\"27d1a9d\" 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>El equipo de marketing advierte a la planta que la producci\u00f3n de veh\u00edculos no est\u00e1 a la altura de la demanda de los clientes. Luego de un estudio de las estad\u00edsticas de ventas del \u00faltimo a\u00f1o, los analistas financieros dedujeron los siguientes datos: se vende un promedio de 10 Transportes por semana, con una desviaci\u00f3n est\u00e1ndar de 2 veh\u00edculos (confianza de 99%); se vende un promedio de 8 Big Work por semana, con una desviaci\u00f3n est\u00e1ndar de 4 veh\u00edculos (confianza de 99%); se vende un promedio de 4 gr\u00faas por semana con una desviaci\u00f3n est\u00e1ndar de 1 gr\u00faa (confianza de 99%). Formule el problema para maximizar las ganancias de la planta.<\/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-96f4a56 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"96f4a56\" 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-0b9c213\" data-id=\"0b9c213\" 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-ee6a15e elementor-widget elementor-widget-toggle\" data-id=\"ee6a15e\" 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-2491\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-2491\" 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-2491\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-2491\"><p>Aqu\u00ed est\u00e1 el programa lineal con las nuevas restricciones:<\/p>\n<p><!-- \/wp:paragraph --><\/p>\n<p><!-- wp:image {\"id\":7357,\"sizeSlug\":\"large\"} --><\/p>\n<figure><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire41.png?w=323\" alt=\"ejercicios corregidos de modelado lineal\" width=\"323\" height=\"249\" title=\"\"><\/figure><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-6632e8a elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"6632e8a\" 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-16a2afd\" data-id=\"16a2afd\" 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-fe1a076 elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"fe1a076\" 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-687b835 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"687b835\" 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-48622e3\" data-id=\"48622e3\" 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-0843f68 elementor-widget elementor-widget-heading\" data-id=\"0843f68\" 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-cb10e9a elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"cb10e9a\" 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-3baeddc\" data-id=\"3baeddc\" 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-a6715c0 elementor-widget elementor-widget-text-editor\" data-id=\"a6715c0\" 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>Gran error de su parte, al querer siempre maximizar las ganancias, \u00a1no tuvo en cuenta el tiempo de trabajo y la comodidad de los trabajadores! Estos \u00faltimos afirman con raz\u00f3n que la producci\u00f3n se ajusta a sus condiciones de trabajo. Estos se dividen en tres talleres.<\/p>\n<p><!-- \/wp:paragraph --><\/p>\n<p><!-- wp:paragraph --><\/p>\n<p>La fundici\u00f3n tiene dos tanques en funcionamiento 24 horas al d\u00eda, 7 d\u00edas a la semana, 1 tonelada de aluminio tarda 30 minutos en fundirse y 1 tonelada de acero tarda 1 hora en fundirse (cada tanque est\u00e1 configurado para uno de los dos metales). La l\u00ednea de montaje est\u00e1 abierta 15 \/ 24h y 6 \/ 7d, un Transporte se monta en 5h, el Big Work en 10h y una gr\u00faa en 10h. El taller de acabado est\u00e1 abierto 12 horas al d\u00eda, 6 d\u00edas a la semana, el acabado dura 3 horas sea cual sea el veh\u00edculo. Formule el problema para maximizar las ganancias de la planta.<\/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-c28547e elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"c28547e\" 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-3294acc\" data-id=\"3294acc\" 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-17ca2ad elementor-widget elementor-widget-toggle\" data-id=\"17ca2ad\" 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-2491\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-2491\" 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-2491\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-2491\"><p>El programa lineal con las nuevas restricciones es:<\/p>\n<p><!-- \/wp:paragraph --><\/p>\n<p><!-- wp:image {\"id\":7360,\"sizeSlug\":\"large\"} --><\/p>\n<figure><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire42.png?w=335\" alt=\"ejercicios corregidos de modelado lineal\" width=\"335\" height=\"319\" title=\"\"><\/figure><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-b859ce6 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"b859ce6\" 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-971bb57\" data-id=\"971bb57\" 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-5194de5 elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"5194de5\" 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-a430d1b elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"a430d1b\" 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-9138883\" data-id=\"9138883\" 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-e2a2687 elementor-widget elementor-widget-heading\" data-id=\"e2a2687\" 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-7\"><\/span>Ejercicio 7<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-02fc328 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"02fc328\" 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-e4dc7ab\" data-id=\"e4dc7ab\" 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-5b4e92d elementor-widget elementor-widget-text-editor\" data-id=\"5b4e92d\" 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>\u00a1El equipo de desarrollo de f\u00e1brica ha creado un veh\u00edculo nuevo y revolucionario! Este veh\u00edculo de prueba solo necesita 2 toneladas de aluminio y 1 tonelada de acero por un precio de venta estimado de 150k \u20ac. La investigaci\u00f3n de mercado muestra que puede vender al menos 10 unidades por semana. Este veh\u00edculo se ensambla en 4 horas y el acabado solo dura 2 horas. Formule el problema para maximizar las ganancias de la planta.<\/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-a91b062 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"a91b062\" 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-00c0ac9\" data-id=\"00c0ac9\" 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-b65a463 elementor-widget elementor-widget-toggle\" data-id=\"b65a463\" 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-1911\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-1911\" 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-1911\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-1911\"><p><!-- wp:heading --><\/p>\n<p><!-- \/wp:list --><\/p>\n<p><!-- wp:heading {\"level\":4} --><\/p>\n<p><!-- \/wp:heading --><\/p>\n<p><!-- wp:list {\"ordered\":true} --><\/p>\n<p><!-- \/wp:image --><\/p>\n<p><!-- wp:heading --><\/p>\n<p><!-- \/wp:heading --><\/p>\n<p><!-- wp:heading {\"level\":4} --><\/p>\n<p><!-- \/wp:heading --><\/p>\n<p><!-- wp:paragraph --><\/p>\n<p><!-- \/wp:heading --><\/p>\n<p><!-- wp:paragraph --><\/p>\n<figure><\/figure>\n<p><!-- \/wp:image --><\/p>\n<p><!-- wp:heading {\"level\":4} --><\/p>\n<p><!-- \/wp:heading --><\/p>\n<p><!-- wp:paragraph --><\/p>\n<p><!-- \/wp:heading --><\/p>\n<p><!-- wp:paragraph --><\/p>\n<figure><\/figure>\n<p><!-- \/wp:image --><\/p>\n<p><!-- wp:heading --><\/p>\n<p><!-- \/wp:heading --><\/p>\n<p><!-- wp:paragraph --><\/p>\n<figure><\/figure>\n<p><!-- \/wp:image --><\/p>\n<p><!-- wp:heading {\"level\":4} --><\/p>\n<p><!-- \/wp:heading --><\/p>\n<p><!-- wp:paragraph --><\/p>\n<p><!-- \/wp:heading --><\/p>\n<p><!-- wp:paragraph --><\/p>\n<figure><\/figure>\n<p><!-- \/wp:image --><\/p>\n<p><!-- wp:heading {\"level\":4} --><\/p>\n<p><!-- \/wp:heading --><\/p>\n<p><!-- wp:paragraph --><\/p>\n<p><!-- \/wp:heading --><\/p>\n<p><!-- wp:paragraph --><\/p>\n<figure><\/figure>\n<p><!-- \/wp:image --><\/p>\n<p><!-- wp:heading {\"level\":4} --><\/p>\n<p><!-- \/wp:heading --><\/p>\n<p><!-- wp:paragraph --><\/p>\n<p><!-- \/wp:heading --><\/p>\n<p><!-- wp:paragraph --><\/p>\n<p>El programa lineal despu\u00e9s de agregar una nueva variable X4<\/p>\n<p><!-- \/wp:paragraph --><\/p>\n<p><!-- wp:image {\"id\":7362,\"sizeSlug\":\"large\"} --><\/p>\n<figure><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/11\/lineaire43.png?w=329\" alt=\"ejercicios corregidos de modelado lineal\" width=\"329\" height=\"357\" title=\"\"><\/figure>\n<p><!-- \/wp:image --><\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>","protected":false},"excerpt":{"rendered":"<p>Soporte para decisiones P\u00e1gina de inicio Wiki Ejercicios corregidos sobre modelado lineal basados en declaraciones Ejercicios de modelado lineal corregidos arriba. Ejercicio 1 \u2026 <\/p>","protected":false},"author":1,"featured_media":0,"parent":1799,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-7347","page","type-page","status-publish","hentry"],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/pages\/7347","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=7347"}],"version-history":[{"count":11,"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/pages\/7347\/revisions"}],"predecessor-version":[{"id":20436,"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/pages\/7347\/revisions\/20436"}],"up":[{"embeddable":true,"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/pages\/1799"}],"wp:attachment":[{"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/media?parent=7347"}],"curies":[{"name":"gracias","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}