{"id":6643,"date":"2011-03-22T02:26:01","date_gmt":"2011-03-22T02:26:01","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=6643"},"modified":"2022-01-25T00:09:07","modified_gmt":"2022-01-25T00:09:07","slug":"como-resultado-de-uma-pesquisa-de-mercado","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=6643","title":{"rendered":"Como resultado de uma pesquisa de mercado"},"content":{"rendered":"<p><ul id='GTTabs_ul_6643' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_6643' class='GTTabs_curr'><a  id=\"6643_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_6643' ><a  id=\"6643_1\" onMouseOver=\"GTTabsShowLinks('Resolu\u00e7\u00e3o'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Resolu\u00e7\u00e3o<\/a><\/li>\n<\/ul>\n\n<div class='GTTabs_divs GTTabs_curr_div' id='GTTabs_0_6643'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Como resultado de uma pesquisa de mercado, o diretor de uma empresa verificou que a procura dos seus produtos era dada, aproximadamente, por uma fun\u00e7\u00e3o linear de equa\u00e7\u00e3o \\[v=30-2p\\] em que v representa a procura, ou seja, o n\u00famero de artigos (em milh\u00f5es) que ser\u00e3o vendidos ao pre\u00e7o de p euros.<\/p>\n<p>Se forem vendidos v artigos ao pre\u00e7o de p euros, ent\u00e3o o rendimento r da empresa (em milh\u00f5es de euros) ser\u00e1 dado por: \\[r=vp=(30-2p)p=30p-2{{p}^{2}}\\]<\/p>\n<ol>\n<li>Encontre $\\frac{dr}{dp}$ e explique o que significa.<\/li>\n<li>Calcule $\\frac{dr}{dp}$ para $p=5$ e para $p=10$.<\/li>\n<li>Para que pre\u00e7os, p, de venda \u00e9 o rendimento crescente?<\/li>\n<li>Qual \u00e9 o melhor pre\u00e7o?<\/li>\n<li>Qual \u00e9 a taxa de varia\u00e7\u00e3o para esse pre\u00e7o.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_6643' onClick='GTTabs_show(1,6643)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_6643'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol>\n<li>Ora, $\\frac{dr}{dp}=(30p-2{{p}^{2}})&#8217;=30-4p$ e traduz a taxa de varia\u00e7\u00e3o do rendimento em fun\u00e7\u00e3o de pre\u00e7o do produto.<br \/>\n\u00ad<\/li>\n<li>Ora, ${{\\left( \\frac{dr}{dp} \\right)}_{p=5}}=30-4\\times 5=10$\u00a0 e \u00a0${{\\left( \\frac{dr}{dp} \\right)}_{p=10}}=30-4\\times 10=-10$.<br \/>\n\u00ad<\/li>\n<li>Ora, $\\frac{dr}{dp}=0\\Leftrightarrow 30-4p=0\\Leftrightarrow p=7,5$.\n<p>O rendimento \u00e9 crescente para pre\u00e7os de venda entre 0 e 7, 5 euros, pois $\\frac{dr}{dp}&gt;0,\\,\\forall p\\in \\left] 0;7,5 \\right[$.<br \/>\n\u00ad<\/p>\n<\/li>\n<li>O melhor pre\u00e7o \u00e9 7,5 euros, pois esse valor maximiza o rendimento.<br \/>\n\u00ad<\/li>\n<li>Para esse pre\u00e7o, a taxa de varia\u00e7\u00e3o do rendimento \u00e9 nula.\n<p>\u00ad<a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/22-03-2011Ecra003.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"6645\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=6645\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/22-03-2011Ecra003.png\" data-orig-size=\"690,468\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;}\" data-image-title=\"G\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/22-03-2011Ecra003.png\" class=\"aligncenter wp-image-6645\" title=\"G\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/22-03-2011Ecra003.png\" alt=\"\" width=\"540\" height=\"366\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/22-03-2011Ecra003.png 690w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/22-03-2011Ecra003-300x203.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/22-03-2011Ecra003-150x101.png 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/22-03-2011Ecra003-400x271.png 400w\" sizes=\"auto, (max-width: 540px) 100vw, 540px\" \/><\/a><\/p>\n<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_6643' onClick='GTTabs_show(0,6643)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Como resultado de uma pesquisa de mercado, o diretor de uma empresa verificou que a procura dos seus produtos era dada, aproximadamente, por uma fun\u00e7\u00e3o linear de equa\u00e7\u00e3o \\[v=30-2p\\] em que&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20936,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[98,97,134],"tags":[145],"series":[],"class_list":["post-6643","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-11--ano","category-aplicando","category-derivadas","tag-derivadas-2"],"views":1629,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/11V2Pag198-50_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6643","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=6643"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6643\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20936"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=6643"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=6643"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=6643"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=6643"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}