{"id":181545,"date":"2025-01-11T02:23:40","date_gmt":"2025-01-11T02:23:40","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=181545"},"modified":"2025-01-11T02:23:42","modified_gmt":"2025-01-11T02:23:42","slug":"a-company-produces-x-units-of-a-product-per-month","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/01\/11\/a-company-produces-x-units-of-a-product-per-month\/","title":{"rendered":"A company produces x units of a product per month"},"content":{"rendered":"\n<p>A company produces x units of a product per month, were R(x) represents the total revenue and C(x) represents the total cost. The profit is calculated by taking the difference between revenue and cost, P(x)=R(x)-C(x). What is the total profit for the given functions? R(x)=350x-125 C(x)=175x-80<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\">The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To calculate the total profit for the given functions, we use the profit formula: P(x)=R(x)\u2212C(x)P(x) = R(x) &#8211; C(x)<\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>R(x)R(x) is the total revenue: R(x)=350x\u2212125R(x) = 350x &#8211; 125<\/li>\n\n\n\n<li>C(x)C(x) is the total cost: C(x)=175x\u221280C(x) = 175x &#8211; 80<\/li>\n<\/ul>\n\n\n\n<p>Substituting these into the profit equation: P(x)=(350x\u2212125)\u2212(175x\u221280)P(x) = (350x &#8211; 125) &#8211; (175x &#8211; 80)<\/p>\n\n\n\n<p>Now, let&#8217;s simplify the equation: P(x)=350x\u2212125\u2212175x+80P(x) = 350x &#8211; 125 &#8211; 175x + 80<\/p>\n\n\n\n<p>Combine like terms: P(x)=(350x\u2212175x)+(\u2212125+80)P(x) = (350x &#8211; 175x) + (-125 + 80) P(x)=175x\u221245P(x) = 175x &#8211; 45<\/p>\n\n\n\n<p>Thus, the total profit function is: P(x)=175x\u221245P(x) = 175x &#8211; 45<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Understanding the Profit Function<\/strong>: The total profit function, P(x)P(x), represents how much profit a company makes when producing xx units of a product. The profit is the difference between the revenue (R(x)R(x)) and the cost (C(x)C(x)) of producing those units.<\/li>\n\n\n\n<li><strong>Revenue Function<\/strong>: The revenue function R(x)=350x\u2212125R(x) = 350x &#8211; 125 suggests that for each unit sold, the company earns 350 units of currency. However, there is a fixed cost (or adjustment) of 125 that reduces the overall revenue.<\/li>\n\n\n\n<li><strong>Cost Function<\/strong>: The cost function C(x)=175x\u221280C(x) = 175x &#8211; 80 implies that the company incurs a cost of 175 units of currency for each unit produced, with a fixed cost of 80.<\/li>\n\n\n\n<li><strong>Profit Calculation<\/strong>: By subtracting the cost from the revenue, we get the profit. The simplified result, P(x)=175x\u221245P(x) = 175x &#8211; 45, shows that for every unit produced, the company gains a profit of 175 units of currency, minus a fixed cost of 45 units.<\/li>\n<\/ol>\n\n\n\n<p>Therefore, the total profit function is P(x)=175x\u221245P(x) = 175x &#8211; 45, and this function will give the total profit based on the number of units produced.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>A company produces x units of a product per month, were R(x) represents the total revenue and C(x) represents the total cost. The profit is calculated by taking the difference between revenue and cost, P(x)=R(x)-C(x). What is the total profit for the given functions? R(x)=350x-125 C(x)=175x-80 The correct answer and explanation is: To calculate the [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-181545","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/181545","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=181545"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/181545\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=181545"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=181545"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=181545"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}