Write an example where rational function is used in real-life situation<\/p>\n\n\n\n
The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n A real-life example of a rational function can be found in business, specifically in pricing and cost analysis<\/strong>. Consider a company that manufactures a product, and it wants to determine the cost per unit when producing a certain number of units. The total cost function<\/strong> might involve both fixed costs<\/strong> and variable costs<\/strong>.<\/p>\n\n\n\n For example, assume the fixed costs for a factory are \\$100,000, and the variable cost per unit produced is \\$10. The cost to produce $x$ units can be expressed as:<\/p>\n\n\n\n $$ Here, the rational function represents the relationship between the cost per unit and the number of units produced. The term $\\frac{100,000}{x}$ reflects the decreasing cost<\/strong> per unit as production increases, because the fixed costs are spread over more units. The $10$ is the variable cost<\/strong> per unit, which remains constant regardless of the production level.<\/p>\n\n\n\n This rational function is used in business to make decisions regarding optimal production levels<\/strong>. The total cost function shows how costs behave as production increases. In particular, the term $\\frac{100,000}{x}$ demonstrates the principle of economies of scale<\/strong>, where fixed costs decrease per unit as production increases. If the company produces just a few units, the cost per unit will be very high, as the fixed costs are distributed over fewer units. But as production increases, each unit “shares” a smaller portion of the fixed costs, lowering the overall per-unit cost.<\/p>\n\n\n\n In practice, rational functions like this one are crucial in determining pricing strategies, understanding profit margins, and identifying break-even points<\/strong>, where total revenue equals total costs. It also helps businesses determine at what point producing more units will no longer result in significant cost savings, guiding decision-makers on efficient production levels<\/strong>.<\/p>\n","protected":false},"excerpt":{"rendered":" Write an example where rational function is used in real-life situation The correct answer and explanation is: A real-life example of a rational function can be found in business, specifically in pricing and cost analysis. Consider a company that manufactures a product, and it wants to determine the cost per unit when producing a certain […]<\/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-240997","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/240997","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=240997"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/240997\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=240997"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=240997"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=240997"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
C(x) = \\frac{100,000}{x} + 10
$$<\/p>\n\n\n\nExplanation:<\/h3>\n\n\n\n