{"id":213804,"date":"2025-05-12T11:43:51","date_gmt":"2025-05-12T11:43:51","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=213804"},"modified":"2025-05-12T11:43:53","modified_gmt":"2025-05-12T11:43:53","slug":"a-woodworker-makes-wooden-checkerboard","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/05\/12\/a-woodworker-makes-wooden-checkerboard\/","title":{"rendered":"A woodworker makes wooden checkerboard"},"content":{"rendered":"\n<p>A woodworker makes wooden checkerboards. Her profit is a function of the price she charges. This graph shows her total profits, y, based on the sales price, x of each checkerboard. Identify any zeros of the function, and interpret what the zeros mean in terms of the situation. A. Zero: y=1512.5. This is the maximum amount of profit she can make. B. Zeros: x=15 and x=70. These are the prices at which she neither makes nor loses money. C. Zero: x=42.5. This is the selling price that will give her the greatest profit. D. Zeros: x=15 and x=70. These are the prices at which she makes the least and greatest amounts of profit.<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-0-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p><strong>Correct Answer: B. Zeros: x = 15 and x = 70. These are the prices at which she neither makes nor loses money.<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Explanation:<\/strong><\/h3>\n\n\n\n<p>In mathematics, the <strong>zeros of a function<\/strong> are the values of the independent variable (in this case, the price per checkerboard, <strong>x<\/strong>) for which the dependent variable (the profit, <strong>y<\/strong>) equals zero. Graphically, these are the <strong>points where the graph of the function crosses the x-axis<\/strong>. At those points, the profit is neither positive nor negative\u2014in other words, <strong>the woodworker breaks even<\/strong>.<\/p>\n\n\n\n<p>Given the problem, we are told that the profit (y) is graphed as a function of the selling price (x). If the graph touches the x-axis at <strong>x = 15<\/strong> and <strong>x = 70<\/strong>, these are the <strong>zeros of the function<\/strong>. This tells us that if the woodworker charges either <strong>$15<\/strong> or <strong>$70<\/strong> per checkerboard, <strong>she will make zero profit<\/strong>\u2014her revenue will just cover her costs, with no gain or loss.<\/p>\n\n\n\n<p>This situation typically arises when a business sets a price too low (like $15), making many sales but not enough margin to cover costs, or too high (like $70), where high prices discourage buyers, resulting in too few sales. In both cases, profit drops to zero.<\/p>\n\n\n\n<p>By contrast:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Option A<\/strong> is incorrect because <strong>y = 1512.5<\/strong> is not a <em>zero<\/em> of the function; it\u2019s likely the <strong>maximum profit<\/strong>, which occurs at the vertex of the parabola.<\/li>\n\n\n\n<li><strong>Option C<\/strong> is incorrect because <strong>x = 42.5<\/strong> is the x-value that gives <strong>maximum profit<\/strong>, not a zero.<\/li>\n\n\n\n<li><strong>Option D<\/strong> misinterprets the meaning of zeros\u2014x = 15 and x = 70 represent points where profit is zero, not the lowest and highest profits.<\/li>\n<\/ul>\n\n\n\n<p>Thus, <strong>option B<\/strong> correctly identifies the <strong>zeros<\/strong> and explains their meaning within the real-world context: <strong>break-even prices<\/strong>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>A woodworker makes wooden checkerboards. Her profit is a function of the price she charges. This graph shows her total profits, y, based on the sales price, x of each checkerboard. Identify any zeros of the function, and interpret what the zeros mean in terms of the situation. A. Zero: y=1512.5. This is the maximum [&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-213804","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/213804","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=213804"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/213804\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=213804"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=213804"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=213804"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}