{"id":216150,"date":"2025-05-18T19:29:49","date_gmt":"2025-05-18T19:29:49","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=216150"},"modified":"2025-05-18T19:29:54","modified_gmt":"2025-05-18T19:29:54","slug":"party-trays-which-cost-14-00-to-make-not-including-labor-are-sold-for-35-00","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/05\/18\/party-trays-which-cost-14-00-to-make-not-including-labor-are-sold-for-35-00\/","title":{"rendered":"Party trays, which cost $14.00 to make not including labor, are sold for $35.00."},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">Party trays, which cost $14.00 to make not including labor, are sold for $35.00. If two people work 8-hour shifts making the trays at $7.00 per hour, how many trays must be sold to cover all costs including labor?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><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 class=\"wp-block-paragraph\">Let&#8217;s break down the problem step-by-step:<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Given:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Cost to make one tray (excluding labor) = \\$14.00<\/li>\n\n\n\n<li>Selling price per tray = \\$35.00<\/li>\n\n\n\n<li>Two people work 8-hour shifts making trays<\/li>\n\n\n\n<li>Labor cost per hour per person = \\$7.00<\/li>\n\n\n\n<li>Need to find: How many trays must be sold to cover <strong>all costs<\/strong>, including labor?<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Calculate total labor cost<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Number of workers = 2<\/li>\n\n\n\n<li>Hours worked per worker = 8<\/li>\n\n\n\n<li>Hourly wage per worker = \\$7.00<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Total labor cost = Number of workers \u00d7 Hours worked \u00d7 Hourly wage<br>= 2 \u00d7 8 \u00d7 \\$7.00<br>= 16 \u00d7 \\$7.00<br>= \\$112.00<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Calculate total cost for making trays<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Let the number of trays made be <strong>x<\/strong>.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Material cost per tray = \\$14.00<\/li>\n\n\n\n<li>Labor cost total = \\$112.00 (fixed for this batch)<\/li>\n\n\n\n<li>Total cost = (Material cost per tray \u00d7 number of trays) + labor cost<br>= 14x + 112<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Calculate revenue from selling trays<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Selling price per tray = \\$35.00<\/li>\n\n\n\n<li>Revenue from selling x trays = 35x<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Step 4: Set revenue equal to total cost to find break-even number of trays<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">To <strong>cover all costs<\/strong>, revenue must be at least equal to total cost:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$<br>35x = 14x + 112<br>$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Subtract 14x from both sides:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$<br>35x &#8211; 14x = 112<br>$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$<br>21x = 112<br>$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Divide both sides by 21:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$<br>x = \\frac{112}{21} \\approx 5.33<br>$$<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Step 5: Interpret the result<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Since you can&#8217;t sell a fraction of a tray, you must sell <strong>at least 6 trays<\/strong> to cover all costs including labor.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Final Answer:<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>6 trays must be sold to cover all costs including labor.<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">This problem involves understanding fixed and variable costs and how they contribute to the break-even point. The <strong>material cost per tray<\/strong> (\\$14) is a variable cost because it changes depending on the number of trays made. The <strong>labor cost<\/strong> (\\$112) is a fixed cost for the shift because it doesn&#8217;t depend on the number of trays \u2014 the workers are paid for 8 hours regardless.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">To break even, total revenue (selling price \u00d7 number of trays) must equal total costs (material + labor). By setting these equal, we solve for the minimum number of trays to sell to avoid losing money.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">It&#8217;s important to note that even though the cost per tray (without labor) is \\$14, the labor adds a significant fixed expense that spreads out over the trays. Selling only 5 trays yields revenue of 5 \u00d7 \\$35 = \\$175 but costs are 5 \u00d7 \\$14 + \\$112 = \\$182, resulting in a loss. Selling 6 trays yields revenue of \\$210 and costs of \\$196, so the business starts to make a profit.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Thus, understanding how fixed costs like labor impact overall profitability is essential in pricing and production decisions in business.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Party trays, which cost $14.00 to make not including labor, are sold for $35.00. If two people work 8-hour shifts making the trays at $7.00 per hour, how many trays must be sold to cover all costs including labor? The Correct Answer and Explanation is: Let&#8217;s break down the problem step-by-step: Given: Step 1: Calculate [&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-216150","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/216150","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=216150"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/216150\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=216150"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=216150"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=216150"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}