The main post office in Tampa, Florida, is due to be replaced with a much larger, more modern facility that can handle the tremendous flow of mail that has followed the city\u2019s growth since 1970. Since all mail, incoming or outgoing, travels from the seven regional post offices in Tampa through the main post office, its site selection can mean a big difference in overall delivery and movement efficiency. Using the data in the following table, calculate the center of gravity location for the proposed new facility.<\/p>\n\n\n\n
Regional Post Office Map Coordinates (x, y) Truck Round Trips Per Day<\/p>\n\n\n\n
Ybor City (10, 5) – 3
Davis Island (3, 8) – 3
Dale-Mabry (4, 7) – 2
Palma Ceia (15, 10) – 6
Bayshore (13, 3) – 5
Temple Terrace (1, 12) – 3
Hyde Park (5, 5) – 10<\/p>\n\n\n\n
The correct answer and explanation is :<\/strong><\/mark><\/p>\n\n\n\n To calculate the center of gravity (CG) for the proposed new post office facility in Tampa, Florida, we need to use the weighted average method, which involves considering the coordinates of each regional post office and the number of truck round trips per day as the weight.<\/p>\n\n\n\n $$ $$ $$ $$ The center of gravity location for the proposed new post office facility is approximately (7.97, 6.69)<\/strong>.<\/p>\n\n\n\n The center of gravity (CG) is a method of determining the ideal location for a facility based on a weighted average of existing locations, considering the importance or “weight” of each location. In this case, the “weight” is the number of truck round trips per day, which represents the volume of mail handled by each regional post office. By calculating the weighted averages of the x and y coordinates, we determine the central point that minimizes the distance traveled by all trucks and improves the efficiency of mail flow.<\/p>\n\n\n\n By locating the new facility near this center of gravity, the overall cost and time for mail transport between regional post offices and the central facility will be minimized, improving the efficiency of the entire system.<\/p>\n","protected":false},"excerpt":{"rendered":" The main post office in Tampa, Florida, is due to be replaced with a much larger, more modern facility that can handle the tremendous flow of mail that has followed the city\u2019s growth since 1970. Since all mail, incoming or outgoing, travels from the seven regional post offices in Tampa through the main post office, […]<\/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-211891","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/211891","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=211891"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/211891\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=211891"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=211891"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=211891"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Steps to Calculate the Center of Gravity:<\/h3>\n\n\n\n
\n
\\text{Weighted } x = \\frac{\\sum (x_i \\cdot W_i)}{\\sum W_i}
$$ $$
\\text{Weighted } y = \\frac{\\sum (y_i \\cdot W_i)}{\\sum W_i}
$$ Where:<\/li>\n<\/ol>\n\n\n\n\n
Data:<\/h3>\n\n\n\n
Post Office<\/th> (x, y) Coordinates<\/th> Truck Round Trips (W)<\/th><\/tr><\/thead> Ybor City<\/td> (10, 5)<\/td> 3<\/td><\/tr> Davis Island<\/td> (3, 8)<\/td> 3<\/td><\/tr> Dale-Mabry<\/td> (4, 7)<\/td> 2<\/td><\/tr> Palma Ceia<\/td> (15, 10)<\/td> 6<\/td><\/tr> Bayshore<\/td> (13, 3)<\/td> 5<\/td><\/tr> Temple Terrace<\/td> (1, 12)<\/td> 3<\/td><\/tr> Hyde Park<\/td> (5, 5)<\/td> 10<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n Calculations:<\/h3>\n\n\n\n
Weighted x-coordinate:<\/h4>\n\n\n\n
\\text{Weighted } x = \\frac{(10 \\times 3) + (3 \\times 3) + (4 \\times 2) + (15 \\times 6) + (13 \\times 5) + (1 \\times 3) + (5 \\times 10)}{3 + 3 + 2 + 6 + 5 + 3 + 10}
$$<\/p>\n\n\n\n
\\text{Weighted } x = \\frac{30 + 9 + 8 + 90 + 65 + 3 + 50}{32} = \\frac{255}{32} \\approx 7.97
$$<\/p>\n\n\n\nWeighted y-coordinate:<\/h4>\n\n\n\n
\\text{Weighted } y = \\frac{(5 \\times 3) + (8 \\times 3) + (7 \\times 2) + (10 \\times 6) + (3 \\times 5) + (12 \\times 3) + (5 \\times 10)}{3 + 3 + 2 + 6 + 5 + 3 + 10}
$$<\/p>\n\n\n\n
\\text{Weighted } y = \\frac{15 + 24 + 14 + 60 + 15 + 36 + 50}{32} = \\frac{214}{32} \\approx 6.69
$$<\/p>\n\n\n\nResult:<\/h3>\n\n\n\n
Explanation:<\/h3>\n\n\n\n