{"id":601,"date":"2024-03-14T21:08:23","date_gmt":"2024-03-14T21:08:23","guid":{"rendered":"https:\/\/sites.rutgers.edu\/yasai\/?page_id=601"},"modified":"2024-03-14T21:08:41","modified_gmt":"2024-03-14T21:08:41","slug":"horse-corral-problem","status":"publish","type":"page","link":"https:\/\/sites.rutgers.edu\/yasai\/horse-corral-problem\/","title":{"rendered":"Horse Corral Problem"},"content":{"rendered":"

A “Wild West” Dynamic Simulation Model<\/h3>\n

As part of its program to restore the area\u2019s natural ecosystem, the federal government is trying to eliminate wild horses from the Grand River National Wilderness.\u00a0 Your company, Westland Wranglers Inc. (WWI), has a contract with the government to capture the horses.\u00a0 Fortunately, ranchers and hobbyists from neighboring areas are willing to purchase the horses, so they do not have to be destroyed.<\/p>\n

The number of horses your cowboys capture each day is well-modeled by a Poisson random variable with a mean value of 4.\u00a0 You charge your customers $150 each for the horses, and at that price the daily demand for them is well-modeled by a Poisson random variable with mean 4.1.\u00a0 If demand exceeds the number of horses you have available, you lose the additional sales.<\/p>\n

Any horses that are not sold at the end of the day are placed in a corral.\u00a0 The cost of keeping a horse in the corral for one night is $8.00, which covers feed, water, and sanitation.\u00a0 These horses are available for sale the following day, along with newly captured horses.<\/p>\n

However, only a limited number of horses can fit in a corral.\u00a0 If there are too many horses to fit, the extra ones must be released.<\/p>\n

WWI is considering four different options for the corral:<\/p>\n

    \n
  1. Rent a small corral, holding up to 5 horses, for $35 per day<\/li>\n
  2. Rent a medium-sized corral, holding up to 10 horses, for $50 per day<\/li>\n
  3. Rent both the small and medium-sized corrals.\u00a0 This option would in effect yield a combined corral holding 5 + 10 = 15 horses at a rent of $35 + $50 = $85 per day.<\/li>\n
  4. Don\u2019t rent a corral.\u00a0 This option may be considered as equivalent to a corral holding zero horses at a cost of $0 per day.<\/li>\n<\/ol>\n

    Which option will earn the greatest expected profit?\u00a0 Evaluate each option based on 1000 trials, each trial simulating 100 consecutive days of operation.\u00a0 Horses left in the corral at the end of 100 days should be assigned a “salvage” value of $130.\u00a0 You are also interested in how many horses, on average, are left in the corral at the end of each day, and the probability that your total profit, without the salvage adjustment, will be less than $45,000.<\/p>\n","protected":false},"excerpt":{"rendered":"

    A “Wild West” Dynamic Simulation Model As part of its program to restore the area\u2019s natural ecosystem, the federal government is trying to eliminate wild horses from the Grand River … Read More<\/a><\/p>\n","protected":false},"author":3356,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"footnotes":""},"class_list":["post-601","page","type-page","status-publish","hentry"],"acf":[],"yoast_head":"\nHorse Corral Problem - YASAI Simulation<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/sites.rutgers.edu\/yasai\/horse-corral-problem\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Horse Corral Problem - YASAI Simulation\" \/>\n<meta property=\"og:description\" content=\"A “Wild West” Dynamic Simulation Model As part of its program to restore the area\u2019s natural ecosystem, the federal government is trying to eliminate wild horses from the Grand River … Read More\" \/>\n<meta property=\"og:url\" content=\"https:\/\/sites.rutgers.edu\/yasai\/horse-corral-problem\/\" \/>\n<meta property=\"og:site_name\" content=\"YASAI Simulation\" \/>\n<meta property=\"article:modified_time\" content=\"2024-03-14T21:08:41+00:00\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data1\" content=\"2 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/sites.rutgers.edu\/yasai\/horse-corral-problem\/\",\"url\":\"https:\/\/sites.rutgers.edu\/yasai\/horse-corral-problem\/\",\"name\":\"Horse Corral Problem - YASAI Simulation\",\"isPartOf\":{\"@id\":\"https:\/\/sites.rutgers.edu\/yasai\/#website\"},\"datePublished\":\"2024-03-14T21:08:23+00:00\",\"dateModified\":\"2024-03-14T21:08:41+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/sites.rutgers.edu\/yasai\/horse-corral-problem\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/sites.rutgers.edu\/yasai\/horse-corral-problem\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/sites.rutgers.edu\/yasai\/horse-corral-problem\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/sites.rutgers.edu\/yasai\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Horse Corral Problem\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/sites.rutgers.edu\/yasai\/#website\",\"url\":\"https:\/\/sites.rutgers.edu\/yasai\/\",\"name\":\"YASAI Simulation\",\"description\":\"\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/sites.rutgers.edu\/yasai\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"en-US\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Horse Corral Problem - YASAI Simulation","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/sites.rutgers.edu\/yasai\/horse-corral-problem\/","og_locale":"en_US","og_type":"article","og_title":"Horse Corral Problem - YASAI Simulation","og_description":"A “Wild West” Dynamic Simulation Model As part of its program to restore the area\u2019s natural ecosystem, the federal government is trying to eliminate wild horses from the Grand River … Read More","og_url":"https:\/\/sites.rutgers.edu\/yasai\/horse-corral-problem\/","og_site_name":"YASAI Simulation","article_modified_time":"2024-03-14T21:08:41+00:00","twitter_card":"summary_large_image","twitter_misc":{"Est. reading time":"2 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/sites.rutgers.edu\/yasai\/horse-corral-problem\/","url":"https:\/\/sites.rutgers.edu\/yasai\/horse-corral-problem\/","name":"Horse Corral Problem - YASAI Simulation","isPartOf":{"@id":"https:\/\/sites.rutgers.edu\/yasai\/#website"},"datePublished":"2024-03-14T21:08:23+00:00","dateModified":"2024-03-14T21:08:41+00:00","breadcrumb":{"@id":"https:\/\/sites.rutgers.edu\/yasai\/horse-corral-problem\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/sites.rutgers.edu\/yasai\/horse-corral-problem\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/sites.rutgers.edu\/yasai\/horse-corral-problem\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/sites.rutgers.edu\/yasai\/"},{"@type":"ListItem","position":2,"name":"Horse Corral Problem"}]},{"@type":"WebSite","@id":"https:\/\/sites.rutgers.edu\/yasai\/#website","url":"https:\/\/sites.rutgers.edu\/yasai\/","name":"YASAI Simulation","description":"","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/sites.rutgers.edu\/yasai\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"en-US"}]}},"_links":{"self":[{"href":"https:\/\/sites.rutgers.edu\/yasai\/wp-json\/wp\/v2\/pages\/601"}],"collection":[{"href":"https:\/\/sites.rutgers.edu\/yasai\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/sites.rutgers.edu\/yasai\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/sites.rutgers.edu\/yasai\/wp-json\/wp\/v2\/users\/3356"}],"replies":[{"embeddable":true,"href":"https:\/\/sites.rutgers.edu\/yasai\/wp-json\/wp\/v2\/comments?post=601"}],"version-history":[{"count":2,"href":"https:\/\/sites.rutgers.edu\/yasai\/wp-json\/wp\/v2\/pages\/601\/revisions"}],"predecessor-version":[{"id":603,"href":"https:\/\/sites.rutgers.edu\/yasai\/wp-json\/wp\/v2\/pages\/601\/revisions\/603"}],"wp:attachment":[{"href":"https:\/\/sites.rutgers.edu\/yasai\/wp-json\/wp\/v2\/media?parent=601"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}