{"id":213289,"date":"2025-05-10T07:58:49","date_gmt":"2025-05-10T07:58:49","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=213289"},"modified":"2025-05-10T07:58:52","modified_gmt":"2025-05-10T07:58:52","slug":"a-construction-company-is-planning-their-projects-for-the-year-2021","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/05\/10\/a-construction-company-is-planning-their-projects-for-the-year-2021\/","title":{"rendered":"A construction company is planning their projects for the year 2021."},"content":{"rendered":"\n

Problem
A construction company is planning their projects for the year 2021. The company is considering the construction of a certain number of 1,000 m’ buildings. 1312018, the company has built 5 similar buildings but with smaller areas, and the material costs associated with those 5 buildings are as shown in the following table:
Buddmg e Cast (3D) 1 700 83,200 2 747 87,800 3 780 90,400 4 810 93,100 5 845 95,500
The material cost index values are displayed in the following table: Year Cost 2017 345 2018 355 2019 357 2020 360 2021 362<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

To determine the estimated material cost<\/strong> of a 1,000 m\u00b2 building in 2021<\/strong>, we must analyze the cost trends of the smaller buildings, normalize them using the cost index, and then project that trend forward using the cost index for 2021.<\/p>\n\n\n\n

\n\n\n\n

Step 1: Standardize historical costs using Cost Index<\/h3>\n\n\n\n

We are given:<\/p>\n\n\n\n

Building<\/th>Area (m\u00b2)<\/th>Cost (USD)<\/th>Year<\/th>Index<\/th><\/tr><\/thead>
1<\/td>700<\/td>83,200<\/td>2018<\/td>355<\/td><\/tr>
2<\/td>747<\/td>87,800<\/td>2018<\/td>355<\/td><\/tr>
3<\/td>780<\/td>90,400<\/td>2018<\/td>355<\/td><\/tr>
4<\/td>810<\/td>93,100<\/td>2018<\/td>355<\/td><\/tr>
5<\/td>845<\/td>95,500<\/td>2018<\/td>355<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

Since all buildings were built in 2018<\/strong>, we will normalize the costs to a base year<\/strong> and then adjust them to 2021<\/strong> using the index.<\/p>\n\n\n\n

Let\u2019s calculate the cost per square meter<\/strong> for each building in 2018:<\/p>\n\n\n\n

    \n
  • B1: 83,200 \/ 700 = 118.86<\/strong><\/li>\n\n\n\n
  • B2: 87,800 \/ 747 \u2248 117.51<\/strong><\/li>\n\n\n\n
  • B3: 90,400 \/ 780 \u2248 115.90<\/strong><\/li>\n\n\n\n
  • B4: 93,100 \/ 810 \u2248 114.94<\/strong><\/li>\n\n\n\n
  • B5: 95,500 \/ 845 \u2248 113.02<\/strong><\/li>\n<\/ul>\n\n\n\n

    The cost per m\u00b2 decreases as the building size increases \u2014 a common occurrence due to economies of scale.<\/p>\n\n\n\n

    Now we fit a linear trend<\/strong> to the cost\/m\u00b2 data.<\/p>\n\n\n\n

    Let\u2019s approximate the trend with linear regression. For simplicity, we can observe that:<\/p>\n\n\n\n

      \n
    • When area increases by 145 m\u00b2 (from 700 to 845), cost\/m\u00b2 drops from 118.86 to 113.02<\/li>\n\n\n\n
    • That\u2019s a drop of \u2248 5.84 across 145 m\u00b2 \u2192 slope \u2248 -0.0403<\/li>\n<\/ul>\n\n\n\n

      We use point-slope form to estimate cost\/m\u00b2 for a 1,000 m\u00b2 building:<\/p>\n\n\n\n

        \n
      • Using Building 5: Cost\/m\u00b2 = 113.02 + (1000 – 845) \u00d7 (-0.0403)<\/li>\n\n\n\n
      • = 113.02 – 6.24 = 106.78<\/strong> (in 2018)<\/li>\n<\/ul>\n\n\n\n
        \n\n\n\n

        Step 2: Adjust cost to 2021 using the material cost index<\/h3>\n\n\n\n

        Use ratio of indices: 362 (2021) \/ 355 (2018) = 1.0197<\/strong><\/p>\n\n\n\n

        So, 2021 cost\/m\u00b2 = 106.78 \u00d7 1.0197 \u2248 108.89<\/strong><\/p>\n\n\n\n

        Total cost for a 1,000 m\u00b2 building = 108.89 \u00d7 1,000 = $108,890<\/strong><\/p>\n\n\n\n

        \n\n\n\n

        \u2705 Final Answer: $108,890<\/strong><\/h3>\n\n\n\n
        \n\n\n\n

        Explanation (300+ words):<\/h3>\n\n\n\n

        The construction company wishes to estimate the material cost of constructing a 1,000 m\u00b2 building in 2021 based on data from 2018. The best approach involves adjusting historical cost data using material cost indices<\/strong> to account for inflation, and extrapolating trends to a larger building size.<\/p>\n\n\n\n

        First, we calculate the unit cost (cost per m\u00b2)<\/strong> for each of the 5 smaller buildings built in 2018. This gives insight into how the cost behaves relative to the size of the building. As expected, we observe that the cost per m\u00b2 decreases<\/strong> as the size increases \u2014 a standard result of economies of scale<\/strong>, where larger projects benefit from bulk purchases and fixed cost dilution.<\/p>\n\n\n\n

        We then estimate a linear trend<\/strong> to predict the cost per m\u00b2 for a building size of 1,000 m\u00b2. This method provides a simple yet effective forecast, considering only a modest extrapolation from 845 m\u00b2 (the largest building) to 1,000 m\u00b2. Using the slope derived from cost\/m\u00b2 versus area, we predict a base 2018 cost per m\u00b2 of about 106.78 USD<\/strong> for the 1,000 m\u00b2 building.<\/p>\n\n\n\n

        Next, we apply index-based cost adjustment<\/strong> to translate this 2018 cost to 2021 values. Using the ratio of the material cost indices (362 in 2021 vs. 355 in 2018), we adjust the predicted cost by about 1.97%, yielding a final 2021 cost per m\u00b2 of approximately 108.89 USD<\/strong>.<\/p>\n\n\n\n

        Multiplying by the area (1,000 m\u00b2), we estimate the total material cost for the proposed building to be $108,890<\/strong>. This systematic method provides a reasonable and industry-standard approach for cost forecasting using historical data and material indices.<\/p>\n","protected":false},"excerpt":{"rendered":"

        ProblemA construction company is planning their projects for the year 2021. The company is considering the construction of a certain number of 1,000 m’ buildings. 1312018, the company has built 5 similar buildings but with smaller areas, and the material costs associated with those 5 buildings are as shown in the following table:Buddmg e Cast […]<\/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-213289","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/213289","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=213289"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/213289\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=213289"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=213289"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=213289"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}