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1 | P a g e COMM121 -Winter22 -Business Mathematics Assignment 1 Explanation : The following is an application of Revenue and Cost problem in Business and Economics. You are required to apply your knowledge of the following: • Construct models (find the best fit trend lines ) • Analyze models • Make business decision • Use Excel Problem . The data in the table gi ve sales revenues and costs and expenses for Company X for various years. Use this table to answer the following questions. Year Sales Revenue (millions $) Cost and Expenses (millions $) 2003 2.4225 2.0121 2004 2.7575 2.4315 2005 2.9332 2.6257 2006 3.7512 2.802 3 2007 3.9768 3.5400 2008 4.5485 3.8231 2009 4.7225 4.0321 2010 5.1668 4.8500 2011 4.96 00 4.9523 2012 5.0927 4.6871 2013 4.6223 5.3 110 2014 4.5012 5.6321 2015 3.8853 6.7423 a) Using the data set in the table , m odel Sales R evenues , (), as a quadratic function of year, with x=0 representing 2000. That is, plot this set of data and find the curve of best fit. (Use Excel ) (Hint : replace 2003 with x=3, 2004 with x=4 , and so forth before plotting the graph and finding the best fit curve. Review “Module 1 -Excel Applications” notes .) b) Use the function () you found in part a to determine the year (round to the nearest integer when necessary) in which the maximum revenue occurs , and the n compare this value with the real data (maximum revenue in the table ). c) Write a sentence to describe how well the function fits the data. d) Using the data set in the table , model Cost and Expenses, (), as a quadratic function of year, with x=0 representing 2000. That is, plot this set of data and find the curve of best fit. (Use Excel ) (Hint : replace 2003 with x=3, 2004 with x=4, and so on before plotting the graph and finding the best fit curve.) Continued on the next page … 2 | P a g e e) Using the data set in the table , model P rofit function, (), as a quadratic . Would a quadratic model be a good fit? Why? (Use Excel ) f) Use the profit function ’s () graph you found in part e to find the year in which maximum profit occurs, and the maxim profit. g) Thro ugh the decade from 2008 to 2015 , does the function () project in creasing or decreasing profits? Do the real data suppor t this trend ? Why? h) How might management respond to this kind of projection? Be specific while you explain your suggestions: use terms like “minimizing cost”, “increasing revenue” , “maximizing profit” , “in the short/ long term”, etc., in your sentences. Please Read Carefully : • Assignment effective as of Jan 2 8, 202 2, 12.00am . • Assignment due date: Feb 4 , 202 2, 11.59pm . • Assignment will be submitted through the drop box provided on Canvas. • Each question is equally weighted and worth 4 points. • Indicate solutions for each part clear ly: For example, Solution (a), Solution (b), and so on. • You need to use “ Excel ” as indicated above . Plot and model each function (), () and () on different chart s. • Use only 1 Excel file : Open separate worksheets in the Excel file you created, name them (part a, question 1, etc.) , and work on them as per question . • Submit your Excel file and any other document including cover page , and your written work (if there is any) separately . • Please also read the “Assignment Submission Instructions” given on Canvas before submitting your work. Sticking with these instructions is the easiest way to get full credit for your valuable work.