01 Feb data analytics question Please answer the questions in the attached PDF. – Answers must be typed and the written solution must be in word (allows to transfer to the PDF format) – S

data analytics question

Please answer the questions in the attached PDF.
– Answers must be typed and the written solution must be in word (allows to transfer to the PDF format)
– Supporting documents: for both problem scenarios, you may use either Excel or R to solve the LP
– Please use RStudio (.R script file) if necessary, please Do Not use spyder/jupter.
– Please submit supporting documents for just one chosen method per problem (either Excel / R).
Requirements: Provide good solutions is fine, explanation can be short
Modeling for Business AnalyticsPROBLEM SET 1Refer to the following description for Q1-4 (85 points total):Foxgloves, a big box store chain, is planning to build a new store in Natick, MA. The parcel ofland the company has purchased is large enough to accommodate a store of up to 140,000square feet of floor space. To maintain consistency with the brand?s identity across otherlocations, each department must have at least 15,000 sq. ft of floor space. Additionally, all typesof clothing combined should take up no more than 40% of overall floor space, and no otherindividual department should take up more than 20% of the overall floor space of the completedstore. Housewares and all categories of clothing keep all stock on the retail floor; however, toys,electronics, and outdoor recreation must separate their floor space between “inventory” and”retail sales.” Excess supply and large items in these categories are held in inventory, whichrequires a dedicated space equal to at least 10% of the department?s total floor space (retail +inventory).Based on marketing and demographic surveys of the area and historical data from its otherstores, Foxgloves estimates its annual profit per square foot of retail space for each of thestore’s departments will be as shown in the following table. Floor space used for inventory doesnot generate any profit. Foxgloves wants to know the floor space that should be devoted to eachdepartment in order to maximize total profit from this store.DepartmentAnnual Profit Per Sq. Ft. (Retail Space)Men’s Clothing$12.75Women’s Clothing$15.30Children’s Clothing$11.50Toys$16.30Housewares$12.30Electronics$13.25Outdoor Recreation$15.751.Write down a complete mathematical formulation of this problem, including the definitionof decision variables, statement of the objective function, and all constraints.Use theformat shown in class and ensure that all constraints have all DVs on the left side and asingle constant on the right side.(30 pts)
2.Formulate and solve the linear programming model for Foxgloves using Excel or R.Upload your Excel workbook or .r script file along with your written submission. In yourwrite-up, indicate the optimal annual profit and the floor space allocated to each of theseven departments in your optimal solution.(30 pts)3.Prepare a table for the company?s finance team that shows how much profit the store isexpected to generate from each department in its first year. In a concise paragraph,summarize the results of the linear program using non-technical language, and indicatewhich departments? floor space allocations are limited by the company?s minimum andmaximum space requirements.(10 pts)4.Suppose Foxgloves gets approval to build a slightly larger store (145,000 square feet)on the parcel of land. Assuming all other constraints remain unchanged, how muchadditional profit should the store expect to make in its first year of operations?For fullcredit, show your work to reach the answerwithoutresolving. For up to 10 points ofcredit, answer by resolving the updated LP. (15 pts)Refer to the following description for Q5-7 (65 pts total):The campaign manager for a Boston mayoral candidate needs to decide on the types andamounts of advertising to buy leading up to the election. The available options are TV ads,which cost $20,000 apiece and reach an average of 28,000 potential voters per ad, and radioads, which cost $9,000 apiece and reach an average of 13,000 potential voters per ad.The campaign has the following goals: (1) reach at least 200,000 voters; (2) reach at least asmany Democrats as Republicans; (3) make sure that at least 40% of the audience is under 55years old. The manager wants to know the optimal number of ads of each type to purchase inorder tominimize total advertising costwhile meetingall stated goals. Available spots limitthe number of television ads to five, and ads must be purchased in integer quantities.The breakdown of audiences for each medium are shown in the tables below.TV Ad Reach55+ years old< 55 years oldRepublicans6,0008,500Democrats4,5009,000Radio Ad Reach55+ years old< 55 years oldRepublicans3,5002,000Democrats5,0002,500
(Example of how to read the table: a TV ad reaches 4,500 Democrats who are at least 55 yearsold and 9,000 Democrats who are < 55 years old, for a total of 13,500 Democrats. The totalreach of a TV ad is the sum of all numbers in the table, 6 + 8.5 + 4.5 + 9 = 28k.)5.Write down a complete mathematical formulation of this problem, including the definitionof decision variables, statement of the objective function, and all constraints.Use theformat shown in class and ensure that all constraints have all DVs on the left side and asingle constant on the right side.(25 pts)6.Formulate and solve the linear programming model using Excel or R. Upload your Excelworkbook or .r script file along with your written submission. In your write-up, indicate thetotal advertising cost and the number of TV and radio ads to purchase in your optimalsolution.(25 pts)7.In a concise paragraph, summarize the results of the linear program using non-technicallanguage. Include the total reach in each category (age groups and political affiliations)and any suggestions you have for the campaign manager about the definition of goalsand objectives.(15 pts)