Student: Stanley

Value: This project is worth 160 points which translates to 10% of your overall grade. This project is intended to be a professional portfolio. Treat it like a report you would submit to your employer. Hence, I expect you to print out a new project from the Blackboard website and insert space below the problem in which to solve each the stated problem. All work must be shown and labeled. If inadequate work is given, no credit will be given for that problem. You may need to insert a Cartesian Coordinate system or table (no hand-drawn Cartesian coordinate system or table is permitted). I will accept handwritten mathematical formulas and work however, your work must be legible and neat. I will refuse to grade anything that I cannot easily read. Any additional pages you may need should be computer paper – no loose leaf. You may use a calculator; however, you must show the formula and the substitution if appropriate. Ten points are available for neatness, professionalism, and completeness of work. Part I- 90 points total Outside of class, Mrs. Lois also a real estate developer and owns a company called Most Affordable Terrific Housing. She has hired you to help do some business analytics for her company. ● ________ (5 points) The first building you are in charge of managing is Analytic Methods Heaven. Analytic Methods Heaven is an apartment complex that consists of one-, two-, three-, and four-bedroom units. The rental rate for each type of unit- low, moderate, or market- is determined by the income of the of the tenant. How many different rates are there? ● Mrs. Lo is looking into a new property. She has decided to form a committee of four to advise her on this new venture. If there are ten people employed by Mrs. Schenk, a. ________ (5 points) How many different committees can be formed? b. ________ (5 points) How many committees of four can be formed with you as a member? c. ________ (3 points) What is the probability that you will be on the committee? ● You have been selected for this committee. The area the property is located has the number of citizens aged 45 – 64 projected to be Where is measured in thousands, and t is measured in years, with corresponding to the beginning of 2006. ________ (3 points) What is this population projected to be in 2016? ________ (3 points) In 2026? ● You have determined the demand and supply functions for apartments in this area is modeled by the equations: Respectively, where p is measured in dollars and x is measured in united of a hundred. ________ (8 points) Find the equilibrium quantity and price. ________ (10 points) Graph the supply function – no hand-drawn Cartesian coordinate system – Graph itself must be hand-drawn. ● Mrs. LO is planning to build a new apartment complex consisting of one-bedroom units, two- and three-bedroom townhouses. A total of 192 units is planned, and the number of family units (two- and three-bedroom units) will equal the number of one-bedroom units. If the number of one-bedroom units will be three times the number of three-bedroom units, find how many units of each type will be in the complex. 1. ________ (5 points) Formulate the equations needed to solve this problem. 2. ________ (10 points) Solve using the Gauss-Jordan elimination method. ● After construction is complete, Most Affordable Terrific Housing realized a monthly profit from renting out x apartments is given by dollars. ________ (5 points) How many units should be rented out in order to maximize the monthly rental profit? ________ (3 points) What is the maximum profit realizable? ●To further boost business, Most Affordable Housing has invested in a furniture manufacturer that makes two types of furniture – chairs and sofas. The production of the sofas and chairs requires three operations – carpentry, finishing, and upholstery. Manufacturing a chair requires 3 hours of carpentry, 9 hours of finishing, and 2 hours of upholstery. Manufacturing a sofa requires 2 hours of carpentry, 4 hours of finishing, and 10 hours of upholstery. The factory has allocated at most 66 labor hours for carpentry, 180 labor hours for finishing, and 200 labor hours for upholstery. The profit per chair is $90 and the profit per sofa is $75. How many chairs and how many sofas should be produced each day to maximize the profit? ________ (5 points) Formulate the equations needed to solve this problem. Please solve this problem using each of the following techniques. ________ (10 points) Method 1: To solve use the method of corners – include the graph. ________ (10 points) Method 2: Simplex Method. Part II - 60 points total Buying a House Choose a neighborhood in the greater Pittsburgh area in which you would like to live. Pick a house that you would buy in that neighborhood. • Briefly describe the reasons behind your choice of neighborhood and your choice of house. • Include a print-out of the listing you found. • Research and discuss how housing prices vary based on neighborhood. What factors are involved in pricing a house? Be specific. Cite your sources. You negotiate with the seller to buy the home for $5000 less than the listing price. You are able to make a 20% down payment. Your bank will finance a loan for the remainder of the price at 3.8% annual interest compounded annually. • Compare a 15 year mortgage and a 30 year mortgage. • What will your annual payment be for each? • How much interest will you pay the bank for each type of loan? • Decide which length of mortgage you will use. Describe your reasoning. • Construct an Amortization Schedule for the one you chose. Show your calculations for the first 5 years only. (Please construct a table/chart- no hand-drawn table/chart) The scenario above is a simplified version of home buying. Research other costs that would have to be taken into account if you were actually buying a house. Cite any sources. You can write this in the first person, but remember this is a business report so be mindful grammar and spelling. Since it is a business report, you should be formal in your writing (no contractions or slang). Helpful links for finding listings: www.zillow.com www.howardhanna.com www.pittsburghmoves.com There are many other sites as well. Requirements Length: 2 pages double spaced. Include a one page print-out of the listing you choose. Include on a separate page the calculations you did to find annual payments and interest paid. You must either write neatly or type these. There should be no scribbles, etc. Works cited – cite any sources you use for information in MLA format. You may not use Wikipedia as an outright source. You must include at least two sources. (Note: If you are not familiar with or need a refresher on MLA citation use the Learning Commons (same room as the Math Café) to help.) Rubric for part II: Content – 15 points Respond to each prompt clearly Organize information logically Use proper inline citations Mortgage calculations – 20 points Include name of formula used Must be presented step by step in full detail Label 15 year mortgage and 30 year mortgage Must be neatly written or typed using Equation Editor in Microsoft Word (or other similar math type-setting), as though it is a report you are turning into an employer CALCULATIONS MUST BE CORRECT Amortization Table and Calculations – 10 points Must be presented step by step in full detail Label which year mortgage you chose Must be neatly written or typed using Equation Editor in Microsoft Word (or other similar math type-setting), as though it is a report you are turning into an employer CALCULATIONS MUST BE CORRECT Length – 3 points Print-out of the listing – 2 points Spelling and grammar – 5 points Works cited – 5 points Include MLA formatted list on a separate page (at least 2 sources)

**Attachments**

120Projectsp2020 (1).docx