General Education Common Graded Assignment Course: MATH 163 - College Algebra Year: 2017 Market Research Assignment College Algebra is a general education course designed to explore the nature and scope of college mathematics through the study of functions and their applications. One of the goals of this assignment is to assess student competence for each of these objectives: I. II. Written Communication Skills articulate a solution to mathematical problems Critical Analysis and Reasoning model numerical data using quadratic functions to further analyze data and predict values III. IV. Technological Competence apply appropriate technology to the solution of mathematical problems Information Literacy model numerical data using quadratic functions to further analyze data and predict values; articulate a solution to mathematical problems V. Scientific and Quantitative or Logical Reasoning construct a solution to real world problems using problem solving methods individually and in groups In addition to the above general education objectives, this assignment assesses students' understanding and application of the following skills and knowledge specific to Quadratic Functions. 1) 2) 3) 4) 5) In this assignment students will address the following general education mathematics objectives: analyze, interpret and evaluate quantitative information; express mathematical information in writing; apply technology in mathematics; apply mathematics to other disciplines of learning; apply mathematics to everyday experience. In addition, the purpose of this assignment is to demonstrate that students can address the following course objectives: 1) Produce the graphs of polynomial functions. 2) Identify the zeros of polynomial functions. 3) Solve inequalities in one variable. 4) Articulate a solution to mathematical problems. 5) Apply appropriate technology to the solution of mathematical problem. November 2016 Submission Guidelines Time Limit: Students have two weeks to complete the project and submit it before _______________. (Faculty insert due date here) Please submit two copies of your answers. o One copy should only include your student ID, course name, and section number; it should omit student and faculty names. o The other copy should include your student ID, your name and the course name, course number and the course section. Submit your response typed in Times New Roman 12-pt font, double-spaced with 1\" margins. You may write the equations by hand or use Equation Editor or MathType. All graphs should be produced using a graphing utility (such as www.desmos.com ), clearly labeled and included in your submission. Use the included 'Instructions on how to determine a best fit quadratic function' to complete part 3. Your facts must be properly cited with a Works Cited page. For citation, use the Modern Language Association (MLA) format and use parenthetical citation with a Works Cited list as the final page of your submission (non-content page). Purdue University offers a very good online reference at their Writing Lab's website below. o http://owl.english.purdue.edu/owl/resource/747/01/ o http://libraryguides.ccbcmd.edu/Citations Grading: This assignment will account for 10% of the total course grade. November 2016 Instructions on how to determine a best fit quadratic function Analysis tools like Microsoft Excel can determine mathematical models very quickly. Your goal for part 3 of the project is to use Microsoft Excel to graph the data and determine a quadratic model for the data. Data table: 1. Open Microsoft Excel and enter the data in two columns: Number of blenders and Shipping cost (dollars). 2. Take a screenshot of the table and paste in into your project. SA E L P M Scatterplot: 1. Create a scatterplot of the data. With your mouse, highlight all the data. On the Insert tab select Scatter (Scatter with only Markers). A scatterplot of Number of blenders v. Shipping cost should appear. November 2016 A S L P M E 2. Add axis titles for both the x and y axes. Click on the Scatter Plot and select + to open Chart Elements. Check the Axis Titles box, uncheck Chart Title box, then make the horizontal axis title \"Number of blenders\" and the vertical axis title \"Shipping cost\". 3. Copy the graph and paste it into the assignment. SA E L P M Quadratic Model: 1. Adding a quadratic trendline to the graph. November 2016 L P M A S E Right-click on one of the data points in the Scatter plot and select Add Trendline. Under Trendline Options, select Polynomial and make sure the Order is set at 2. At the bottom, check the box for Display Equation on Chart and then click x to close the tab. A quadratic trendline (quadratic model) should now appear on your Scatter plot. 2. Copy the graph and paste it into the assignment. L P M A S E Market Research Project Suppose you are a Market Analyst working for a small appliance manufacturer. Your firm is designing and launching sales of a new blender. Before your firm will actually represent and manufacture the product, you need to determine if it will be in the firm's best financial interest to do this. 1 In the following questions, you will do some research and planning for the launch of your new blender. In order to launch your new appliance business, you need to first convince your investors with some market research. There are few considerations you should make. In four well developed paragraphs using the highlighted vocabulary, respond to the following questions. How do production costs impact your profit? Will advertising also impact your profit margins? Identify and describe other costs associated with trying to produce, market, and sell a product? How will these impact your profit? Will it always be the case that the more of an item you produce and sell, the more profit you will make? How do businesses determine their breakeven point and calculate losses? Shipping of goods often depends upon the weight and the dimensions of the container that is being transported to various stores. How might this impact the number of blenders produced and shipped, as well as the size of the blender? November 2016 Why might it not be a good idea to overproduce a product? How can this impact the profit? How does sales price and expected revenue impact the profit? 2 Suppose you find that a firm produces and sells x blenders annually, with their total profit (in hundreds of dollars) given by P ( x )=1.11 x 23.9430.003 x 2 a Using a graphing utility produce the graph of P in such a way that the appropriate features of the graph are displayed. Print this graph and include it with your submission. In 1-3 sentences explain how you chose what features of the graph you are attempting to display and why? b Does the graph of P ever dip below the x-axis? In 1-3 sentences explain what this c o u l d indicates using the vocabulary from part 1. c Using the graph obtained in part a) estimate the following in interval notation: i For what values of x will P be negative? ii For what values of x will P be positive? d Determine when P (x) = 0 and in 1-3 sentences explain what it indicates using the vocabulary from part 1. e Using algebraic methods determine how many blenders must the company produce and sell in order to maximize profit? f For what values of x is the profit increasing? 3 Consider the following data that you have obtained regarding the shipping of the item. Number of Blenders 10 20 50 100 200 Shipping Cost (dollars) 38 70 154 254 304 a Determine the equation of a quadratic function that best fits the above data. This will be your shipping cost function C(x). Use the given instructions to produce the equation and the graph in Excel. Include these in your submission. b How much will it cost to ship the number of blenders that yields the company its maximum profit? How much will it cost the company to ship the number of blenders that yields the company a profit of 0? c Assuming it costs $20 to produce each blender, complete the following chart and calculate the revenue. Fill in the empty rows with data obtained for the number of blenders that yield maximum profit and a profit of zero. Number of November 2016 Production Cost Shipping Cost Profit (dollars) Revenue Blenders 10 30 60 100 d (dollars) 200 (dollars) 38 (dollars) -1314.30 Do the revenue amounts make sense? If not, what could possibly be a reason? What other factors could be influencing the profit? In 3-5 sentences elaborate on your findings. 4 Based on your market research, how many blenders would you propose to the firm that they make? Give your reasoning in at least 1 well developed paragraph. In your suggestions make sure you discuss at least two options that the firm can consider. Include information about the type of area in which you are looking to market this product: a small town, a large mall, online retailer? Make sure to keep in mind that you have to pay for the production of all these blenders and make a reasonable profit. November 2016