MAT 1073 - Fall 2017 Name: ____________________________________________ Core Communication Assignment 2 Introduction: This assignment presents an example of using polynomial functions to model a given data set, and then using that model to make predictions and come to conclusions about the given situation. Part of this process will involve using Microsoft Excel to graph a set of data and add \"trendline\" models to that graph. (See handout.) Your submission may be typed and submitted on Blackboard as a Word document or PDF file, with all questions answered in the order given below. Group Submission: One of the communication aspects of this assignment is that students work collaboratively; this is a skill that is necessary for all aspects of life outside of this class, and so is crucial to your education as part of the core curriculum. As such, each group will make a single submission of this assignment on Blackboard with the names of the contributing group members listed at the top of the first page. Any group member who does not significantly contribute to the submission should not be listed, and will receive a zero for the assignment. Due Date: Your submission for this assignment is due by 8:30 am on Tuesday, 11/7. Any questions or concerns on your submission should be directed to the instructor before the end of the business day on Monday, 11/6. Problem Statement: A business that produces mobile phones is analyzing its cost structure to determine the price at which they should sell their phones in order to maximize profit. (Reality Check: This scenario does not take into account the variable demand for the product, instead assuming a constant and sufficient demand.) The business has the following data for the cost of producing various quantities of phones. Quantity Cost 1000 $195,400 2000 $282,500 3000 $310,000 4000 $325,000 5000 $402,800 6000 $497,300 Our first goal is to use Excel to chart this data and give an equation that best fits the data (called a model), through a process called regression. Don't worry, Excel does all the heavy lifting in the background, but it only gives the most accurate information when using relatively small inputs. 1. So, our first step will be to convert the given data by letting represent the quantity of phones in thousands, and represent the cost of producing those phones in thousands of dollars. Thus, the first data point would be converted to the ordered pair (1, 195.4). In your submission, redraw the above table with the converted data values. 2. Input the converted data into Excel, and follow the handout (if needed) to chart the data in a basic scatter plot, adding appropriate axis and chart labels. Copy this chart into your submission document. MAT 1073 - Fall 2017 Core Communication Assignment 2 3. Next, you'll add \"trendline\" models to your chart, with the eventual goal of determining which of the following models best fits your data. (a) Create a copy of your chart and add to it a linear trendline, with equation. Copy this chart into your submission document. (b) Create another copy of your original chart and add to it a quadratic (Polynomial, Order: 2) trendline, with equation. Copy this chart into your submission document. (c) Create another copy of your original chart and add to it a cubic (Polynomial, Order: 3) trendline, with equation. Copy this chart into your submission document. 4. In 2-3 complete sentences, evaluate the models you generated in 3(a)-(c), and conclude, based on a comparison of your charts, which model best fits the data. 5. Find and, in at least one complete sentence, accurately interpret the -intercept of the model you have chosen. 6. Suppose the business wants to set the price of their phone so that they break even on selling 2500 phones. Call the model you have chosen (), the cost function. Using () and the revenue function, () = , determine the price, , in dollars that should be charged so that () = () when 2500 phones are produced and sold. Show your work, and answer in the form of a complete sentence. 7. With the revenue function () as defined in question 6 above, the business will make a profit when selling more than 2500 phones. However, due to rising costs after that point, there will eventually come a point when producing more phones becomes so expensive that it is no longer profitable (this is due to the law of diminishing returns). To find that production level, we need to set the profit function, () = () () equal to zero. This equation is not solvable by hand, but you can use trial and error to approximate the value of we seek. Show your work, and answer in the form of a complete sentence. 8. Finally, graph the profit function () using technology, and copy this graph, with appropriate scale, into your submission document. Use this graph to approximate the production level at which profit is maximized, and find the maximum profit. Answer in the form of a complete sentence. Your grade for this assignment will be based partly on demonstrating correct mathematical calculations, but just as important is the \"communication\" aspect of this communication assignment. That is, you must convey your results, both visually (through charts and graphs) and verbally (through complete sentences), in a way that is understandable to the reader and demonstrates your comprehension of the material. (Another important aspect of communication here is to ask if you need help!)