The Scenario: You want to start your own 3-D printing and manufacturing business. Use what you know about shifting functions to plan your business and find a profitable model. The Project: Use the information provided in the Performance Task to design a product, determine your costs, and estimate your revenue. Then use this information to see if your new 3-D printing business will be profitable. Identify and Organize Your Information Product Design (6 points total) Before you get started, you need to choose a product to build with your 3-D printer. 1. What are you going to make? (6 points) (Note: The maximum build size is 25 cm by 16 cm by 15 cm about the size of a small shoe box.) Operations (33 points total) How much is it going to cost to make your object? Use the questions below to determine your initial investment and how much it will cost to produce each item. 2. For each expense category - complexity, design, and quality - decide whether your product has high, medium, or low requirements. In the table below, fill in the three boxes that apply to your project with the operational costs associated with those expenses. (6 points: 2 points for each box) Category Expense Low Medium High Complexity 3-D printer Computer and software Design Planning and development Quality Per-unit cost (materials) 3. What are the total initial start-up costs? (Note: This initial investment cost does not include the cost of producing each item.) (8 points) 4. How much do the raw materials to produce each item cost? (3 points) The cost of running a business is a function of how much it costs to start up the business, plus the ongoing monthly expenses of running the business: total cost to produce x items = C(x) = initial investment + (cost per item) x, where x = number of items produced. 5. Use the formula above to model the cost of operating your business as a function of the number of items produced. (6 points) 6. Sketch a graph of your cost function. (3 points) 7. On your graph, sketch the cost function for a company that does not need any initial investment and that has a per-item cost of $1. Use transformations to describe the differences between the slopes and y-intercepts of the two functions. (7 points: 3 points for the sketch, 4 points for the description) Sales and Marketing (86 points total) Part I: Price (45 points total) Now that you know your costs, you need to determine how much you will charge for your product and how much money you can make. 8. Fill out the following table with the information from the seller. Refer back to your answers to Question #2 to remember what you have chosen for your product's level of complexity, design, and quality. (6 points: 2 points for each cell) (6 points: 2 points per blank) What is a good starting price for your product? (unit price) How many can you expect to sell each week? (base sales) How many sales do you gain for every dollar that you lower the price? (sales rate) 9. Consider the seller's information. How many items would you expect to sell at different price points? Write each set of answers as a coordinate pair. (18 points: 2 points for each cell) Price (Starting price - $1) = ___________ Starting price = ___________ (Starting price + $1) = ___________ Number of items sold each week (price, number of items) 10. What type of function represents the relationship between price and number of items sold? (1 point) 11. Find the equation of the line where x = price and y = number of items sold. Write your answer in slope-intercept form. (9 points: 3 points for the slope, 3 points for the y-intercept, and 3 points for the final equation) 12. Sketch the graph of your price function below: (3 points) 13. What is the parent function of your price equation? Explain what transformations you would use to change the parent function into your price equation. (5 points: 2 points for the parent function, 3 points for the explanation) 14. Look at the graph of the price equation. At what price will you sell the most items? Do you want to use this price or not? (3 points: 2 points for the answer, 1 point for the interpretation) Part II: Revenue (41 points total) 15. A product's price is the amount of money you get from selling one of the item. Revenue is the total amount of money from all the items you sell. The formula for one week of revenue is given below. Use your answers from question 8 to write an equation for the revenue of your business, where x = the change in price (in dollars). (6 points: 2 points for each constant term) Revenue = (unit price)(number of units sold) Revenue = (unit price + change in price)(base sales - sales rate change in price) 16. Use any method to determine the roots and vertex of R(x), and then sketch the graph of your revenue equation below. Calculators and other graphing tools are acceptable. (9 points: 3 points for the roots, 3 points for the vertex, 3 points for the graph) 17. What is the parent function for R(x)? (1 point) 18. What shape does R(x) have? (1 point) 19. Look at the graph. How was the revenue equation transformed from the parent function? Fill out the table. (16 points: 2 for each blank) Transformation Yes or no? By how many units? By which arithmetic operation? Reflected? Which axis? Shifted vertically? Up or down? Shifted horizontally? Left or right? Compressed or stretched? (Which?) 20. What price gives you the maximum revenue? Explain your reasoning. (5 points: 2 for the answer, 3 for the reasoning) 21. If the above graph gives you the revenue per week, what is the maximum revenue you can expect for the first year? (There are 52 weeks in a year, and you should assume the same revenue each week.) (3 points: 2 for the calculation, 1 for the answer) Your Business Plan: Putting things together (25 points total) Now it's time to see how profitable your business really is! 22. What was your optimum price point (question 20)? (1 point) 23. How many items will you sell per week at your optimum price point (question 11)? (3 points) 24. How many items will you sell per year at your optimum price point? (3 points) 25. How much will it cost for you to produce all the items in the first year? Use the cost formula from question 5 to determine this. (3 points) 26. What is the expected revenue for the first year (question 21)? (3 points) 27. What is your estimated profit for the first year? (2 points) Use this formula: profit = revenue - expenses. 28. Did your business make a profit? Explain. (1 point) 29. You can make your business more profitable by increasing revenue (money coming in) or decreasing cost (money going out). What could you change about your object to increase profits? Explain how this change would affect either your cost graph or your revenue graph. (6 points: 2 points for identifying a change, 2 points for the effect on profit, 2 points for the effect on the graph) 30. Does buying a 3-D printer seem like a profitable business for you? Why or why not? (3 points) Please help it's math 3 related from Apex