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...

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 for an equation for the revenue of your business, where x = the change in price (in dollars).

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.

17. What is the parent function for R(x)? (

18. What shape does R(x) have? (

19. Look at the graph. How was the revenue equation transformed from the parent function? Fill out the table.

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.)

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)

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)