Transcript: Performance Task: 3-D Printer Business
This interactive animation that shows a box with four squares titled "Product Design," "Sales &
Marketing," "Operations," and "Your Proposal." Each square can be clicked on to reveal more
information about the task.
Click each option below to gather information that will help you make decisions about how to launch
your new business.
Product Design [An image is shown with three puzzle pieces, one with a light bulb, a machine
piece, and a sales graph with an arrow going up. Click. The text onscreen is read aloud.]:
You will first design a model of an object on your computer, and then you will send the design file to
the 3-D printer. Instead of ink in a page, a 3-D printer creates an object by adding layers of material,
one on top of another. You can design objects with complex patterns, moving parts, and even
electrical circuits - and then watch them "print" right in front of you!
Click the printer icon to get some ideas about what people are making with 3-D printers. [Click. Four
images appear. The first is a stack of brightly colored Lego blocks labeled "Building Toys," the
second is of colored board game pieces and a dice] labeled, "Game Pieces," the third shows a silver
chess piece of a horse called a knight and is labeled "Chess Pieces," and the fourth shows a black
box with multi-colored, interlocking gears and is labeled "Gears."
Sales and Marketing [An image is shown with a tag on a chain that says "Price." Click. The text
onscreen is read aloud.]:
You need to find the right price for the product you're creating. With a high price, you will make more
per item, but you might not sell as many. You've found a successful seller in your market. Click the
"Skype" button to ask his advice. [A tablet is shown.] Click the tablet to Skype Bill. Then click the
buttons to ask him questions. [Click the tablet. An image of a man in professional attire wearing a
headset is shown. A phone ringing noise is heard. Questions are shown that can be clicked to ask to
Bill and hear his answers.]
Bill: Hello. How can I help you?
Question 1: How much do you think I should charge for my item? [Click.] Well, that depends.
Something small and simple should be about $2; something with more detail would go for about $5;
something with lots of features or moving parts will start around $10.
Question 2: How many can I expect to sell each week when I'm starting out? [Click.] If the design is
pretty plain, you should expect to sell about 30 units per week. An item with better style and color
could move 50 units a week. Objects with really professional designs will sell around 70 units every
Question 3: What if I change the price? [Click.] For every dollar that you lower the price, each week
you can expect to gain 20 extra sales for low-quality items, 10 extra sales for average-quality items,
or 5 extra sales for high-quality items. Good luck! Let me know how it all works out.
Operations [An image is shown with a stack of cash. Click. The text onscreen is read aloud.]:
You want to determine your initial investment costs and how much it will cost to produce your items.
Use the following box to help you find your initial costs. [An image of a game controller is shown with
"Design," a green pair of headphones is shown with "Quality," a white toy robot helicopter is shown
with "Complexity." [Click to reveal information about each.]
Design: Is it important that your object
have eye catching style?
be easy to use?
Better designs take more thought and investment up front.
Low: $500 start up cost
Medium: $1000 start up cost
High: $1500 start up cost
Quality: Is it important that your object
use nice materials?
last a long time?
Low: $1 per unit cost
Medium: $3 per unit cost
High: $5 per unit cost
Is it important that your object
have lots of intricate detail?
be made out of several different materials, like plastics, rubber, or metal?
have moving parts or electrical circuits?
Complex objects need stronger tools to model and manufacture them.
Low: $400 computer software; $1200 printer
Medium: $800 computer & software; $2200 printer
High: $1400 computer and software; $500 printer
Your Proposal [An image is shown with a sales graph with an arrow going up. Click. An image is
shown with a block wall and machine putting he last block in place. The text onscreen is read
Now you're ready to plan your business. You will collect the information shown below to demonstrate
you product, estimated costs, and estimated revenue. Verify that you have a profitable business
model, and then get ready to look for investors! [A chart is shown that says:
Initial investment costs:
Expected sales volume (units):
Projected revenue for first year
Projected profit for first year]
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)
Computer and software
Planning and development
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
(6 points: 2 points per blank)
What is a good starting price for your product?
How many can you expect to sell each week?
How many sales do you gain for every dollar that you lower the
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)
(Starting price - $1)
(Starting price + $1)
Number of items sold
(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)
Yes or no?
By how many units?
By which arithmetic
Up or down?
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
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
30. Does buying a 3-D printer seem like a profitable business for you? Why or why not? (3
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