PLEASE HELP 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.
1. What are you going to make? (The maximum build size is 25 cm by 16 cm by 15 cm)
I’m going to make a small organizer for office. Like an empty cube 6cm by 6 cm by 6 cm
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.
Category Expense Low Medium High
Complexity
3-D printer 2000
Computer and software 400
Design
Planning and development
200 $
Quality
Per-unit cost 5
3. What are the total initial start-up costs?
2600$
4. How much do the raw materials to produce each item cost? 5$
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 xitems = 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.
C(x)=2600+5x
6. Sketch a graph of your cost function.
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 $1. Use transformations to describe the differences between the slopes and y-intercepts of the two functions.
Now that you know your costs, you need to determine how much you will charge for your product and how much money you can make.
8. Fill out the following table with the information from the seller. Refer back to your answers to Question #2 to remember what you have chosen for your product's level of complexity, design, and quality.
What is a good starting price for your product?
7$
How many can you expect to sell each week?
70$
How many sales do you gain for every dollar that you lower the price?
15$
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.
Price
(Starting price - $1) = _
Starting price = _
(Starting price + $1) = __
Number of items sold each week
20
10
5
(price, number of items)
(6;20)
(7;10)
(8;5)
10. What type of function represents the relationship between price and number of items sold?
Linear function represents the relationship between price and the number of items sold.
11. Find the equation of the line where x= price and y= number of items sold. Write your answer in slope-intercept form.
Slope y2-y1/x2-x1=10-20/7-6=-10
y-intercept (0;30)
final equtiony=30-10
12. Sketch the graph of your price function below:
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.
I think that my parent function is y=x, and to change the parent function to my function i need multiply it by -1 to reflect it across x axis and i need to multuply x by 10 to vertically stretch it, also i'll translate it up 30 units
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?
15. A product's priceis the amount of money you get from selling one of the item. Revenueis 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).
Revenue = (unit price)(number of units sold)
Revenue = (unit price + change in price)(base sales - sales rate • change in price)