## Real World Applications – Algebra I

### Topic

How much profit does Nike make off their shoes?

### Student Exploration

It’s rumored that it costs Nike about $5 to make each pair of shoes they make.

- 1. How can we interpret this sentence as a function, \begin{align*}f(x)\end{align*}? Let’s assume the input is the number of shoes Nike makes and the output is the total cost.
- 2. What’s the domain of this function? What’s the range? How do you know?
- 3. How would you graph this relationship? What are realistic values for the \begin{align*}x\end{align*}? What are realistic values for \begin{align*}y\end{align*}?
- 4. How many pairs of shoes did Nike sell in order for their net income to be $549 million?
- 5. What is \begin{align*}f(100)\end{align*}? Interpret this into words.
- 6. What is \begin{align*}f(x) = 255,000\end{align*}? Interpret this into words.
- 7. Why is it important to be able to represent this relationship using functions?

The people that make Nike shoes in Vietnam make about $10 for about 65 hours of work per week.

- 8. How can you interpret this sentence as a function, \begin{align*}g(x)\end{align*}? What would be the input, and why? What would the output, and why?
- 9. Graph this relationship on a set of axes. What are realistic values for \begin{align*}x\end{align*}? What are realistic values for \begin{align*}y\end{align*}? How are they different from your domain and range from the previous graph?
- 10. What is \begin{align*}g(20)\end{align*}? Interpret this into words.
- 11. What is \begin{align*}g(x) = 100\end{align*}? Interpret this into words.
- 12. Compare your functions, graphs and calculations from both relationships. What conclusions can you draw about the company?

### Resources Cited

http://www-personal.umich.edu/~lormand/poli/nike/nike101-4.htm