## 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,
f(x) ? 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
x ? What are realistic values fory ? - 4. How many pairs of shoes did Nike sell in order for their net income to be $549 million?
- 5. What is
f(100) ? Interpret this into words. - 6. What is
f(x)=255,000 ? 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,
g(x) ? 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
x ? What are realistic values fory ? How are they different from your domain and range from the previous graph? - 10. What is
g(20) ? Interpret this into words. - 11. What is
g(x)=100 ? 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