Mason wants to start his own business in which he prints images on hats to sell for various organizations. The cost of the machinery he needs to get started is $400. The cost of the hat and the materials needed to print the image is $7 per hat. He wants to sell the hats for $15 each. You need to help Mason evaluate his pricing ideas to see if they are reasonable and to look for ways he might be able to increase his profit.

Let’s Get Started!
1. What do we know from the information above? What is our “unknown”? Define a variable for the unknown quantity.
2. .
3. .
4. GiventhatMason’s“Profit=Income-Cost ”, earn. (Let P = profit)
5. Solve your equation from #4 for the variable you defined in #1. (Note that this will be in terms of P because we do not know that yet.)
6. Are the equations from #4 and #5 equivalent? Explain your reasoning.
7. How much profit can Mason make by selling 100 hats? Be sure to show the equation you used at the beginning of your work, and then show all work with units.
8. “break-even”?(Notethatbreak-even means that Mason would have a profit of $0 because his income and costs would be equal.)

9. How many hats would Mason need to sell in order to have $300 in profits? Be sure to show the equation you used at the beginning of your work, and then show all work with units.
10. Based on your answers to #7 - 9, do you think that Mason’s price per hat is reasonable? Explain why or why not.
11. What do you think Mason could do in order to increase his profits? Justify/Explain your answer.
12. Do you think it would be wiser to raise or lower the price of the hat in order for Mason to increase his profits? Explain your reasoning by giving examples.