Maximum revenue Imagine this scenario: You are trying to fulfill you dream of opening your own business, designing and selling coffee mugs. After many years and hours of studying for college, you feel that there is a big demand for coffee mugs. You are trying to get a contract with a local store to be the sole provider of coffee mugs. You and your company partner are researching how many coffee mugs must be produced and sold for maximum revenue. After extensive research, you concluded that you could give away 50 coffee mugs without charging anything. If you charge $10.00, nobody will buy the coffee mugs. Your job is to find the maximum possible revenue from selling the coffee mugs. Answer the following questions:
1. Graph the linear relationship between the price of coffee mugs p, and the number of coffee mugs sold S . Hint: To give away 50 coffee mugs means when the price p=0 , S(0) = 50. Plot that point on the graph. Find one more point using the other given condition. Keep in mind S(p) is a linear function.
2. Find the equation of the linear function S(p) that describes the situation.
3. The revenue is determined by R = S p. Express the revenue as a function of the price p.
4. Graph the revenue function. Make sure to label the x - and the y - axis with the appropriate units.
5. At which price per coffee mug do you not make any money?
6. Find the price per coffee mug that makes the most revenue.
7. How many coffee mugs must be made to maximize the revenue?
8. What is the maximum revenue? 9. How many coffee mugs must be sold to make at least $50 in revenue?