Your friend has designed a new teapot and plans to open a teapot shop on Etsy. After learning that you are taking BUAD 311, your friend comes to you for suggestions on pricing. Based on the sales data of other similar teapot shops on Etsy, you estimate the demand to be a function of the price p: D(p) = 400 - 20p, 0<=p<=20.

a) For a "single-price" policy, what is the optimal price to set to maximize the total revenue? What is the optimal revenue?

b) Your friend tells you that at most 180 teapots can be made. With this new information in mind, how should you adjust the optimal price from a)? What is the new revenue?

c) Ignore part b). Realizing that price differentiation might bring more revenue, you plan to divide the market into 2 different segments. For the customers with high willingness to pay, you offer a price of $15; for the customers with low willingness to pay, you offer a price of $5. What is the new revenue under price differentiation?

d) Following from part c), suppose we fix the price for the customers with high willingness to pay at $15. For the customers with willingness to pay lower than $15, what is the optimal price to set for them? How much does the total revenue change compared to d)?