1. Embassy Suites is facing a linear demand function for its two-room suites in the form of dp=550-3p . For each suite, the service costs are about $50. The hotel management is interested to find the optimal price that generates the highest revenue per night.
   1. Using the above demand function, write down the basic price optimization problem, and find the optimal price and optimal total revenue (5pts) (Please show your work)
   2. What is the total customer surplus if the management team uses your optimal price from part (a)? (5pts)
   3. Instead of a one-price policy from part (a), Embassy Suites has decided to try price differentiation and use the following two-price policy ($75, $140). That is quoting $75 for price-sensitive customers and quoting $140 for business customers. Find the total revenue generated by this new policy (7pts)
   4. Find the total customer surplus for the two-price strategy in part (c). (8pts)
   5. Based on your answers to part (a) through (d), comment on the performance and fairness of the two pricing strategies that Embassy Suites can adopt. (5pts)