The Arms Hotel has 56 rooms. A rented room represents $150 in profit, while turning away a customer who made a reservation (but the Arms Hotel did not have a room available) costs $100. However many reservations the Arms Hotel accepts, there is an 50% chance that exactly that number of customers will show up to claim their reservations, and a 50% chance that one less than the total number of reservations will show up.
a. What are the two future states of nature the Arms Hotel faces?
b. What is the expected value of the policy of accepting exactly 56 reservations?
c. What is the expected value of the policy of accepting exactly 57 reservations?
d. The Arms Hotel already has 56 reservations for tomorrow, and a customer has just called who wants to book a room for tomorrow. Should Arms Hotel tell this customer “yes” or “no”?