You are the manager of a mail room which is frequently subject to theft. A period of N
days is about to occur, such that on the i
-th day, the following sequence of events will occur in order:
- A package with a value of
Vi
dollars will get delivered to the mail room (unlessVi = 0
, in which case no package will get delivered). - You can choose to pay
C
dollars to enter the mail room and collect all of the packages there (removing them from the room), and then leave the room. - With probability
S
, all packages currently in the mail room will get stolen (and therefore removed from the room).
Note that you're aware of the delivery schedule V1..N
, but can only observe the state of the mail room when you choose to enter it, meaning that you won't immediately be aware of whether or not packages were stolen at the end of any given day.