Once a day (weather permitting) a ferry transports cars from Island A to Island B. The ferry can carry up to 4 cars at a time. The number of cars, Y, that come to the port to be transported to Island B has the following mass function. {0.2 y = 0
Py(y) = 0.4 y = 1
0.4 y = 2
If a car arrives and finds 4 other cars already waiting, then it will leave and return some other day. The return of cars from Island B back to Island A is not of interest. The weather in this area can be so bad that the ferry cannot make its trip. Assume this happens 50% of the time. When this happens, any cars that are waiting for the ferry trip will continue to wait. Also, any day there are no cars waiting to go to Island B, the ferry does not leave.
a. Assume you want to be able to answer the questions below. Build a Markov model of this process. Specifically do the following: define the states of the system, define the time period between observations of the state, a list of the events that can occur that affect the next state of the system and the P matrix.
b. What is the expected number of cars on the ferry when it makes a trip to Island B?
c. What is the probability the ferry does not make the trip on a given day?
d. If each car is charged $25 for the trip and it costs $75 in fuel for the ferry, what is the expected revenue/day for the ferry?