Rent-2-Suit, a small rental car agency in Oak Hill, Florida, has 5 cars available to rent during the busy tourist season. Larry Maytown, the owner/operator of Rent-2-Suit also operates a charter fishing business and since he spends his day out on his boat, Rent-2-Suit is only open to rent cars out in the early morning and only accepts returns in the late afternoon. Larry does not accept reservations and rents cars on a firstcome-first-served basis. Larry charges $50/day to rent one of his cars. Part of his marketing strategy is to not require clients to specify ahead of time when they will return the car. Based on historical data, Rent2-Suit has found that the probability that a client will return a car at the end of day is 0.5 independent of how long the client has had the car already. A person renting a car this morning may return this afternoon (and pay $50 for the rental), or the next afternoon (and pay $100 for the rental), or the one after that, etc. Daily demand to rent cars, D, has the following mass function. PD (d) = 0.2 d = 0
0.2 d = 1
0.3 d = 2
0.2 d = 3
0.1 d = 4
Given the questions below, specify a discrete-time Markov model of this business. Your model must include the following: state definition, list of system events, and the one-step state transition matrix (P matrix).1. What is the expected number of rented cars at the end of a day?2. What is Larry’s expected daily income?3. A customer calls in on Thursday just as Larry opens for the day and wants to know the chances a car will be available to rent first thing on Saturday morning. What is the probability of this?