QUESTION1) Determine the number of bikes to be transferred among the stations during a day. Your solution should be a schedule where for each hour of operation and for each station there will be the expected number of bikes transferred-out or transferred-in (the values could be zero if there is no need to transfer) reducing the likelihood of shortage or surplus. In the current system, there are 400 bikes, 48 stations and 851 slots in the bike racks among all stations. You will see a more detailed list in the project file. Assumptions: (If necessary, make additional assumptions as long as you declare them explicitly in your report). Your analysis should cover a timeline from 5:00 am to 23:59 pm (regardless of the day of the week). Assume that in the beginning of each day you distribute the bikes to all stations, so that the initial state of the system is the same every day (you should also determine this bike allocation). This will make each day independent from the previous days, and hence you only need to focus on operations of a single day. Assume that the customer arrival and departure at each station follow an independent non- homogeneous Poisson process with rates changing each hour. Let Ish, and Osh be independent random variables, denoting the number of incoming bikes to and outgoing bikes from each station s and each hour h. More formally, Ish~Poisson (Ash) and Osh~Poisson (AshO), where AshI and sho are the rates of incoming and outgoing bikes to station s at hour h. The rates must be "bikes / hour". Assume that your review period is 1 hour. This means you can ignore shortage or surplus of bikes in any station within the review period. You can focus only on the amount of bikes at the end of each hour. You may think, for example, that if customer A arrives to borrow a bike and there is no available bike in the station, customer A may wait until somebody (say customer B) returns a bike at that station as long as this wait of customer A does not extend to the next hour. Otherwise, there is a shortage of bikes at that station. Similarly, if customer C arrives to a station and could not find an empty slot to return a bike, she will wait until another customer arrives to borrow a bike from that station as long as the wait of customer C does not extend to the next hour. Otherwise, there is a surplus at that station. If a bike is set to be transferred from a station to another station, this bike will be available to use the hour after the next hour the destination station. For example, if a bike is transferred from "Exchange Place" station at the end of 1 pm to "Hamilton Park" station, it will be ready there in the beginning of 3 pm. No transfer-outs are performed after 10 pm. No transfer-ins are performed before 7 am. Costs: When there is a shortage (no bike remains) at the end of the hour, then this costs $10(1 + sh 0) for each stations and hour h. When there is a surplus (no empty space to dock a bike i.e., the station is full) at the end of the hour, then this costs $8(1 + sh L) for each station s and hour h. There is a fixed cost of $10 per each bike transferred. You may ignore the variable cost of transferring. You may assume that the initial distribution of bikes in the beginning of each day comes without any cost.