a) The demand for Yulu bikes is 15/day. There are only 5 bikes allocated to your zone. Customers take the bike from a zone and return it back to the same zone with an average usage time of 6 hours. Assume that the system operates 24 hours a day. You would like to take a Yulu ride. What is the probability that on visit, you do not find any bikes available at your Yulu zone? b) Now assume that the customers rent Yulu bike at the beginning of the day at 10am and returns them at the end of the day, which is 6pm. The bikes are repositioned to the zones at the beginning of the day. Further, Yulu staff maintains the battery and the bike at the beginning of each day. It costs Yulu about Rs. 100 to maintain and operate each bike at a zone per day. Bikes do not fail during its operation. Assume that Yulu charges the customer Rs. 10 to unlock a bike and Rs. 10 for every 10 minutes of usage. The distribution of bike demand at the beginning of the day is given in the following table. 9 Demand (D) P(D=d) 121 0.2 15 0.18 18 0.22 21 0.1 24 0.1 0.2 How many bikes should Yulu stock at your zone to maximize its expected zonal profit? What is the value of maximum expected zonal profits? c) Assume that some bikes malfunction and fail to unlock during customer pickup with a probability of 20%. Now, how many bikes should Yulu stock at your zone to maximize its expected zonal profit? a) The demand for Yulu bikes is 15/day. There are only 5 bikes allocated to your zone. Customers take the bike from a zone and return it back to the same zone with an average usage time of 6 hours. Assume that the system operates 24 hours a day. You would like to take a Yulu ride. What is the probability that on visit, you do not find any bikes available at your Yulu zone? b) Now assume that the customers rent Yulu bike at the beginning of the day at 10am and returns them at the end of the day, which is 6pm. The bikes are repositioned to the zones at the beginning of the day. Further, Yulu staff maintains the battery and the bike at the beginning of each day. It costs Yulu about Rs. 100 to maintain and operate each bike at a zone per day. Bikes do not fail during its operation. Assume that Yulu charges the customer Rs. 10 to unlock a bike and Rs. 10 for every 10 minutes of usage. The distribution of bike demand at the beginning of the day is given in the following table. 9 Demand (D) P(D=d) 121 0.2 15 0.18 18 0.22 21 0.1 24 0.1 0.2 How many bikes should Yulu stock at your zone to maximize its expected zonal profit? What is the value of maximum expected zonal profits? c) Assume that some bikes malfunction and fail to unlock during customer pickup with a probability of 20%. Now, how many bikes should Yulu stock at your zone to maximize its expected zonal profit