[Q3: Newsvendor] Raman starts a car rental store. Being environmentally friendly, he stocks only hybrid cars. He charges $60/ day for each rental. When a customer comes to rent the car, she states the duration of the rental and pays $60/ dey for this duration upfront. If she returns the car after the deadline, Raman charges a penalty of $100/ day for each day in excess of the deadline. Raman cuts a deal with a distant Auto dealership who is willing to rent him cars at $20/ day. This dealership is about 50 miles away, so each morning before Raman opens his store, he decides how many cars he needs that day and passes the order to the dealership, who deliver the cars before store opening. At the end of the day, all cars remaining in the store are returned to the dealership. a) Raman notes that all his customers seem to rent cars only for 1 day at a time and are never late and the daily demand has the following probability distribution. How many cars should Raman order each morning to maximize his profits? b) Suppose you want to rent a hybrid car from Raman. You believe your requirement for the car to be Normally distributed with a mean of days and a standard deviation of days. Suppose you contract for a rental duration that ensures the lowest expected payment to Raman. What is the probability you return the car late, l.e., have to pay the penalty