Q3. (30 pts) A cafe orders Kombucha tea from a supplier every Monday morning. Once they decide on the amount of Kombucha tea to be ordered on Monday morning, they cannot give any additional orders during the week as their order policy. Kombucha tea is sold in cases and a case contains 20 bottles. It costs the cafe tA to order each bottle, and each bottle is sold for tB. The weekly demand for Kombucha tea (in cases) a random variable described by the following table: Weekly demand (in cases) 2 4 6 8 10 Probability 0.30 0.25 0.20 0.15 0.10 a) (4 points) Find the overage cost and shortage cost for a case of Kombucha tea. b) (4 points) Based on the given empirical probability distribution, how many cases of Kombucha tea should be ordered? c) (5 points) Based on the given empirical probability distribution, compute the expected number of cases sold in a week according to the order size that you obtained in part b). d) (5 points) Based on the given empirical probability distribution, compute the expected weekly revenue according to the order size that you obtained in part b). e) (5 points) Based on the given empirical probability distribution, compute the expected weekly profit according to the order size that you obtained in part b). f) (4 points) If the weekly demand in cases of Kombucha tea is normally distributed with mean u and standard deviation o, how many cases should be ordered? g) (3 points) If the weekly demand in cases of Kombucha tea follows continuous uniform distribution with lower and upper bounds [K, L], how many cases should be ordered? 4 B 12 6 S 2 K 3 3 IL 11