1. Case: "Ee sala cup namde" Hopefully... (Marks 05) The next season of the Indian Premier League (IPL-2022) is expected to start in April 2022. The past seasons have not been very good for Royal Challengers Bangalore (RCB), the home team of Karnataka. Though RCB has always been a star-studded team with world class players like Chris Gayle, A.B. De Villiers, and Virat Kohli, the team has never made into the finals in since 2016. Puma is the official merchandise supplier for all RCB apparels for the forthcoming season. A typical RCB jersey-is priced at Rs 1800 at the Puma Retail stores. Mr Srinivas Pai, the owner of Puma franchisee showroom at Manipal is worried about ordering the optimal quantity of the jerseys at his store for the upcoming IPL season. Puma will supply jerseys to the franchisees at Rs 1200 per unit. Owing to the past performance of the RCB team, Srinivas is not sure if it still has the same fan following amongst the 20000 odd student community in Manipal. What adds to his worries is that, once, the IPL season is over, the demand drops to almost zero and the unsold t- shirts will have to be sold at a clearance price of Rs. 500 per unit (undergoing a loss of Rs. 700 per piece). The following table shows the probability of the various sales quantities. What is the optimal order quantity that Srinivas should place on the RCB Jersey? 100 200 Quantity 300 400 500 600 0.05 Probability 0.05 0.11 0.34 0.30 0.15 (Note: The characters in this case are purely fictitious, and any resemblance to living or dead is purely coincidental.)