1 The Company NMSports is a retailer that offers sport clothes and equipment. The store of NMSports is located in the capital city of the country. The offer of NMSport can be categorized into two groups: (i) families, whose main interest is the sport clothes; and (ii) schools and sport clubs, interested in equipment. With the aim of having stocks for the next months, NMSports should place an order to its supplier at the end of January 2023. Such planning became a challenge because the situation of one of the suppliers: KPVara ATH. 2 The Supplier KPVara ATH. manufactures soccer kits and equipment. KPVara ATH. do not sell directly to final customers. Instead of that, KPVara ATH. offers products to different retailers, which sell the products to the final customers. NMSports is one of these retailers. In 2018, KPVara ATH. became the official brand of the Soccer National Team, a.k.a the Eagles. Moreover, KPVara ATH. has been the official provider of balls for the National Soccer League (NSL). The Eagles' t-shirt and the NSL balls constitute the two main products offered by KPVara ATH. Even though KPVara ATH. has been successful in selling their main products during 2018-2022, the Eagles and the NSL decided to switch sponsor. Thus, since February 2023, WINGS Football will be the official brand of the Eagles and the NSL. In other words, from February 1st February of 2023, KPVara ATH. cannot offer its licensed products anymore. Nevertheless, a last business opportunity arises for KPVara ATH. In December 2022, the Eagles reached the final of a prestigious international tournament, so KPVara ATH. will launch to the market special editions of the Eagles's t-shirt and the NSL ball. KPVara ATH. will launch this line under the name of Champions. 2 3 Champions Editions The Champions edition will be offered to final customers with the following prices. Note that, KPVara ATH. decided these prices and retailers cannot change them. Item Price Eagles t-shirt $ 75 NSL Ball $ 32 Further, KPVara ATH. and NMSport reached an agreement about the wholesale price that KPVara ATH. will charge per unit (see table below). Item Wholesale Price Eagles t-shirt $ 55 NSL Ball $ 15 As the license of KPVara ATH. will expire in August 2022, this firm offers to its direct customers (retailers) to reimburse the unsold units at such date. Thus, NMSport can send back the unsold t-shirts and balls; afterward, KPVara ATH. will return 15 % and 25 % of the wholesale price, respectively. In terms of the expected demand, the demand manager of KPVara ATH. and representatives of the retailers project that the demand for both the Eagles t-shirts and the NSL balls for July 2022 will follow the same pattern that their historical monthly demands. This is explained by the balance between the increase of the expected sells due to the current success of the Eagles, and the decrease of the demand due to the incoming expiration of the license. 4 NMSports Demand The Demand Manager of NMSport aims to forecast the demand of the Champions edition under the basis of the regular monthly demand. The file Data.xlsx contains the historical demand for licensed products. In this file, the demand for balls is 3 expressed in packs of 10 balls, because the main buyers of this product are schools and clubs, that prefer to buy in larger volumes. 5 The Challenge The challenge for NMSports is to determine the amount of t-shirts and balls that should be ordered for January 2023. The goal is to get a balance between meeting the demand and the cost of buying too many units that may be unsold. 6 Discussion 1. Could you shed some lights about the probability distribution of the demand faced by NMSport. Provide quantitative evidence and if possible, assoviate a well-known probability distribution function to the demands of t-shirt and balls. (5 points) 2. How many Eagles t-shirt NMSport should be ordered? How many NLS balls? Hint: determine the order sizes that maximizes the profits of NMSport. (5 points) (5 points) 3. NMSport would like to have an estimation of the profits tat can be obtained through the order policies derived in the previous questions. Provide an estimation of such value for the case of t-shirts? (5 points) 4. At the beginning of January 2023, NMSport faced a demand for 71 t-shirts. Compute the profit obtained in January and compare it with the results of the previous question. How could you explain the results? What could you propose to the firm? (5 points)