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Problem 2: Two echelon problem You have been hired by Faraday Protonic Company (FPC) to serve as their Pellet Transhipment Manager. FPC is a joint public-private energy company dedicated to generating clean and safe nuclear energy. FPC uses a new technology based on radioactive pellets. These pellets can generate electricity for years in FPC's nuclear plants. Once the radioactive pellets are depleted, they are removed from active use and collected at the plants for removal at the end of the month. Once a month, the depleted pellets are removed from the plants, transported to an inspection site for examination, and then moved again to a dedicated storage site for safekeeping. You have been informed that two of FPC's nuclear plants, called Plant One and Plant Two, need to move out depleted pellets in the following amounk: - Plant One wants to ship out up to 280 pellets per month - Plant Two wants to ship out up to 360 pellets per month This is how many pellets these two plants want to ship out per month. However, the exact number of pellets that will actually be moved out from each plant depends on the space that is available at the dedicated storage sites that would ultimately receive them. FPC is mandated by law to move as many pellets out of the plants as the storage sites are able to receive. You have been informed that two of FPC's dedicated storage sites, called Storage X and Storage Y, are ready to receive depleted pellets from FPC's plants, in the following amounts: - Storage X is ready to receive a total of 305 pellets per month - Storage Y is ready to receive a total of 325 pellets per month Since the two plants want to ship out more pellets per month than the two storage sites can receive, you know that some pellets will have to stay in their plant of origin until a later time. This is not a problem, however, since every one of FPC's plants has the capacity to temporarily store whatever pellets are not shipped out, and the law allows this. At this time, only one inspection site is available to receive the pellets from the two plants, inspect them, and send them out to the two storage sites. It is called Inspection Ste A. Notice that inspection sites do not have storage capacity: the pellets come in, are inspected, and continue their trip to the storage sites. Moving radioactive material is not easy and therefore it is not cheap either. There is a lot of planning and security involved. Each shipment of pellets has to be closely monitored and protected to prevent the loss of radioactive material. Also, the vehicles transporting the material have to move relatively slowly, to avoid accidents. Therefore, it is very expensive to transport the radioactive pellets from the plant to the inspection site and from there to the storage site. Based on estimates and historical data, FPC has calculated the following transportation costs, in dollars per pellet moved: - It costs 13.58 dollars to move one pellet from Plant One to Inspection Site A - It costs 16.54 dollars to move one pellet from Plant Two to Inspection Site A - It costs 7.57 dollars to move one pellet from Inspection Site A to Storage X - It costs 16.46 dollars to move one pellet from Inspection Saite A to Storage Y For this problem there is no preliminary Excel Model. You have to make one. 1. You decide to optimize the transshipment of depleted pellets from the plants to the storage sites (stopping on the way at Inspection Site A, of course) in order to minimize the overall monthly transportation cost. In this optimized solution, how many pellets will Plant Two be able to ship out to the Inspection Site A every month? 2. In this optimized solution, how much is the overall monthly transportation cost for FPC? Good news! A second inspection site has become available to receive pellets from the two plants, inspect them, and send them out to the two storage sites. It is called Inspection Site B. To the extent that it is more economical to use this inspection site, it can be used. FPC has calculated the following transportation costs for Inspection Site B, in dollars per pellet moved: - It costs 12.6 dollars to move one pellet from Plant One to Inspection Site B - It costs 16.2 dollars to move one pellet from Plant Two to Inspection Site B - It costs 9.45 dollars to move one pellet from Inspection Site B to Storage X - It coses 15.64 dollars to move one pellet from Inspection Site B to Storage Y 3. As before, you will optimize the transshipment of depleted pellets from the plants to the storage sites, stopping first at the inspection sites, so as to minimize the overall monthly transportation cost. How much will this cost FPC every month