You are the operations manager of the Company ABC that produces apple juice. Apples are harvested in the region by local farmers. Bulk trucks carrying process apples arrive at your plant randomly throughout the day. On average, about 10 trucks arrive per hour to your plant, each truck with a total of 100 tons of apples. That is, about 1000 tons of apples arrive to your plant per hour. In a high-season day, trucks with apples arrive to your plant from 7am to 7pm. In a low-season day, trucks with apples only arrive to you plant from 7am to 2pm. Once the trucks arrive to your plant, they dump the apples into one of the 3 conveyor belts. Each conveyor belt can move a total of 800 tons of apples per hour. If the farmer arrives to the plant and the conveyor belts are in used by other farmers, the farmer will have to wait in a parking lot until one of the conveyor belts is released. The conveyor belts move the apples into one of the 10 temporary holding bins. Each bin can store 320 tons of apples. Then, from those bins, apples are moved into the production process. The production process consists of 5 steps: 1. Washing: Apples are thoroughly washed to remove any dirt or debris. The plant has 3 washing machines, each of them can wash a total of 600 tons of apples per hour. 2. Milling: Apples are then chopped and ground into pulp. The plant has 4 milling machines, each of them can process a total of 500 tons of apple per hour. 3. Pressing and clarification: Pulp is then pressed to extract the juice, and the juice is clarified to remove any solids. The pressing and clarification process is conducted in the XP Machines. You have a total of 2 XP machines, each of which can process a total of 300 tons of pulp per hour. After the pressing and clarification process, 50% of the pulp becomes solids and 50% clarified juice. The solids are separated from the process and used to produce other products for the company. Therefore, solids are not longer part of the juice production process. The clarified juice in moved to step 4 in the process. 4. Pasteurization: The clarified juice is heated to a high temperature to kill any bacteria or other harmful microorganisms. The juice is heated in some heat exchangers. The plant has 3 heat exchangers, each of them can process a total of 150 tons of apple juice per hour. 5. Bottling: The pasteurized juice is then packed and bottled in a sterile environment. The plant has a bottling machine that can bottle a total of 500 tons of apple juice per hour. You have two shifts in your plant. The first shift of workers at you plant starts operations at 7am and the workers of the last shift get to go home once they can process all apples that arrived at the plant that day. When it is necessary to work beyond 11pm, a crew of only 8 people is required to run the operations, and you pay each of them an average of $18 per hour. Trucks arriving Demand = Parking Lot C=ConveyorbeltsU= Washing C= U=
