Q2) Distribution Network Design (20 points) A firm has two plants, A and B, located at two different places. Both plants produce products to satisfy demands at three markets, 1, 2, and 3. Refer to Figure 1 for the supply chain network. The demands at the three markets 1,2 , and 3 are 250, 240, and 230. The retail prices of each unit of product at markets 1,2 , and 3 are $8,$9, and $10. The production capacity at plants A and B are 300 and 320 . The cost of producing and shipping one unit of product from the plant to the market are given in Table 2. Now the firm has an opportunity to open a new plant C in the system with a potential fixed cost $40. The production and transportation cost per unit of product from plant C (if plant C exists) are also given in table 2. The capacity of plant C is 200 . The firm aims to decide on whether to open plant C, and the corresponding optimal production and transportation plan to maximize the net profit. You need to help the manager to find out the optimal strategy. Ensure that you clearly show the analysis process. You only need to show the conceptual model and NO need to use solver to solve the optimal solution