Case problem 2: Given the same conditions as in problem 1, now the firm faces a different situation: there is a potential location to open a new plant C to satisfy the demands in the two markets. See Figure 2 for more details. The potential capacity of plant C is 110. It will cost the firm $50 to open the new plant. Producing and transportation costs are given in Table 2. Please build a model to find out the optimal decisions on whether to open the new plant C, and the production and transportation plan