Exhibit A. The ABC Company operates 5 plants and 3 distribution centers, all in different cities. Following table lists the unit shipping costs for its supply network of a major product. The annual demand at the distribution centers are as follows. The annual capacity and annual fixed cost at plants are as follows. Currently, the plants produce multiple products and the fixed cost assigned to the major product is $600,000 per year for all five plants together. Since the company has decided to stop other product lines next year and therefore is also planning to consolidate its production to fewer plants. Starting next year, if a plant is used to produce the major product, the annual fixed cost would be as given in the last row of the table. There is no fixed cost if the plant is not used. Overall, the company wants find out what plants to operate to minimize the total relevant costs (fixed cost plus shipping costs). A-1. Formulate the problem to find the optimal shipping plan for this year. What is the minimum total cost? Is there any capacity that is not used? If so, how many units and where? How many units are shipped from each plant to distribution center 1? A-2. Formulate the problem to find the optimal shipping plan for next year. What is the minimum total cost? Which plants are to be closed? A-3. For next year, Plant A and Plant E cannot be both used as they are very close. Solve the problem. How would the optimal solution change? The total cost? A-4. Answer independently from A-3. The capacity of Plant D can increase by up to 10,000 units at the (additional) cost of $1 per unit. Formulate the problem to find the optimal shipping plan for next year. What is the minimum total cost? Compare the cost with that of A-2