please answer questions 4-6

Case: Titan Electric Company The Titan Electric Company (TEC) manufactures and distributes electronic transformers used to distribute electric power throughout the US. The company started with a small manufacturing plant in Reno and gradually built a customer base throughout the Southwest. A distribution center was established in Denver, and later, as business expanded, their second and third distribution centers were established in Tucson and Sacramento. To date, the company operates two plants, three distribution centers and nine warehouse locations. Manufacturing costs differ between the company's production plants. The cost of each transformer produced at the Reno plant is $1200. The newer Las Vegas plant utilizes more efficient equipment; as a result, manufacturing costs $1050 per transformer. The cost of shipping a transformer from each of the two plants to each of the three distribution centers is shown in Table 1, below. Note that due to lack of Interstate highways, no shipments are allowed from Reno plant to the Tucson distribution center. The annual production capacity is 30,000 transformers at the Reno plant and 20,000 at the Las Vegas plant. Table 1. Shipping Costs to Distribution Centers Distribution Center Plants Sacramento Denver Reno 23.50 38.20 Las Vegas 38.00 Tucson 32.00 33.00 The company serves their nine warehouses from the three distribution centers. The forecast of the number of meters needed in each warehouse for the next quarter is shown in Table 2, below. Table 2. Demand Forecast Warehouse Demand More Hints Albuquerque 6300 Dallas 4900 Transshipment (548.8M) Los Angeles 2100 Objective is for lowest total cost Omaha 1200 (manufacturing and shipping) Phoenix 6100 How much of total cost is shipping? Salt Lake City 4800 Yes, you can arrange the decision variables San Francisco 2800 in tables, similar to the cost data. Seattle 8600 Wichita 4500 The cost per unit of shipping from each distribution center to each warehouse is given in Table 3, below. Note that some distribution centers cannot serve certain warehouses. These are indicated by a dash, Titan is interested in developing manufacturing plans for its plants, and shipping plans for its distribution centers that result in the lowest total costs. Table 3. Shipment Costs to Customer Zones Distribution Center Customer Zone Sacramento Denver Tucson Albuquerque 27.00 27.50 Dallas 30.00 29.00 Los Angeles 24.50 32.00 27.00 Omaha 26.00 32.00 Phoenix 32.55 25.75 18.50 Salt Lake City 31.50 27.50 San Francisco 19.75 47.50 Seattle 28.00 38.80 Wichita 22.00 Assignment Questions 1. With the current supply chain design, how many transformers are produced at each plant and how many are shipped from each distribution center? 2. What is Titan's total manufacturing costs for the year? What is Titan's total distribution costs for the year? 3. How much could Titan save if they could produce more transformers at the Las Vegas plant? How many more transformers could they produce and ensure that the same set of binding constraints remain binding? 4. Which warehouse is the most expensive to stock one additional transformer? 5. Over the next five years, Titan is anticipating moderate growth in demand of 5000 transformers. Would you recommend that Titan consider plant expansion at this time? If so, at which plant and why? 6. Titan is considering a proposal to ship up to 2000 transformers directly from its Las Vegas plant to the Salt Lake City warehouse. The cost of shipping directly is estimated to be $50 per transformer, with no change in manufacturing costs. Under this new plan, what are the new manufacturing and shipping plans? How much would Titan save