The Worldwide Textile Company, is a Hong Kong-based firm that distributes textiles worldwide. Present plans are to remain in Hong Kong through the transition in governments. Should the People's Republic of China continue its economic renaissance, the company hopes to use its current base to expand operations to the mainland. Worldwide Textile has mills in the Bahamas, Hong Kong, Korea, Nigeria, and Venezuela, each weaving fabrics out of two or more raw fibers: cotton, polyester, and/or silk. The mills service eight company distribution centers located near the customers' geographical centers of activity. Because transportation costs historically have been less than 10% of total expenses, management has paid little attention to extracting savings through judicious routing of shipments. The manager believes that each year he can save Worldwide Textile hundreds of thousands of dollars just by better routing of fabrics from mills to distribution centers. One glaring example of poor routing is the current assignment of fabric output to the Mexico City distribution center from Nigeria instead of from Venezuela, less than a third the distance. Similarly, the Manila center now gets most of its textiles from Nigeria and Venezuela, although the mills in Hong Kong itself are much closer. Of course, the cost of shipping a bolt of cloth does not depend on distance alone. Table (1) provides the actual costs supplied to the manager from company headquarters. Distribution center demands are seasonal, so a new shipment plan must be made each month. Table (2) provides the fabric requirements for the month of March. Worldwide Textile's mills have varying capacities for producing the various types of cloth. Table (3) provides the quantities that apply during March. Table (1): Shipping Cost Data (dollars/bolt) Distribution Center Mexico City Manila MIN Los Angeles Chicago London Rome Tokyo New York - 1 4 9 10 Bahamas Hong Kong Karta Nigeria Venez 6 1 5 7 7 10 4 Table (2): Fabric Demands for March (Bolts) Distribution Center Mexico City Manila Fabric Chicago London Rome Tokyo New York Cotton Polyester Suk Los Angeles 500 1.000 100 800 2.000 100 900 3.000 200 900 1,500 SO 800 400 400 100 700 200 200 900 700 700 2.500 200 Table (3): March Production Capacities (Bolts) Production Capacity Cotton Polyester Mill SILK 3,000 2.500 Bahamas Hong Kong Korea Nigeria Venezuela 1,000 2,000 1.000 2.000 1,000 0 1.000 500 3,500 0 2,000 The manager wants to schedule production and shipment in such a way that the most costly customers are shorted when there is insufficient capacity, and the least-efficient plants operate at less than full capacity when demand falls below maximum production capacity. 1. Find the optimal March shipment schedule and its total transportation cost for each of the following: a. Cotton b. Polyester cloth C. Silk 2. The company will be opening a silk-making department in the Nigeria mill. Although it will not be completed for several months, a current capacity of 1,000 bolts for that fabric might be during March for an added one-time cost of $2,000. Find the new optimal shipment schedule and the total cost for that fabric. Should the Nigeria mill process silk in March