Wheat is harvested in the Midwest and stored in grain elevators in three different cities ...

 

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Wheat is harvested in the Midwest and stored in grain elevators in three different cities – Kansas City, Omaha, and Des Moines. These grain elevators supply three flour mills, located in Chicago, St.Louis, and Cincinnati. Grain is shipped to the mills in railroad cars, each car capable of holding one ton of wheat. Each grain elevator can supply the number of tons (i.e., railroad cars) of wheat to the mills on a monthly basis. Grain Elevator Supply 1. Kansas City 2. Omaha 150 175 3. Des Moines 275 Total 600 tons Each mill demands the following number of tons of wheat per month. Mill Demand A. Chicago B. St. Louis 200 100 C. Cincinnati 300 Total 600 tons The cost of transporting one ton of wheat from each gain elevator (source) to each mill (destination) differs according to the distance and rail system. These costs are shown in the following table. Mill Grain Elevator A. Chicago B. St. Louis C. Cincinnati 1. Kansas City $6 $ 8 $10 2. Omaha 7 11 11 3. Des Moines 4 5 12 The problem is to determine how many tons of wheat to transport from each grain elevator to each mill on a monthly basis in order to minimize the total cost of transportation. Address the following questions: (a) Formulate a balanced transportation problem to minimize the transportation costs – specify the LP and corresponding transportation tableau (10 points). (b) Use the minimum-cost method to determine an initial basic feasible solution (BFS) for this problem (10 points). Wheat is harvested in the Midwest and stored in grain elevators in three different cities – Kansas City, Omaha, and Des Moines. These grain elevators supply three flour mills, located in Chicago, St.Louis, and Cincinnati. Grain is shipped to the mills in railroad cars, each car capable of holding one ton of wheat. Each grain elevator can supply the number of tons (i.e., railroad cars) of wheat to the mills on a monthly basis. Grain Elevator Supply 1. Kansas City 2. Omaha 150 175 3. Des Moines 275 Total 600 tons Each mill demands the following number of tons of wheat per month. Mill Demand A. Chicago B. St. Louis 200 100 C. Cincinnati 300 Total 600 tons The cost of transporting one ton of wheat from each gain elevator (source) to each mill (destination) differs according to the distance and rail system. These costs are shown in the following table. Mill Grain Elevator A. Chicago B. St. Louis C. Cincinnati 1. Kansas City $6 $ 8 $10 2. Omaha 7 11 11 3. Des Moines 4 5 12 The problem is to determine how many tons of wheat to transport from each grain elevator to each mill on a monthly basis in order to minimize the total cost of transportation. Address the following questions: (a) Formulate a balanced transportation problem to minimize the transportation costs – specify the LP and corresponding transportation tableau (10 points). (b) Use the minimum-cost method to determine an initial basic feasible solution (BFS) for this problem (10 points).