Operation Research

Please solve on paper

150 2 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 is able to supply the following number of tons (i.e., railroad cars) of wheat to the mills on a monthly basis. Grain Elevator Supply 1. Kansas City 2. Omaha 175 3. Des Moines 275 Each mills demands the following number of tons of wheat per month. Mill Demand A. Chicago 200 B. St. Louis 100 -C. Cincinnati 300 The cost of transporting one ton of wheat from each grain elevator (source) on each mill (destination) differs according to the distance and rail system. These costs are shown in the following table. For example, the cost of shipping one ton of wheat from the grain elevator at Omaha to the mill at Chicago is $7. 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 trans- portation. A. Is this a balanced transportation problem? Explain B. Formulate a transportation problem in a tableau form. C. Use the NW corner method to find an initial bfs. D. Find the optimal solution to this problem, using the transportation simplex algorithm