Question 4 Cocoa in Ghana is grown in farms mainly in Obuasi, Sunyani and Wenchi. Awuku Chocolate Company contracts cocoa farmers in Obuasi, Sunyani and Wenchi to grow cocoa seeds for the company. The cocoa beans are then shipped to factories along the sea in Accra, Takoradi and Cape Coast to be processed into cocoa butter and chocolates, which are then transported to three warehouses in Kumasi, Tema and Tamale. The transport cost per bag from the farms to the factories and from the factories to the warehouses, and the supply at the farms and demand at the warehouses are summarized below: FACTORY FARM 4. Accra 5. Takoradi 6. Cape Coast Supply (1000 bags) 1. Obuasi GH 420 390 610 55 2. Sunyani 510 590 470 78 3. Wenchi 450 360 37 WAREHOUSE FACTORY 7. Kumasi 8. Tema 9. Tamale 4. Accra 75 63 81 5. Takoradi 125 110 95 6. Cape 68 82 95 Demand 60 45 50 (1000 bags) a) Create a network model for Awuku Chocolate Company CR (10 marks) b) Formulate a linear programming model to determine the optimal shipments from farms to factories and warehouses to minimize total transportation costs. AN (10 marks) c) Is the transhipment a balanced model? Give reason for your answer EV (5 marks) 480 Question 4 Cocoa in Ghana is grown in farms mainly in Obuasi, Sunyani and Wenchi. Awuku Chocolate Company contracts cocoa farmers in Obuasi, Sunyani and Wenchi to grow cocoa seeds for the company. The cocoa beans are then shipped to factories along the sea in Accra, Takoradi and Cape Coast to be processed into cocoa butter and chocolates, which are then transported to three warehouses in Kumasi, Tema and Tamale. The transport cost per bag from the farms to the factories and from the factories to the warehouses, and the supply at the farms and demand at the warehouses are summarized below: FACTORY FARM 4. Accra 5. Takoradi 6. Cape Coast Supply (1000 bags) 1. Obuasi GH 420 390 610 55 2. Sunyani 510 590 470 78 3. Wenchi 450 360 37 WAREHOUSE FACTORY 7. Kumasi 8. Tema 9. Tamale 4. Accra 75 63 81 5. Takoradi 125 110 95 6. Cape 68 82 95 Demand 60 45 50 (1000 bags) a) Create a network model for Awuku Chocolate Company CR (10 marks) b) Formulate a linear programming model to determine the optimal shipments from farms to factories and warehouses to minimize total transportation costs. AN (10 marks) c) Is the transhipment a balanced model? Give reason for your answer EV (5 marks) 480