3.1 Your company produces breakfast cereal at five different plants. The monthly capacity (in tons) of...

 

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3.1 Your company produces breakfast cereal at five different plants. The monthly capacity (in tons) of each plant is given below. The cereal is stored at one of the three warehouses. The per ton cost of producing cereal at each plant and shipping it to each warehouse is given below. You have four customers. The cost of shipping a ton of cereal from each warehouse to each customer is also given below. Each customer must receive the amount (in tons) of cereal given below. The annual fixed cost of operating each plant and warehouse is also given below. Your goal is to minimize the annual cost of meeting customer demands. Which plants and warehouses should be open, and what is the optimal shipping plan? Capacities (tons) 1 2 3 4 5 Plant 300 200 300 200 400 Customers 1 2 3 4 Requirements (tons) 200 300 150 250 Shipping Costs To Warehouses To Customers 1 2 3 1 2 3 4 Fixed Cost Plant 1 $800 $1000 $1200 $35,000 Plant 2 $700 $500 $700 $45,000 From Plant 3 $800 $600 $500 $40,000 Plant 4 $500 $600 $700 $42,000 Plant 5 $700 $600 $500 $40,000 Warehouse 1 From Warehouse 2 Warehouse 3 1 1 1 $40 $80 $90 $50 $40,000 $70 $40 $60 $80 $30,000 $80 $30 $50 $60 $50,000 3.1 Your company produces breakfast cereal at five different plants. The monthly capacity (in tons) of each plant is given below. The cereal is stored at one of the three warehouses. The per ton cost of producing cereal at each plant and shipping it to each warehouse is given below. You have four customers. The cost of shipping a ton of cereal from each warehouse to each customer is also given below. Each customer must receive the amount (in tons) of cereal given below. The annual fixed cost of operating each plant and warehouse is also given below. Your goal is to minimize the annual cost of meeting customer demands. Which plants and warehouses should be open, and what is the optimal shipping plan? Capacities (tons) 1 2 3 4 5 Plant 300 200 300 200 400 Customers 1 2 3 4 Requirements (tons) 200 300 150 250 Shipping Costs To Warehouses To Customers 1 2 3 1 2 3 4 Fixed Cost Plant 1 $800 $1000 $1200 $35,000 Plant 2 $700 $500 $700 $45,000 From Plant 3 $800 $600 $500 $40,000 Plant 4 $500 $600 $700 $42,000 Plant 5 $700 $600 $500 $40,000 Warehouse 1 From Warehouse 2 Warehouse 3 1 1 1 $40 $80 $90 $50 $40,000 $70 $40 $60 $80 $30,000 $80 $30 $50 $60 $50,000