The company produces lettuces at three plants, which are delivered to two customers via two warehouses....

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The company produces lettuces at three plants, which are delivered to two customers via two warehouses. Shipments between plants are allowed after the packaging has been completed. This also applies to between the warehouses and between the customers. The cost of producing the lettuces at each plant is different. As a result, the company is concerned with both production and shipping costs while meeting customer demands. The production capacity of each plant (in tonnes per year), the product cost at each plant (in dollars per tonnes), and the customer demand (in tonnes per year) are summarised in the table below: Plant Capacity Plant 1 340 Cost $950 Plant 2 300 $900 Plant 3 400 $960 Customer Customer 1 Demand 560 Customer 2 370 The cost (in thousands of dollars) of shipping a tonne of the product between each pair of locations is listed in the table below where a blank indicates that the company cannot ship on that route: From node To node Plant 1 Plant 1 Plant 2 1 Plant 3 Warehouse 1 Warehouse 2 Customer 1 Customer 2 Plant 2 1 1 1 4 5 3 4 Plant 3 1 1 5 3 Warehouse 1 2 6 7 Warehouse 2 2 8 5 Customer 1 2 Customer 2 2 The management has set the maximum flow for each route to be 250 tonnes. Since sometimes the demands are fluctuated, the company plans to have safety stock of 15 and 20 tonnes at Warehouses 1 and 2 respectively. Based on the information above, the management wants you to design a network flow solution for their strategic plan to minimise the total costs that can meet the demands. Any change in the current scenario (e.g. plant capacities or route capacities) can be proposed if it is reasonable and based on the evidence that you find. The company produces lettuces at three plants, which are delivered to two customers via two warehouses. Shipments between plants are allowed after the packaging has been completed. This also applies to between the warehouses and between the customers. The cost of producing the lettuces at each plant is different. As a result, the company is concerned with both production and shipping costs while meeting customer demands. The production capacity of each plant (in tonnes per year), the product cost at each plant (in dollars per tonnes), and the customer demand (in tonnes per year) are summarised in the table below: Plant Capacity Plant 1 340 Cost $950 Plant 2 300 $900 Plant 3 400 $960 Customer Customer 1 Demand 560 Customer 2 370 The cost (in thousands of dollars) of shipping a tonne of the product between each pair of locations is listed in the table below where a blank indicates that the company cannot ship on that route: From node To node Plant 1 Plant 1 Plant 2 1 Plant 3 Warehouse 1 Warehouse 2 Customer 1 Customer 2 Plant 2 1 1 1 4 5 3 4 Plant 3 1 1 5 3 Warehouse 1 2 6 7 Warehouse 2 2 8 5 Customer 1 2 Customer 2 2 The management has set the maximum flow for each route to be 250 tonnes. Since sometimes the demands are fluctuated, the company plans to have safety stock of 15 and 20 tonnes at Warehouses 1 and 2 respectively. Based on the information above, the management wants you to design a network flow solution for their strategic plan to minimise the total costs that can meet the demands. Any change in the current scenario (e.g. plant capacities or route capacities) can be proposed if it is reasonable and based on the evidence that you find.