The company produces a potato product at three plants, which can be delivered directly to the two customers or it can first be shipped to the two warehouses and then to the customers. Shipments between plants are allowed. This also applies to between warehouses and between customers.
The cost of producing the potato product is the same at each plant; as a result, the company is only concerned with minimising the total shipping cost incurred in meeting customer demands. The production capacity of each plant (in tons per year) and the customer demand are summarised in the table below:
|Plant 1||150||Customer 1||500|
|Plant 2||250||Customer 2||220|
The cost (in thousands of dollars) of shipping a ton 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 2||Plant 3||Warehouse 1||Warehouse 2||Customer 1||Customer 2|
The road regulation does not allow truck to load more than 200 tons of the product between any two nodes. The company wants to determine a minimum-cost shipping strategy.