A shipper on the river Rhine owns a barge of carrying capacity 1500 m3 . Over time he has specialized in the transport of wheat. He has seven regular customers who load and unload practically at the same places. The shipper knows his costs of transport from long experience and according to his personal preferences has concluded agreements with his clients for the price charged to them for the transport of their wheat.

The objective of the shipper is to maximize his profit from transporting the wheat with lots that may be divided.

Question 1: As a first step, assuming that every client has an unlimited quantity of wheat, which clients wheat should be transported?

Question 2: If in addition the actual availability of wheat lots from the customers is taken into account, which strategy should the shipper adopt?

Question 3: What happens if the lots cannot be divided?

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Table 9.3: Lots to transport Table 9.3: Lots to transport