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Linear Programming on a network

OK, goods are transported from both docks m and n to depots a b and c (see attached image). m can handle up to twice as many goods as n and the capacity of each depot is equal. I have the distances between each point and my task is to use linear programming to minimize the total distance traveled.

My problem is I don't know how linear programming can be adapted to this kind of problem with both capacities and distances. Can anyone start me off please?

Moved to Analysis for lack of replies. Please delete.