Four types of items are under consideration for loading on a plane, with an unlimited supply of each type. The weights and values of various types of items are given below:

Determine as to which items should be loaded on the plane, and in what quantities, if the maximum capacity of the plane is 13 tons and the objective is to maximise the value of the shipment. Give a mathematical representation of the problem and solve it by dynamic programming.

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Item Weight (tons) Value A 3 22 B 6 44 5 35 D 4 24