Cutting cloth. You are given a rectangular piece of cloth with dimensions X × Y, where X and Y are positive integers, and a list of n products that can be made using the cloth. For each product i ∈ [1, n] you know that a rectangle of cloth of dimensions ai × bi is needed and that the final selling price of the product is ci. Assume the ai, bi, and ci are all positive integers. You have a machine that can cut any rectangular piece of cloth into two pieces either horizontally or vertically. Design an algorithm that determines the best return on the X × Y piece of cloth, that is, a strategy for cutting the cloth so that the products made from the resulting pieces give the maximum sum of selling prices. You are free to make as many copies of a given product as you wish, or none if desired.
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