In a textile plant, cloth is manufactured in rolls of length L. Defects sometimes occur along the length of the cloth. Consider a specific roll with (N − 1) defects appearing at distances y1, y2, . . . , yN−1 from the start of the roll (yi+1 > yi for all i). Denote the start of the roll by y0, the end by yN .
The roll is cut into pieces for sale. The value of a piece depends on its length and the number of defects. Let
Assume that all cuts are made through defects and that such cutting removes the defect
Specify how to determine where to cut the cloth to maximize total value.
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