How to find where to cut the cloth to maximize total value

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Reference no: EM131162715

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, . . . , y_N-1 from the start of the roll (y_i+1 > y_i 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

v(x, m) = Value of a piece of length x having m defects.

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.

Reference no: EM131162715

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