A seamstress works exclusively on one stage of the process of a special garment design. This phase requires exactly half an hour to finish the garment. Every 30 minutes an assistant arrives at the seamstress's table to collect those finished garments and deliver those that require the process (unprocessed garments). The number of raw garments brought by the assistant to the seamstress is uncertain; 30% of the occasions arrive without garments; 50% of the time he wears one garment and 20% of the time he wears 2 garments. The assistant is instructed that there are never more than three unprocessed garments left on the seamstress's table (those that cannot be left are taken to another seamstress). Determine the transition graph and matrix that models the number of raw garments on the seamstress's table just before the assistant arrives.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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A seamstress works exclusively on one stage of the process of a special garment design. This phase requires exactly half an hour to finish the garment. Every 30 minutes an assistant arrives at the seamstress's table to collect those finished garments and deliver those that require the process (unprocessed garments).
The number of raw garments brought by the assistant to the seamstress is uncertain; 30% of the occasions arrive without garments; 50% of the time he wears one garment and 20% of the time he wears 2 garments. The assistant is instructed that there are never more than three unprocessed garments left on the seamstress's table (those that cannot be left are taken to another seamstress).

Determine the transition graph and matrix that models the number of raw garments on the seamstress's table just before the assistant arrives.

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