Zola Gastons family business involved machining of standard and custom steel parts for a wide variety of customers. One of the parts produced (SKU #1284) had a long history of experiencing defects during production. After graduation from Ryerson Universitys Mechanical and Industrial Engineering program, Zola was tasked with studying the production process for part #1284. Although the process was fairly automated, Zola observed that the machine could undergo an adjustment by a skilled tradesperson but at a cost of $6.00 for a given batch of three. The adjustment resulted in zero defects in that batch.

Zola examined historical data and concluded that without adjustment, the probabilities of 0, 1, 2, and 3 defects in each batch of three parts produced was 40%, 30%, 20%, and 10% respectively. Normally, parts sell for $10.00 each and cost $5.00 each to produce. However, parts that are defective must be sold as scrap for $5.00 per piece, or reprocessed at a cost of $6.00, $10.00, or $12.00 for a bundling of 1, 2, or 3 defective items. Note that defects in a given batch must be either all sold as scrap, or all reprocessed as a bundle (eg, if there are 3 defects in a given batch, then all 3 must be scrapped or all 3 reprocessed).

(a) Drawadecisiontreeanddeterminetheoptimalstrategy.(16marks)