Question
Parts have already been partially processed before they reach a certain shop. When a part enters the shop, the company has already spent $10,000 for
Parts have already been partially processed before they reach a certain shop. When a part enters the shop, the company has already spent $10,000 for both raw material and previous processing. More processing is required before they can be sold or assembled onto a final product. In that shop, machine takes one minute to do an operation. It costs $500 to do that operation. The machine is always operational, but it has a probability 0.1 of creating a defective part. In other words, a part that is operated on by M has probability 0.1 of being unacceptable and probability 1-0.1 of being acceptable. If the operation on it is good, the cost-based value of the part is $10,000+$500. That is, its value has increased by $500. If the operation is bad, the part must be scrapped and its market value is 0. (In that case, the company has lost $10,500 since it the money spent on the operation was lost.)Now suppose that the part must undergo two operations, first at machine M1 and then at machine M2. Both operations take one minute and both have a probability 0.1 of causing a defect. If both operations are successful, the value of the part is $10,000+2($500). If either operation is bad the value of the part is 0.The situation is the same as in the previous section of the question except that now there is inspection of parts after they receive operations at M1. Assume that the inspection is perfect; that is, the inspection rejects every part that received a bad operation (10%) at M1 and it accepts every part that gets a good operation (90%). Assume also that the inspection time is 0 and ignore the cost of inspection.What is the expected value of a part when it leaves the shop?What is the expected increase of a part's value due to both operations?What is the production rate of good parts?Now we consider the costs involved in Part 3. The cost of doing an inspection at M1 is $200. (Consider this cost as separate from $500.) What is the expected cost is incurred at M1 per operation?
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