Dear,

please explain to solve this case.

A manufacturer produces items that have a probability p of being defective. These items are formed into batches of 150. Past experience indicates that some batches are good quality (p=0.05) and others are of bad quality (p=0.25). Furthermore, 30% of batches produced are of good quality and 20% of the batches are of bad quality. These items are then used in an assembly, and ultimately their quality is determined before the nal assembly leaves the plant. The manufacturer can either screen each item in a batch and replace defective items at a total average cost of $10 per item or use the items directly without screening. If the latter action is chosen, the cost of rework is ultimately $100 per defective item. For these data, the costs per batch can be calculated as follows: m EE- $1500 $1500 $750 $3750 Because screening requires scheduling of inspectors and equipment, the decision to screen or not screen must be made 2 days before the potential screening take place. However, the manufacturer may take one item taken from a batch and sent it to a laboratory, and the test results (defective or non-defective) can be reported before the screenon-screen decision must be made. Aer the laboratory test, the tested item is returned to its batch. The cost of this initial inspection is $125. Also note that the probability that a random sample item is defective 1s 0.8 * 0.05 + 0.2 * 0.25 = 0.09 and the probability that an item in a lot is a good quality given a randomly sampled item is defective is 0.444 and the probability that an item in a lot is of good quality given a randomly sampled item is not defective is 0.835. The manufacture wants to minimize his or her cost. A. Derive the cost gures in the table above. Clearly show your calculations B . What Law of Probability was used in deriving B_(,Randomly Sampled Item is Defective) C . Show that: Batch of Good Wltem is Defective) = 0.44 P(Batch of Good Wiggltem is Not Defective) = 0.835 D. Model the decision problem in a DECISION TREE and ll in ALL the details E. Describe in words the optimal decision strategy