The Best Corporation is considering making either minor or major repairs to a malfunctioning production process.  When the process is malfunctioning, the percentage of defective items produced seems to be a constant with either   p = 0.10 or p = 0.25.  Defective items are produced randomly, and there is no way Best can tell for sure whether the machine needs minor or major repairs.  If minor repairs are made when p = 0.25, the probability of a defective item is reduced to 0.05.  If minor repairs are made when p = 0.10 or major repairs are made when p = 0.10 or p = 0.25, the proportion of defectives is reduced to zero. The company's prior probability that p = 0.10 is 0.70.  Best has recently received an order for 1000 items.  This item yields Best a profit of $0.50 per unit, except when the company has to pay a $2 penalty cost for each defective item.  Major repairs to the process cost $100 and minor repairs to the process cost $60.  The process cannot be adjusted once a production run has begun. Prior to starting a production run, however, Best can sample (at a cost of $1 per item) items from a trial rum.

Questions

i)      Find Best's optimal course of action if the company is trying to decide between not sampling at all and sampling one item. (Draw, properly label and evaluate the decision tree).

ii)     Find the optimal action for Best if it is willing to consider a sample of either one or two item, (Draw, properly label and evaluate the decision tree).

iii)    Compute the joining probabilities, marginal probabilities and posterior probabilities for (i) and (ii) using MS Excel.

iv)    Use Decision Tree Analysis and find the best strategy.