A manufacturer receives regular contracts for large consignments of parts for the automo- bile industry. This manufacturer's production process is such that when it is operating cor- rectly, 10% of all parts produced do not meet industry specifications. However, the pro- duction process is prone to a particular malfunction, whose presence can be checked at the beginning of a production run. When the process is operated with this malfunction, 30% of the parts produced fail to meet industry specifications. The manufacturer supplies parts under a contract that will yield a profit of $20,000 if only 10% of the parts are defective and a profit of $12,000 if 30% of the parts are defective. The cost of checking for the mal- function is $1,000, and if it turns out that repair is needed, this costs a further $2,000. If in- curred, these costs must be subtracted from the profit of the contract. Historically, it has been found that the production process functions correctly 80% of the time. The manufac turer must decide whether to check the process at the beginning of a production run.

(a) According to the expected monetary value criterion, what is the optimal decision?

(b) Draw the decision tree.

(e) Suppose that the proportion of occasions on which the production process operates correctly is unknown. Under what range of values for this proportion would the deci sion selected in part

(a) be optimal, according to the expected monetary value criterion?