8. A supermarket receives various types of eggs from a factory. Assume that there are three possible events: A, B, and C, which represent that the incoming lot may contain 3%, 8% or 15% defectives and that each of these events happens with probabilities 50%, 30% and 20% respectively. The manager's action is to accept the lot with 3% or 8% defectives and reject the lot with 15% defectives. In one time, the manager need to decide if one type of eggs that was just delivered from the factory is acceptable or not. The payoff for each event is given below: A Reject -$500 -$200 $700 Accept $300 $100 -$800 B (a) Find the optimal payoff and EOL act respectively before sampling. N 2 (b) Find EVPI. (c) Now a random sample of 11 units was drawn and 3 defectives were found. Find the optimal EOL act. Give your answer correct to 4 decimal places