11. A fruit shop receives 4 types of apples from a farm. Assume that there are four possible events: A, B, C, and D, which represent that the incoming lot may contain 5%, 10%, 15% or 20% bad apples and that each of these events happens with probabilities 40%, 30%, 20% and 10% respectively. The manager's action is to accept the lot with 5% or 10% defectives and reject the lot with 15% and 20% defectives. In one time, the manager need to decide if one type of apples that was just delivered from the farm is acceptable or not. The payoffs for each event are given below: A B D Reject ($000) -$300 -$100 $100 $200 Accept $700 $600 -$300 -$500 (a) Find the optimal payoff act before sampling. (b) Now a random sample of 4 units was drawn. Find the optimal courses of action and calculate the EVSI. Give your answer correct to 4 decimal places. 11. A fruit shop receives 4 types of apples from a farm. Assume that there are four possible events: A, B, C, and D, which represent that the incoming lot may contain 5%, 10%, 15% or 20% bad apples and that each of these events happens with probabilities 40%, 30%, 20% and 10% respectively. The manager's action is to accept the lot with 5% or 10% defectives and reject the lot with 15% and 20% defectives. In one time, the manager need to decide if one type of apples that was just delivered from the farm is acceptable or not. The payoffs for each event are given below: A B D Reject ($000) -$300 -$100 $100 $200 Accept $700 $600 -$300 -$500 (a) Find the optimal payoff act before sampling. (b) Now a random sample of 4 units was drawn. Find the optimal courses of action and calculate the EVSI. Give your answer correct to 4 decimal places