2. (15 pts) Suppose that an operator should detect the problem on a machine based on his experience. However, he does not know which response criterion is optimum for detection task. Consider the following payoff and probability information regarding to signal detection task of a machine breakdown problem, and determine the optimal response criterion for the operator. He checks machine surface for detection five times every day and only three times breakdown risk situation appeared during 10 subsequent working days. Suppose that if machine is down it will cost to $5000 loss of production and $500 for repairing, however if operator can understand that it is a risk of breakdown and warn the maintenance it will cost only $500 repairing and no production loss since it can be repaired between two production bathes. If operator call maintenance for a machine which has no risk of breakdown it will cause a loss of $350 maintenance operation resource. What will be the value of Bopt