Suppose a critical resource is leased for a large project. There is a graduated cost associated with using the resource at a certain percentage level U. The cost is specified as $10,000 per 10% increment in the utilization level above 40%. A flat cost of $5000 is charged for utilization levels below 40%. The utilization intervals and the associated costs are presented as follows:
Suppose the utilization level is normally distributed random variable with mean 60% and standard deviation of 4%. Find the expected cost of using this resource.