A scarce resource is to be leased for an engineering project. There is a graduated cost associated with using the resource at a certain percentage level, U. A step function has been defined for the cost rates for different levels of utilization. The step cost function is presented as follows:

If U < 50%, cost = $0 If 50% ≤ U < 60%, $5,000 If 60% ≤ U < 67%, $20,000 If 67% ≤ U < 85%, $45,000 If U ≥ 85%, $55,000 Suppose the utilization level is a random variable following a triangular distribution with a lower limit of 40%, a mode of 70%, and an upper limit of 95%.

(a) Plot the step function for the cost of leasing the resource.

(b) Plot the triangular probability density function for the utilization level.

(c) Find the expected cost of using this resource.