Chapter 4.11, Problem 155E

A builder of houses needs to order some supplies that have a waiting time Y for delivery, with a continuous uniform distribution over the interval from 1 to 4 days. Because she can get by without them for 2 days, the cost of the delay is fixed at $100 for any waiting time up to 2 days. After 2 days, however, the cost of the delay is $100 plus $20 per day (prorated) for each additional day. That is, if the waiting time is 3.5 days, the cost of the delay is $100 + $20(1.5) = $130. Find the expected value of the builder’s cost due to waiting for supplies.