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 $200 for any waiting time up to 2 days. After 2 days, however, the cost of the delay is $200 plus $30 per day (prorated) for each additional day. That is, if the waiting time is 3.5 days, the cost of the delay is: $200 + $30(1.5) = $245.

Find the expected value of the builder's cost due to waiting for supplies.