6.121 A builder of houses has to order some supplies that have a waiting time for delivery Y uniformly distributed over the interval 1 to 4 days.

Because she can get by without the supplies for 2 days, the cost of the delay is fixed at $100 for any waiting time up to 2 days. However, after 2 days the cost of the delay is $100 plus $20 per day for any time beyond 2 days. 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.