Question: Sanitation trucks dump refuse seven days a week at a single garbage dump in the village of Thomas Lee. A barge removes the garbage from the dump and transports it to an incinerator where it is burned. The barge has a capacity of 2500 tons of garbage. It takes one week from the time it is called for the barge to arrive at the dump site. The dump site has a capacity of 2100 tons of garbage. Each time the barge is used the dump incurs a cost of $5000 regardless of the amount of garbage removed. For each ton of garbage held at the dump for a year the village incurs a cost of $50. (The cost reflects the cost of periodically disinfecting the pile and the social cost--the greater the amount of garbage the greater the annoyance of local residents). Assume that it takes essentially no time for the barge to remove the garbage from the dump, i.e., removal is instantaneous. Suppose the supply of garbage to the dump is uncertain. Suppose the expected daily demand is 50 tons per day with a standard deviation of 20 tons and that daily demands are independent. If the dump is filled to capacity, arriving trucks are turned away. Assume that each ton of garbage that cannot be unloaded at the dump (because it is full) costs the village $100. Suppose the village calls the barge when the pile reaches a level of 1750 tons.

(a) What is the expected annual cost to the village for garbage that cannot be unloaded at the dump?

(b) What is the expected total annual cost for the village's policy?