In Mr. X City sanitation trucks dump refuse seven days a week at a single garbage dump. 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 City 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 a normally distributed random variable. Furthermore, the expected daily supply of garbage to the dump is 50 tons per day with a standard deviation of 20 tons and that daily supply of garbage to the dump 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 City $100. Suppose the City calls the barge when the pile reaches a level of 1700 tons.

(a) What is the probability that during the time from when the barge is called until it arrives one week later that arriving garbage is turned away because the dump is full?

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

(c) What is the expected total annual cost for the City's policy?

Use the (r,Q) model. What is Q?