A firm operates a docking facility for container ships in Singapore. At present, the facility consists of two identical docks. Ships typically arrive during the night. The number of ships that arrive during a single night varies from night to night, as given in the distribution below. Each dock can unload one ship during the day. Ships unable to unload must wait until the following day. The cost of delaying a ship (called a demurrage charge) is $10,000 per day. A new dock will cost $5 million a year, including amortized construction costs, maintenance, and operating costs.

a. With the current system, what is the average demurrage charge per year?
b. Can you justify adding one or more additional docks?
c. How sensitive are your results to the assumption you make about the number of ships waiting at the beginning of the simulation?