GourmetFood.com is a famous virtual food store. Online orders arrive at the store at a rate of 5 per hour according to a Poisson process and it is estimated that a single order is worth $120 on average. Currently the company has a single distribution center that has enough capacity to process and ship out an average of 6 orders per hour (orders are processed one at a time. Assume exponential service time.), with an operating cost of $300/hour. Due to fierce competition, the company is offering a 20% reduction in a customer's bill if the order is not shipped within an hour since it is placed.

a) What is the average number of orders in the system?

b) What is the total hourly cost (operating cost and the cost due to loss in revenue)?

c) The management is considering adding a new distribution center at another location. In this scenario, the demand will be split evenly between the two distribution centers. In this case, each center will be able to process and deliver an average of 5 orders per hour, and the operating cost will be $160 for each center.Would the average total cost rate be lower under this scenario? Should the management take this action from a financial point of view?