The manager of a new regional warehouse of a company must decide on the number of loading docks to request in order to minimize the sum of dock-crew and driver-truck costs. The manager has learned that each driver-truck combination represents a cost of $300 per day and that each dock plus crew represents a cost of $ 1,100 per day.
a. How many docks should she request if trucks will arrive at average rate of four per day, each dock can handle an average of five trucks per day, and both rates are Poisson?
b. An employee has proposed adding new equipment that would speed up the service rate to 5.71 trucks per day. The equipment would cost $100 per day for each dock. Would this change the answer to part a? Should the manager invest in the new equipment?