The manager of a regional warehouse must decide on the number of loading docks to request for a new facility in order to minimize the sum of dock costs and driver-truck costs. The manager has learned that each driver-truck combination represents a cost of $800 per day and that each dock plus loading crew represents a cost of $600 per day. Due to space limitations, there is an upper limit if five docks.
a. How many docks should be requested if trucks arrive at the rate of 9 per day, each dock can handle 5 trucks per day, and both rates are Poisson?
b. An employee has proposed adding faster equipment that would speed up the loading rate to 3.6 trucks per day. The equipment would cost $50 per day for each dock. Would this be a good investment?