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 $300 per day and that each dock plus loading crew represents a cost of $1,100 per day.

a. How many docks should be requested if trucks arrive at the rate of three per day, each dock can handle five trucks per day, and both rates are Poisson?

b. An employee has proposed adding new equipment that would speed up the loading rate to 4.2856 trucks per day. The equipment would cost $100 per day for each dock. Should the manager invest in the new equipment?