In waiting-line models, customers are the entities that arrive and require some form of service. Examples of customers include trucks arriving at a receiving dock (like the example we saw in Lecture 11), pallet loads of materials arriving at a stretchwrap machine, cases arriving at a case sealing station, employees arriving at a tool crib, and airplanes arriving at an airport. The followings come from two applications of the waiting-line models. (a) Trucks arrive at the receiving area of a distribution center at a Poisson rate of 10 per hour. The time required to unload a truck is exponentially distributed with a mean of 30 minutes. With 10 docks available for unloading trucks, what is the average number of trucks waiting to be unloaded? What is the average waiting time a truck spends? What is the average number of docks at which a truck is being unloaded? (b) A fleet of lift trucks is used to place pallet loads of materials in storage and to retrieve pallet loads from storage. Job requisitions are received in a Poisson fashion at a rate of 10 per hour. The time required to perform the required material handling for a requisition is exponentially distributed with a mean of 15 minutes. If management wishes for the lift trucks to be utilized at least 80% of the time ( 80%), how many lift trucks are needed? What is the average time a requisition is delayed before processing begins (Wq)? If management wishes to reduce the average order waiting time (i.e., the average time a requisition is delayed before processing begins or Wq) to less than 10 minutes, how many lift trucks are needed? What is the utilization of the lift trucks