Hint, separate the whole process into 'substages' and analyze each substage with I=R*T. Note that the throughput rate from 1st stage to the last stage (with all branches) will be the same, which is 'flow balanced'.]

Q5 (W6) Container ships from Asia arrive at the Port of Los Angeles (PLA) constantly. When the ship is docked, the unloading process starts immediately. Based on PLA's current system, all unloading cranes can unload 5000 TEU (Twenty-ft Equivalent Unit) containers per hour. This 5000 TEU is the theoretical maximum capacity of PLA, but it does not mean PLA always operates at its maximum capacity. PLA currently works 12 hours per day to handle all containership calls at the port. After unloading at PLA, all containers will be sent to UP (Union Pacific, US class I railroad that handles Intermodal containers for PLA)'s railyard near PLA, The traffic time from PLA to UP's railyard is 8 hours in average (including all handlings for all railcars & containers, also an ideal traffic time, in reality it takes slightly longer). UP rail tracks and railyards operate 24/7. After containers arrive at the railyard, containers will wait for volume aggregations such that there are enough containers to be shipped out by rail locomotives to their destinations. Assume the current container volume is 50,000 TEUs per day. On average, from the ship is docked till the container is loaded to the railcar, it takes 11 hours. UP's IT system shows that their track systems (from PLA to UP Railyard) have an average of 18,500 TEUs. Once containers arrive at UP's railyard, it takes an average of 37.8 hours to be shipped out. Please run all numbers to its nearest tenth. Please use the " PLA + Transship to UP Railyard + UP Railyard" as your system's scope for analysis, and answer the following questions.

(1). What is the expected total time from when a container's ship arrives at PLA to the container is leaving UP's railyard to the destinations?

(2). What is the total number of TEU inventory that exist in the whole system?

(3). What is the capacity utilization for the crane system at PLA? [Hint: please use day/hour carefully, since all entities operate at different hours. I recommend to use 'hour' as your analysis time unit]