Compute the total hourly crew-and-dock costs

Question

Problem:

Trucks arrive at a warehouse at a rate of 27.0 per hour during business hours. Each crew-and-dock can unload the trucks at a rate of 10 trucks per hour. Each crew-and-dock is assumed as a server, crew-and-dock are NOT separate units. The waiting line of trucks have caused the warehouse manager to have 3 crew-and-docks. Each crew-and-dock can unload one and only one truck at a time.

The cost rates are as follow:

Each crew-and-dock costs $90 per hour; truck & driver waiting cost is $100 per hour. Assume Poisson arrival and Exponential processing time.

Question 1) Compute the total hourly crew-and-dock costs.

Question 2) Compute the utilization of the crew-and-docks.

Question 3) What percentage of time the crew-and-docks are idle?

Question 4) Compute the total hourly truck-and-drivers cost during the time that the trucks are unloading.

Question 5) Compute the total hourly truck-and-drivers cost when trucks are in the waiting line.

Question 6) Compute the maximum amount you are willing to pay to have one additional crew-and-dock.

Question 7) After adding one crew-and-dock, what is the maximum you can save by adding more and more crew-and-docks? Solve the given numerical problem and illustrate step by step calculation.