Document Inspection Vehicles arrive at the Canadian border at the rate of 140 vehicles per hour, 20% of which are commercial vehicles. All commercial vehicles are required to present documents detailing their freight at the border and these are reviewed by a border security officer ("Document Inspection"). On average, document inspection requires 6 minutes and is exponentially dist. A total of 3 border security officers work doing this task. If the officer is concerned, she directs the vehicle to an inspection station where the trailer is opened up and a inspected by one of four specially trained inspection officers dedicated to this task ("Freight Inspection"). Generally, the inspection averages 45 minutes. In the inspector determines that the freight is illegal, he confiscates the freight ("Confiscation"). This takes an additional fifteen minutes of the same inspector's time. Approximately 2% of the vehicles inspected have their freight confiscated. Commercial Traffic - Freight Inspection Non-commercial traffic are also expected to present documentation when first questioned by a border security officer ("Document Inspection"). This stage of the process takes, on average, 2 minutes and is split evenly across 6 officers. Confiscation If the vehicle occupant has made purchases while in the United States, they will be required to pull over and enter the customs station to pay the applicable taxes or duties. It's estimated that 10% of all arriving non-commercial traffic will be told to pullover and pay taxes or duty. Serving these arrivals takes, on average, 5 minutes. A total of 2 officers are dedicated to this process stage. Non-Commercial Traffic Either the officer responsible for document inspection OR the officer accepting payment for taxes and duties may direct traffic towards an inspection station where inspectors specially trained in the search of non-commercial traffic spend, on average, 25 minutes inspecting the vehicle and seizing contraband (if applicable). Vehicles undertake this at a rate of 12 per hour. Document Inspection All officers and inspectors receive pay of $40 per hour. a) Considering only the document inspection of commercial traffic, what is the total hourly cost (including both serving and waiting) if the driver & truck combination is expected to cost approximately $50 per hour? [5 points) Pay Duty or Taxes Search and Seizure b) Suppose a goal has been set to reduce the average time in the system to 5 minutes for commercial traffic that doesn't require freight inspection. How many border security officers must be working at "Document Inspection" in order to achieve this goal? [6 points] c) How many border security officers are required, at a minimum, at "Search and Seizure" to keep utilization below 100%? [2 points) d) Supposing the number of officers identified in c), what is the average flowtime through the system for a non-commercial vehicle? [12 points] Document Inspection Vehicles arrive at the Canadian border at the rate of 140 vehicles per hour, 20% of which are commercial vehicles. All commercial vehicles are required to present documents detailing their freight at the border and these are reviewed by a border security officer ("Document Inspection"). On average, document inspection requires 6 minutes and is exponentially dist. A total of 3 border security officers work doing this task. If the officer is concerned, she directs the vehicle to an inspection station where the trailer is opened up and a inspected by one of four specially trained inspection officers dedicated to this task ("Freight Inspection"). Generally, the inspection averages 45 minutes. In the inspector determines that the freight is illegal, he confiscates the freight ("Confiscation"). This takes an additional fifteen minutes of the same inspector's time. Approximately 2% of the vehicles inspected have their freight confiscated. Commercial Traffic - Freight Inspection Non-commercial traffic are also expected to present documentation when first questioned by a border security officer ("Document Inspection"). This stage of the process takes, on average, 2 minutes and is split evenly across 6 officers. Confiscation If the vehicle occupant has made purchases while in the United States, they will be required to pull over and enter the customs station to pay the applicable taxes or duties. It's estimated that 10% of all arriving non-commercial traffic will be told to pullover and pay taxes or duty. Serving these arrivals takes, on average, 5 minutes. A total of 2 officers are dedicated to this process stage. Non-Commercial Traffic Either the officer responsible for document inspection OR the officer accepting payment for taxes and duties may direct traffic towards an inspection station where inspectors specially trained in the search of non-commercial traffic spend, on average, 25 minutes inspecting the vehicle and seizing contraband (if applicable). Vehicles undertake this at a rate of 12 per hour. Document Inspection All officers and inspectors receive pay of $40 per hour. a) Considering only the document inspection of commercial traffic, what is the total hourly cost (including both serving and waiting) if the driver & truck combination is expected to cost approximately $50 per hour? [5 points) Pay Duty or Taxes Search and Seizure b) Suppose a goal has been set to reduce the average time in the system to 5 minutes for commercial traffic that doesn't require freight inspection. How many border security officers must be working at "Document Inspection" in order to achieve this goal? [6 points] c) How many border security officers are required, at a minimum, at "Search and Seizure" to keep utilization below 100%? [2 points) d) Supposing the number of officers identified in c), what is the average flowtime through the system for a non-commercial vehicle? [12 points]