Students are going through a three-step process to obtain their ID cards. Each student will spend 2 minutes at the registration desk before going to one of three cashiers to pay a fee for the ID card. After that, he/she will visit one of four ID processing stations to have his/her picture taken and ID card printed. Visits to the cashier and ID processing station take 10 and 20 minutes respectively. If the demand rate is 0.125 student per minute, how long does it take to process 20 students assuming the system is full?

A. 100 minutes

B. 152 minutes

C. 160 minutes

D. 184 minutes

C) 160 minutes

Explanation:

Given:

Time spent at registration desk = 2mins

Time spent at the cashier = 10 mins

Time spent at the ID processing station = 20 mins

Number of registration desk = 1

Number of cashiers = 3

Number of ID processing stations = 4

Let's calculate the capacity of each process using the expression: number of agents / process time

Therefore,

Capacity of registration desk =

Capacity of cashiers =

Capacity of ID processing stations =

The process capacity is equal to the bottleneck process. Here, the bottleneck process is the process with the longest time per minute which is the ID processing station.

Therefore, given a rate of 0.125 student per min and Process capacity of 0.2 student per min, we'll take 0.125 as the number of students per minute since it is lower than the process capacity.

Therefore, time taken to serve one student =

Time taken to serve 20 students would be = 20 * 8 = 160 minutes

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