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Answer:
Time taken to process 20 students is 100 minutes.
Step-by-step explanation:
Given that:
Students are going through a three-step process to obtain their ID cards.
Let Have a table below illustrating what the question means:
Unit Number of Number of
<u> servers minutes spent</u>
Registration 1 2
desk
Cashier 3 10
ID processing 4 20
<u>station </u>
Demand Rate = 0.5 student per minute
To calculate how long it take to process 20 students assuming the system is full; we need to run through the following process:
The Capacity of each of the server at three-processes is calculated as;
Capacity = Number of students served per minute
At the Registration desk
Number of minutes spent to serve 1 student = 2 minutes
Number of servers to be = 1
Therefore, the Capacity=
= 0.5 students per minute
At the Cashier Unit
Number of minutes spent to serve 1 student = 10 minutes
and we have number of servers to be = 3
Thus, the Capacity =
= 0.3 students per minute
Over to the ID processing station
Number of minutes spent to serve 1 student = 20 minutes
Number of servers = 4
The capacity=
= 0.2 students per minute
In the three-step process, the bottleneck process is the ID processing stations and this process also have the highest time to serve 1 student.
As such, the process capacity is equivalent to the bottleneck process
Process Capacity = 0.2 students per minute
As we know that our demand rate = 0.5 students per minute
Since, the demand rate is higher than the Process capacity, the number of students served per minute will still be:
Number of students served per minute = 0.2
Time taken to serve 1 student = 1 / 0.2 = 5 minutes
Time to process 20 students = 5 × 20 =100 minutes.