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 0.5 student per minute, how long does it take to process 20 students assuming the system is full

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

                                          servers                         minutes spent

Registration                            1                                    2

desk            

Cashier                                    3                                   10

ID processing                          4                                   20

station                                                                                                

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.

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step-by-step explanation: