31. 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 students per minute, how long does it take to process 20 students, assuming the system is empty?

The answer is 72 minutes.

Step-by-step explanation:

The first step will be the registration desk, which last 2 minutes.

The second step is going to one of the three cashiers, this step takes 10 minutes.

The third step is to visit one of the four ID processing stations, to take their picture and to print the ID card. this step take 20 minutes.

Demand rate= 0.5 students per minute

This means 1 student every 2 minutes.

The total amount of time of the three-step process  is 32 minutes.

During 40 minutes 20 students will start their process. These means that the student number 20 will start his/hers process at the minute number 40 of the whole process. As he/she is the last one, no one will finish their process before him/her.

The process takes 32 minutes.

We just need to add 40 minutes to the total amount of time of the three-step process takes, which is 32 minutes.

Therefore to process 20 students it will take 72 minutes.  

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