XYZ College is planning for the next commencement and has the following estimates to work with.

There are $409$ students$/$hr on average going through the commencement process. The school wishes to complete the commencement exercise within an hour.

The commencement is a $4$ step process.

An average of $12$ students are hooded per minute.

Names are called @ one student every $7$ seconds.

The walk to go to the center of the stage, and physically receive the diploma, takes a student $8\mathrm{.}2$ seconds, on average.

It takes an additional $2$ seconds for a student to walk on and exit.

There are $5$ students on stage, on average $-$ some being hooded, some waiting for their names to be called, some walking to receive their diplomas, and some exiting the stage.

Can $409$ students be processed in an hour at this commencement, based strictly on the provided data?

Hint: Find out the bottleneck capacity

Step

Hooding

Name Calling

Walking and Receiving

Time$/$student

$5$ second$/$student $($@$12$ students$/$min$)$

Capacity $($students$/$hr$)$

$12**60$min$=720$ students $\frac{?}{hr}$

Implied Capacity Utilization

demand