QUESTION $22(10$ points$)-$ Little's Law in Multiple Stages

An online university has a stable average student population of $23,220$ over the years. The

university offers modular courses and curricula such that all tracks of majors and concentrations

have the following sequential stages with their corresponding designed durations:

Stage $1-$ General education courses $(6$ months$)$

Stage $2-$ Foundation courses $(9$ months$)$

Stage $3-$ Major courses $(18$ months$)$

Stage $4-$ Concentration courses $(15$ months$)$

The university does not take transfer students. New students can enroll at any time during the

year and start with Stage $1.$ After enrolling, students can choose their tracks and start taking

online courses. With online courses, there is no wait time between stages. Students can choose

to drop out at the end of some stage. Hence, students have their own start and end dates.

Statistics show that, at any point in time, the average number of students in the first

stage is $3,250$ ; in the second stage $4,530$ ; in the third stage $8,610$ ; and in the fourth stage $6,830.$

After the fourth stage, $210$ students drop out on average $($recorded over $15$ months$),$ and the

remaining students graduate. Note that all drop outs are recorded at the end of the stages.

The retention rate at each stage is the proportion of students who finish the stage and

move on to the next one or graduate. The retention rates do not only affect revenues but also

the university's rankings. The university's president observes the retention rates very closely

and takes actions if there are signs of declining retention rates.

In the following questions, you should convert all quantities into yearly numbers.

$($a$)[2]$ Draw a process flow diagram showing how students move through different stages. Make

sure to have process boundaries in the diagram. Note that there is no wait time.

$($b$)[1]$ What is the number of new enrollments every year?

$($c$)[2]$ What are the yearly dropouts from individual stages? $(4$ separate dropout numbers$)$

$($d$)[1]$ What is the retention rate of Stage $1?$ decimals, for example $79\mathrm{.}54\%$

$($e$)[1]$ What is the retention rate of Stage $2?(\%,2$ decimals$)$

$($f$)[1]$ What is the retention rate of Stage $3?$ decimals$)$

$($g$)[1]$ What is the retention rate of Stage $4?$ decimals$)$

$($h$)[1]$ What is the proportion of newly enrolled students who would eventually graduate? $(\%)$

Note: the retention rates & graduation rate can be understood as the yleld $=$#outputs$/$#inputs.