Filename:

Write a script.

Bel has decided to start an academy for crazy ideas. Bel has asked you to forecast the academy's growth for the first $20$ years. Bel wishes the calculation to be conducted monthly.

$-$ The academy consists of $5$ tiers of schooling. One being the lowest tier. Five being the highest tier.

$-$ Graduation from one tier to the next tier is rare, as you must first be knighted by Monty Python and then Bel As such graduation rates, per month, are very slim. The following represent the fraction of students in one tier who move to the next tier per month:

$-$ Tier $1>2$: $0\mathrm{.}05$

$-$ Tier $2>3$: $0\mathrm{.}07$

$-$ Tier $3>4$: $0\mathrm{.}08$

$-$ Tier $4>5$: $0\mathrm{.}10$

$-$ Tier $5>$out: $0\mathrm{.}15$

$-$ Students also drop out $($actually get kicked out by Bel on a regular basis$).$

Bel $\text{'}$s reject rate is shown below. This is presented as the fraction of students in a tier who are kicked out of Bel Academy altogether:

$-$ Tier $1$: $0\mathrm{.}50$

$-$ Tier $2$: $0\mathrm{.}40$

$-$ Tier $3$: $0\mathrm{.}30$

$-$ Tier $4$: $0\mathrm{.}25$

$-$ Tier $5$: $0\mathrm{.}20$

$-$ Challenging: Only Tiers $1-2$ are responsible for recruiting new students into Bel Academy. Each student in each tier is responsible for recruiting $5$ students. But no student has ever achieved Bel $\text{'}$s ambitious goals. Recruiting is hard! So$,$ each month, the true number of students recruited by each student in tiers $1-2$ is a random number between $0$ and $2.$

$-$ Think through this dynamic carefully.

$-$ You will need to use rand$().$

$-$ Carefully apply rand$()$ in your algorithm so that the result is consistent with the framing above.

$-$ There is no such thing as a fraction of a student recruited, promoted, or eliminated.

$-$ All recruited students start in Tier $1.$

$-$ The initial population consists of $400$ carefully selected students in Tier $1.$

PROGRESSING HINT:

$1.$ The recruiting part of this problem is more challenging. I advise starting with a system that has no recruiting. Start with a system that only has graduation and drop outs.

$2.$ Once that works... add a constant multiplier recruiting $($that is not random$).$ Do this with variables in preparation of the random recruiting.

$3.$ Finally, implement the system of random recruiting shown above.

The matlab script should:

$-$ Clearly document the solution approach $/$ algorithm

$-$ Clearly show the Leslie matrix creation $($hint$,$ and possibly updates to Leslie also!$)$

$-$ Be as dynamic as possible. Minimize hard coded values throughout

$-$ Output to the console a table of all tiers progressing through all months.