A$.$ Transition Probability matrix year $1$ year $2$ year $3$ year $4$ year $5$ Exit

$1.$ store associate $0\mathrm{.}530\mathrm{.}060000\mathrm{.}41$

$2.$ shift leader $00\mathrm{.}50\mathrm{.}16000\mathrm{.}34$

$3.$ department manager $000\mathrm{.}580\mathrm{.}1200\mathrm{.}3$

$4.$ assistant store manager $000\mathrm{.}060\mathrm{.}460\mathrm{.}080\mathrm{.}4$

$5.$ store manager $00000\mathrm{.}660\mathrm{.}34$

B$.$ Forcast of availabilities year $1$ year $2$ year $3$ year $4$ year $5$ exit

current workforce

$1.$ store associate $8500$

$2.$ shift leader $1200$

$3.$ department manager $850$

$4.$ assistant store manager $150$

$5.$ store manager $50$

total $($years end total forcast$)$

d$.$ Next year gap projections

$12345$

current workforce $8500$

years end total forcast $4505$

external hires needed $3995$