An IT company has $N$ number of experienced developers. Each month new developers are hired but

none are fired. Training of a new developer takes $1$ month and each trainee needs $1$ experienced

developer to spend $1$ month acting as a supervisor rather than working in the projects. Each month

some $d_i$ number of experienced developers are needed $(i=1,2,$dots,$T),$ excluding the ones who acts as

supervisor. $p\%$ of experienced developers leave the job every month but none of the trainees leave.

Trainees are paid $$TS and experienced developers $$EDS$.$ Assume that at the end of the planning period

$(T^{th}$ month$)$ there should be at least $N$ number of experienced employees.

a$)$ Set up a dynamic programming formulation to minimize payroll cost in months $1,2,$dots,$T.$

Identify the states$/$stages and define variables, write recursion formula and solution

procedure.

b$)$ Solve the dynamic programming recursion using a software $($python or excel$)$ with the

following parameters $($Do not forget to submit your findings in the report$)$:

T $($planning period$)$ : $12$ months

Initial number of experienced developers $(N)$:$70$

Salary of a trainee $($TS$)$: $40$K

Salary of an experienced developer $($EDS$)$: $60$K

Turnover rate $(p)$:$10\%$

Demand for experienced developer:

Assume that number of experienced developers leave the job is calculated by rounding down $10\%$ of

experienced developers.

c$)$ Suppose that if the salary of an experienced developer $($EDS$)$ is increased to $70$K$,$ the turnover

rate $(p)$ will decrease to $5\%.$ Should such a change be made in terms of total payroll cost?