A software company conducts a job$-$training program for programmers. Expert programmers are

used as teachers in the program at a ratio of one for every ten trainees. The training program lasts

for one month $($Assumption: No$.$ of trainees multiple of $10).$ From past experience it has been

found that out of ten trainees hired, only seven complete the program successfully $($the

unsuccessful trainees are released$).$ Expert programmers are also needed for ongoing projects and

$3$do

the company's requirements for the next three months are as follows.

in addition, the company requires $250$ expert programmers by April. There are $130$ expert

programmers available at the beginning of the year. Payroll costs per month are as followe

Each trainee

$ $400$

Each expert programmer $($programming or teaching$)$ S $700$

Each idle expert programmer

$$500$

Set up the linear programming problem that will produce the minimum cost hiring and trainina

Schedule and meet the company's require