A software company is anticipating increased demand for its products. However, management is concerned about

their programmers' adequacy to meet the increased demand given the history of workforce turnover $(5$ percent of the

programmers leave the company at the end of each month$).$

Rather than hiring new workers, management is contemplating enrolling some or all of their programmers in a monthlong intensive training program. After successfully completing the training program, a programmer would receive a

salary increase and sign a contract not to leave the company for at least $6$ months. Successfully trained programmers

would therefore be immune from normal turnover and lay$-$offs.

Management believes that successful completion of the program would increase a programmer$$s productivity by $20$

percent and plans to implement a no$-$lay$-$off policy to encourage participation. However, only $90$ percent of the

programmers are predicted to complete the training program successfully. Those who enroll in training but do not

complete the program successfully will return to the workforce at their pre$-$training skill level. $($For simplicity, we

assume that they are not candidates for a normal turnover during their training month but are candidates for normal

turnover after the training month, and that they can enroll in the training program again later.$)$

The monthly demand for untrained programmers for the next six months is shown in the table below. If trained

programmers are available, their higher productivity allows management to satisfy demand with fewer programmers.

For example, the demand in January can be satisfied with $100$ untrained programmers, or with $82$ untrained and $15$

trained programmers $($since $82+1\mathrm{.}20*15=100)$