Suppose there are $300$ associates, $90$ managers, and $30$ partners on

average in a consulting firm. The firm only promotes from within and

wants to determine the appropriate number of recruits to hire each

year to maintain its size. Associates are either canned or promoted to

manager after $4$ years. Similarly, managers are either promoted to

partner or released after $6$ more years. Once promoted, a partner

stays for $10$ more years $($total of $20$ years with the firm$).$

$$ How many recruits should it hire each year?

$$ What is the probability any given new hire has to become partner?

Example #$2$

Rady $|$ MGT In

Class

Adapted from Cachon $(2006)$