You are the President of Newpex Consulting Firm, and you are concerned about the high level of turnover in company employees. After reviewing data from employee exit interviews and HR$,$ you have determined that employees who leave the firm after only a few years often report high levels of stress, burnout, or $$needing an extended break$$ as a reason for leaving. Recruiting and training replacements for employees who have left has proven costly$.$ You are reluctant to reduce workloads by increasing staffing because that would increase costs considerably.

Instead, in your effort to address the problem of employees' burnout, you$$ve decided to revise the company$$s current vacation policy. $($Your decision is partly based on a $2013$ study jointly conducted by the Society for Human Resource Management and the U$.$S$.$ Travel Association which showed that a strong majority of human resource professionals thought vacation time impacted creativity $(70\%),$ employee engagement $(68\%),$ staying with the organization longer $(60\%),$ and taking fewer sick days $(58\%).)$

Currently Newpex$$s policy allows employees to take paid time off $($PTO$)$ based on number of years of employment: $5$ vacation days for employees with fewer than $3$ years of employment; $10$ vacation days for employees with between $3$ and $5$ years of employment; $15$ days for employees with between $5$ and $10$ years of employment, and $20$ days for employees with more than $10$ years of employment. The current policy also allows employees to rollover vacation days at the end of the year. Data from HR indicated that the average employee had $27$ days of accumulated $($unused$)$ PTO. Further, when employees left the firm, they received a payout for unused vacation days, at a rate of $$350/$day$.$ You$$ve concluded that the current policy, which has been in place since $2011,$ doesn$$t incentivize employees to use their vacation time.