Scenario You have received a position that requires you to oversee a group of 30

Scenario
You have received a position that requires you to oversee a group of 30 correctional officers. This job will be challenging, because these officers are noted for holding negative, and sometimes even hostile, attitudes toward the institution’s leadership, as well as the prisoners they oversee.
Your job is to try to create a better rapport between the officers and prisoners in an attempt to ensure better behavior from the prisoners as a whole. The facility is designed to hold 1,200 male inmates, but it currently houses 1,376. Most are classified as medium security, though there is a minimum-security dormitory that is used to reward good behavior. You have been assigned to oversee one of the three minimum-security units. It houses 345 inmates in a space designed to hold 275. All indoor recreation areas have been converted into makeshift dormitories, and portable toilets have recently been installed in the only accessible exercise yard.
The prison that you have been assigned to has also received many complaints of abuse from prisoners, and you are directed to correct this problem with the officers. These complaints range from relatively minor issues, such as failure to distribute mail in a timely manner, to serious violations, including deliberate denial of access to daily meals. The unit is currently down six officers, which has disrupted shift schedules, and the administration recently increased mandatory overtime and announced suspension of all vacation and personal leave until further notice. The CO shortage has also made it difficult to move inmates for meals, medical care, visitation, and classes. Officers have also complained that they are not getting breaks and that they do not have the opportunity to eat, go to the bathroom, or sit down, sometimes for an entire 12-hour shift.
What challenges do you foresee in overseeing the correctional officers? Why? How can you apply the principles of the path-goal theory to ensure the success of the task entrusted to you?
How will you use supportive and directive leadership to motivate the correctional officers assigned to you?
Can you apply the situational leadership theory to improve the relationship with your officers? If yes, how? If not, then why? Can situational leadership be applied to the inmates?
How can participative and achievement-oriented leadership motivate these officers? Can it be used to motivate the inmates?
What are the situational variables that might affect the application of the path-goal theory of leadership?