Nurse Ratched is in the process of developing a daily schedule for the emergency staff at Claymoore Hospital. Based on past emergency records she has determined the number of staff needed during each two hour segment of the day as shown in the table below. There are six work shifts. Emergency workers can report at 8:00 AM, Noon, 4:00 PM, 8:00 PM, Midnight, or 4:00 AM. Each worker must work at least 8 hours. Their pay is $25 per hour. Emergency staff members may be required to work an addition two hours of overtime (for a total of ten hours). However, they are paid one and a half times their regular hourly wage during the two overtime hours. Determine how many staff members should report at each of the six time shifts and how many should work overtime in order to meet the staffing requirements at a minimum labor cost.
Time Emergency Staff Needed
8:00 AM to 10:00 AM 11
10:00 AM to Noon 7
Noon to 2:00 PM 9
2:00 PM to 4:00 PM 9
4:00 PM to 6:00PM 12
6:00 PM to 8:00 PM 10
8:00 PM to 10:00 PM 8
10:00 PM to Midnight 8
Midnight to 2:00 AM 6
2:00 AM to 4:00 AM 4
4:00 AM to 6:00 AM 4
6:00 AM to 8:00 AM 2
1a. How many workers will need to report for duty each day?
1b. How many workers will work overtime for each of the six time shifts?
1c. How much will be spent to cover the cost of overtime pay.
1d. How many workers will work the 4:00 PM shift and how many of these nurses must work overtime?
1e. What would be the implications for the solution (change in optimal solution value) if 13 workers were required between the hours of 4 and 6 PM?