9. Dr Shilpa Soni, the head administrator at XYZ hospital must determine a schedule for nurses to make sure there are enough nurses on duty throughout the day. During the day, the demand for nurses varies.

Dr. Shilpa has broken the day in to 12 two-hour periods. The slowest time of the day encompasses the three periods from 12:00 AM to 6:00 AM, which, beginning at midnight, require a minimum of 30, 20 and 40 nurses respectively.

The demand for nurses steadily increases during the next four daytime periods. Beginning with the 6:00 AM to 8:00 AM periods, a minimum of 50, 60, 80 and 80 nurses are required for these four periods respectively. For the five two-hour periods beginning at 2:00 PM and ending at midnight, 70, 70, 60, 50 and 50 nurses are required respectively. A nurse reports for duty at the beginning of one of the two hour periods and works eight consecutive hours (which is required in the nurses' contract). Dr Shilpa Soni wants to determine a nursing schedule that will meet hospital's minimum requirements throughout the day while using the minimum number of nurses.

Formulate the above as an LPP.