The intensive care unit (ICU) at a certain hospital operates 24 hours a day. Doctors report for duty at 6 a.m., 12 p.m., 6 p.m., or 12 a.m., and the following table below shows the minimum number of doctors that should be available during different periods.

The hospital administration wants to determine how many doctors should report for work at the start of each time period in order to minimize the total staff required each day if:
a) Doctors work a 12-hour shift.
b) Doctors works either a 12-hour shift or a 24-hour shift.

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PERIOD 1 2 3 4 TIME 6 A.M.-12 P.M. 12 P.M.-6 P.M. 6 P.M.-12 A.M. 12 A.M.-6 A.M. NUMBER OF DOCTORS REQUIRED 8 10 12 6.0