The Clark County Sheriffs Department schedules police officers for 8-hour shifts. The beginning times for the shifts are 8:00 a.m., noon, 4:00 p.m., 8:00 p.m., midnight, and 4:00 a.m. An officer beginning a shift at one of these times works for the next 8 hours. During normal weekday operations, the number of officers needed varies depending on the time of day. The department staffing guidelines require the following minimum number of officers on duty:

	Time of Day	Minimum No. of Officers on Duty
	8:00 a.m.noon	7
	Noon4:00 p.m.	6
	4:00 p.m.8:00 p.m.	7
	8:00 p.m.midnight	7
	Midnight4:00 a.m.	4
	4:00 a.m.8:00 a.m.	6

Determine the number of police officers that should be scheduled to begin the 8-hour shifts at each of the six times to minimize the total number of officers required. (Hint: Let x₁ = the number of officers beginning work at 8:00 a.m.,x₂ = the number of officers beginning work at noon, and so on.) If your answer is zero, enter 0.

	Starting Time	Officers Starting
	8:00 a.m.
	Noon
	4:00 p.m.
	8:00 p.m.
	Midnight
	4:00 a.m.