Model 3: Toll Booth Scheduling

The Northeast Tollway out of Chicago has a toll plaza with the following staffing demands during each 24-hour period:

HOURS	COLLECTORS NEEDED
12 a.m. to 6 a.m.	2
6 a.m. to 10 a.m.	8
10 a.m. to noon	4
noon to 4 p.m.	3
4 p.m. to 6 p.m.	6
6 p.m. to 10 p.m.	5
10 p.m. to 12 midnight	3

Each collector works 4 hours, is off one hour, and then works another 4 hours. A collector can be started at any hour. Assume the objective is to minimize the number of collectors hired, formulate the appropriate LP.