On most university campuses, students are contracted by academic departments to do office errands. The need for such service fluctuates during work hours (8:00 A.M. to 5:00 PM.). In one department, the minimum number of students needed is 2 between 8:00 A.M. and 10:00 A.M., 3 between 10:01 A.M. and 11:00 A.M., 4 between 11:01 A.M. and 1:00 PM., and 3 between 1:01 PM, and 5:00 PM. Each student is allotted 3 consecutive hours (except for those starting at 3:01 who work for 2 hours, and those who start at 4:01 who work for 1 hour). Because of their flexible schedule, students can usually start at any hour during the workday, except at lunchtime (12:00 noon). Develop the LP model, and determine a time schedule specifying the time of the day and the number of students reporting to work.