The laboratory department of a large hospital is developing the shift schedule for the overnight period on weekdays, which lasts from 12:00 a.m. to 8:00 a.m. The table below indicates the number of technicians needed during each hour, based on the average number of laboratory requests over the period. Time 12:00 a.m. 1:00 a.m. 1:00 a.m. 2:00 a.m. 2:00 a.m. - 3:00 a.m. 3:00 a.m. - 4:00 a.m. 4:00 a.m. 5:00 a.m. - 6:00 a.m. 7:00 a.m. 5:00 a.m. 6:00 a.m. 7:00 a.m. 8:00 a.m. Technicians Needed 5 4 3 5 7 9 8 6 Technicians are classified into two groups, lead technicians and assistant technicians. During the overnight period, each lead technician starts on the hour and is on site for 3 hours, takes a mandatory break of 1 hour, and then works another 2 hours. Each assistant technician starts on the hour and is on site for a continuous 4 hours. Hospital policy mandates that technicians must work their complete designated shifts, that no technician is allowed to work an extra shift, and that at least one lead technician must be on site at all times. The number of technicians is measured using a metric known as "labor units," which factors in salaries, benefits, and other costs. Each lead technician counts as 1.7 labor units, while each assistant technician counts as 1.2 labor units. Let Li and A, be the number of lead technicians and assistant technicians, respectively, who start at hour i, i = 12, 1, 2,.... Formulate an integer programming model to develop a schedule that will satisfy the laboratory department's staffing requirements while minimizing the total number of labor units. Include only those decision variables that are necessary, taking into account the latest time at which each type of technician may start. You do not need to solve the LP.