A call center has 60 staffs to be scheduled in three 8-hour shifts. However, the number of incoming calls varies significantly according to the time of day. The slowest period is between midnight and 4:00 am. It is estimated that the average number of calls served by a staff is 8 during that period. The average number of calls served by a staff in different time period of day is shown in the following table: Time period Duration Average number of calls served 0:00 am to 4:00 am 4:00 am to 8:00 am 8:00 am to 12:00 noon 12:00 noon to 4:00 pm 4:00 pm to 8:00 pm 8:00 pm to 12:00 midnight 15 30 35 32 20 4 To retain customers and acquire new ones, the call center must maintain a high customer service level To do so, it has determined the minimum number of staffs it needs to work during every 4-hour time segment is as follows: 8 from midnight to 4:00 am, 12 from 4:00 to 8:00 am, 24 from 8:00 am to noon, 28 from noon to 4:00 pm, 20 from 4:00 to 8:00 pm, and 14 from 8:00 pm to midnight Tasks: 1) Formulate and solve an integer programming model to help the call center schedule its staffs (10 marks) 2) If the call center has a maximum of only 13 staffs who will work the late shift from midnight to 8:00 am, reformulate the model to reflect this complication and solve it. (10 marks) 3) All staffs like to work the day shift from 8:00 am to 4:00 pm, so the call center has decided to limit the number of staffs who work this 8-hour shift to 24. Reformulate the model in 2) to reflect this restriction and solve it