8. The Clark County Sheriff's 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 num- ber of officers on duty: Time of Day 8:00 A.M.-Noon Noon-4:00 PM 4:00 P.M.-8:00 P.M. 8:00 P.M.-Midnight Midnight-4:00 A.M. 4:00 A.M.8:00 A.M. Minimum Officers on Duty 5 6 10 7 4 6 Determine the number of police officers that should be scheduled to begin the 8-hour shifts at each of the six times (8:00 A.M., noon, 4:00 P.M., 8:00 P.M., midnight, and 4:00 A.M.) 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.) 25. Western Family Steakhouse offers a variety of low-cost meals and quick service. Other than management, the steakhouse operates with two full-time employees who work 8 hours per day. The rest of the employees are part-time employees who are scheduled for 4-hour shifts during peak meal times. On Saturdays the steakhouse is open from 11:00 AM to 10:00 P.M. Management wants to develop a schedule for part-time employ ces that will minimize labor costs and still provide excellent customer service. The aver age wage rate for the part-time employees is $7.60 per hour. The total number of full-time and part-time employees needed varies with the time of day as shown. Total Number of Employees Needed Time 11:00 AM -Noon Noon-1:00 PM 1:00 PM - 2:00 PM 2:00 P.M.-3:00 PM 3.00 PM 4:00 PM 4:00 PM-5:00 PM 5:00 PM-6:00 PM 6:00 PM - 7:00 PM 7:00 PM 8:00 PM 8:00 PM 9:00 PM 9:00 PM-10:00 PM 3 3 One full-time employee comes on duty at 11:00 A.M., works 4 hours, takes an hour off, and returns for another 4 hours. The other full-time employee comes to work at 1:00 PM and works the same 4-hours-on, 1-hour-off, 4-hours-on patter. 202 Chapter 4 Linear Programming Applications in Marketing, Finance, and Operations Management a. Develop a minimum-cost schedule for part-time employees b. What is the total payroll for the part-time employees? How many part-time shifts are needed? Use the surplus variables to comment on the desirability of scheduling at least some of the part-time employees for 3-hour shifts. c. Assume that part-time employees can be assigned either a 3-hour or a 4-hour shift. Develop a minimum-cost schedule for the part-time employees. How many part-time shifts are needed, and what is the cost savings compared to the previous schedule