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# Epsilon Airlines services predominately the eastern and southeastern United States. The vast majority of Epsilon's

customers make reservations through Epsilon's website, but a small percentage of customers make reservations via phone. Epsilon employs callcenter personnel to handle these reservations along with any problems with the website reservation system and for the rebooking of flights for customers if their plans change or their travel is disrupted. Staffing the call center appropriately is a challenge for Epsilon's Minimum Officers Time of Day on Duty 8:00 a.m.-Noon 5 Noon-4:00 p.m. 6 4:00 p.m.-8:00 p.m. 10 8:00 p.m.-Midnight 7 Midnight-4:00 a.m. 4 4:00 a.m.-8:00 a.m. 6 Security Current Price Rate (%) Years to Maturity 1 \$1055 6.750 3 2 \$1000 5.125 4 Assume that interest is paid annually. The plan will be submitted to the judge and, if approved, Hoxworth will be required to pay a trustee the amount that will be required to fund the plan. a. Use linear programming to find the minimum cash settlement necessary to fund the annual payments. b. Use the dual value to determine how much more Hoxworth should be willing to pay now to reduce the payment at the beginning of year 6 to \$400,000. c. Use the dual value to determine how much more Hoxworth should be willing to pay to reduce the year 1 payment to \$150,000. d. Suppose that the annual payments are to be made at the end of each year. Reformulate the model to accommodate this change. How much would Hoxworth save if this change could be negotiated? 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 number of officers on duty: Copyright 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. 194 Chapter 4  Linear Programming Applications in Marketing, Finance, and Operations Management Annual Rate of Investment Return (%) Risk Stocks 10 0.8 Bonds 3 0.2 Mutual funds 4 0.3 Cash 1 0.0 management team. Having too many employees on hand is a waste of money, but having too few results in very poor customer service and the potential loss of customers. Epsilon analysts have estimated the minimum number of call-center employees needed by day of week for the upcoming vacation season (June, July, and the first two weeks of August).

These estimates are as follows: Minimum Number of Day Employees Needed

Monday 75

Tuesday 50

Wednesday 45

Thursday 60

Friday 90

Saturday 75

Sunday 45

The call-center employees work five consecutive days and then have two consecutive days off. An employee may start work any day of the week. Each call-center employee receives the same salary. Assume that the schedule cycles and ignore start-up and stopping of the schedule. Develop a model that will minimize the total number of call-center employees needed to meet the minimum requirements. Find the optimal solution. Give the number of call-center employees that exceed the minimum required. I NEED EXCEL SPREADSHEET AND SENSITIVITY REPORT TO SOLVE THIS PROBLEM

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