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EMGT 501 Fall 2008 Midterm Exam Due Day: October 21, 2008

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EMGT 501 Fall 2008 Midterm Exam Due Day: October 21, 2008. Note : (a) Do not send me after copying your computer results. Answer what are your decision variables, formulation and solution, only. See my HW answer on my HP.

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  1. EMGT 501 Fall 2008 Midterm Exam Due Day: October 21, 2008

  2. Note: (a) Do not send me after copying your computer results. Answer what are your decision variables, formulation and solution, only. See my HW answer on my HP. (b) Put your mailing address so that I will be able to return your exam result via US postal service. (c) Answer on a single series of PPS (-20 points). (d) Do not discuss the exam with other students. (e) Return your answer attached to your e-mail.

  3. Q – 1 Adirondack Savings Bank (ASB) has $1 million in new funds that must be4 allocated to home loans, personal loans, and automobile loans. The annual rates of return for the three types of loans are 7% for home loans, 12% for personal loans, and 9% for automobile loans. The bank’s planning committee has decided the at least 40% of the new funds must be allocated to home loans. In addition, the planning committee has specified that the amount allocated to personal loans cannot exceed 60% of the amount allocated to automobile loans.

  4. Q – 1 cont’d • Formulate a linear programming model that can be used to determine the amount of funds ASB should allocate to each type of loan in order to maximize the total annual return for the new funds. • b. Prepare the dual formulation and examine the complementary slackness condition. • c. How much should be allocated to each type of loan? What is the total annual return? What is the annual percentage return?

  5. If the interest rate on home loans increased to 9%, would the amount allocated to each type of loan change? Explain. • Suppose the total amount of new funds available was increased by $10,000. What effect would this have on the total annual return? Explain. • Assume that ASB has the original $1 million in new funds available and that the planning committee has agreed to relax the requirement that at least 40% of the new funds must be allocated to home loans by 1%. How much would the annual return change? How much would the annual percentage return change?

  6. Q – 2 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 A.M. to 10:00 P.M. Management wants to develop a schedule for part-time employees that will minimize labor costs and still provide excellent customer service. The average 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.

  7. Q – 2 cont’d

  8. Q – 2 cont’d 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 P.M. and works the same 4-hours-on, 1-hours-off, 4-hours-on pattern. • Develop a minimum-cost schedule for part-time employees. • 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. • 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?

  9. Q – 3 Data envelopment analysis can measure the relative efficiency of a group of hospitals. The following data from a particular study involving seven teaching hospitals include three input measures and four output measures. a. Evaluate the relative efficiency scores of all hospitals. b. Is hospital D relatively inefficient? What is a reference set?

  10. Q – 3 cont’d

  11. Q – 3 cont’d

  12. Q – 3 cont’d c. Considering hospital A, show the primal and dual formulations. d. How about the complementary slackness condition between the two formulations?

  13. Q – 4 Consider a game in which each player selects one of three colored poker ships: red, white or blue. The players must select a chip without knowing the color of the chip selected by the other player. The players then reveal their chips. Payoffs to Player A in dollars are as follows:

  14. Q – 4 cont’d • What is the optimal strategy for each player? • What is the value of the game? • Would you prefer to be Player A or Player B? Why?

  15. Q – 5 • The Manager of the Oak Hills Swimming Club is planning the club’s swimming team program. The first team practice is scheduled for May 1. The activities, their immediate predecessors, and the activity time estimates (in weeks) are as follows. • Draw a project network. • Develop an activity schedule. • What are the critical activities, and what is the expected project completion time? • If the club manager plans to start the project on February 1, what is the probability the swimming program will be ready by the scheduled May 1 date (19 weeks)? Should the manager begin planning the swimming program before February 1?

  16. Q – 5 cont’d

  17. EMGT 501 HW Solutions Chapter 10 - 3 Chapter 10 - 7 Chapter 10 - 17

  18. Ch. 10 – 3 a. r = dm = 20(5) = 100 Since , both inventory position and inventory on hand equal 100. b. r = dm = 20(15) = 300 Since , both inventory position and inventory on hand equal 300.

  19. c. r = dm = 20(25) = 500 Inventory position reorder point = 500. One order of Q* = 400 is outstanding. The on-hand inventory reorder point is 500 - 400 = 100. d. r = dm = 20(45) = 900 Inventory position reorder point = 900. Two orders of Q* = 400 are outstanding. The on-hand inventory reorder point is 900 - 2(400) = 100.

  20. Ch. 10 – 7 Where is the revised order quantity for the new carrying charge . Thus

  21. Ch. 10 – 17 EOQ Model Total Cost Planned Shortage Model

  22. Total Cost • Cost Reduction with Backorders allowed • $848.53 - 791.25 = $57.28 (6.75%) • Both constraints are satisfied: • 1. S / Q = 39.56 / 303.32 = 0.13 • Only 13% of units will be backordered. • Length of backorder period = S / d = 39.56 / (800/250) • = 12.4 days