Question 2 (40 points) The Sinclair Corporation is opening a new 24-hour cafeteria in Tupelo, MS. The facility will operate 5 days a week, opening at 6:00 A.M. every Wednesday and closing at 6:00 A.M. on the following Monday. For convenience in planning, each 24-hour workday is broken down into six 4-hour time blocks (or periods), as shown in the table below. This table also shows the minimum number of workers needed during each of these time blocks every day, in order to operate the cafeteria efficiently and provide high quality service to its customers. Time Block Minimum No. of Employees Needed 7 2 12 3 Hours 6:00 AM 10:00 A.M. 10:00 A.M. - 2:00 P.M. 2:00 P.M. - 6:00 P.M. 6:00 P.M. - 10:00 P.M. 10:00 P.M. -2:00 A.M. 2:00 A.M. - 6:00 A.M. 4 4 15 5 10 6 3 Each employee will work a continuous 8-hour full shift per day, starting his/her workday at the beginning of any of the six time blocks shown above. Management wishes to minimize the total workforce size necessary for satisfying the minimum worker requirements in the various time blocks or periods, as outlined in the table above. Question 2 (Continued) (a) Formulate a linear programming model (i.e. clearly and precisely define all decision variables used, then construct the objective function and all constraints in algebraic format) for finding a solution for Sinclair's employee scheduling problem. (b) Find the optimal solution to your model in part (a) using Excel/Solver and generate the associated Sensitivity Report. What is the minimum total workforce size and the employee schedule? (c) If, during the 10:00 P.M. 2:00 A.M. time block, each day, a minimum of 5, instead of 10 workers are needed, what would be the effect on the total workforce size? (d) Resetting the 10 P.M. - 2 A.M. worker need back to its original value, how would the total workforce size be affected if 15, instead of 12 employees, at a minimum, are required to be available during the period 10:00 A.M. 2:00 P.M. each day? Do not solve the model again for answering parts (c) and (d)]