Q1 (100 points) A factory manufactures power drills. It is December and the projected demand for the next five months is Demand (Aggregate units) Workdays 20 2630 18 3850 21 7270 22 2790 20 4440 Assume normal working day has 8 work hours. Hiring costs are $375 per worker and firing costs are $650 per worker. Holding costs are $4 per unit held per month. Backlog costs are $8 per unit help per month. Assume it takes an average of 2 hours for one worker to assemble one product. The end inventory for December is 775, and the plant aims to have at most 900 units on hand and at most 220 units of backlog by the end of May. Assume the current work force level in December is 33 workers. Month January February March April May The manufacturer would like to identify a cost-efficient plan by minimizing labor and holding costs. a) (25 points) Please write the mathematical formulation (i.e. linear program) to solve this aggregate planning problem. What is the planning strategy for this manufacturer? b) (30 points) Solve the problem using MS Excel's Solver. c) (30 points) Solve the problem in parts (a) and (b) again assuming a "level" production strategy. Which strategy would you recommend the manufacturer? d) (15 points) Solve the problem again using the charting/graphical approach. Is this solution feasible? Is it optimal? How does your solution compare to solutions in parts (b) and (c)?

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