2. Staffing at a Distribution Center (35 points) A large distribution center is open for business from 8AM to 5PM on Mondays through Fridays. The center has a number of full-time workers. In addition, the manager of the center wants to increase the quality of customer service by adding some part-time workers. Based on her estimates, the minimum number of part-time workers needed varies hour-by-hour as summarized below. Time 8-9 9-10 10 - 11 11 - 12 12-1 1-2 2-3 3-4 4-5 Minimum #required 5 12 15 12 11 18 17 19 14 Part-time workers will work 4-hour shifts. a. State the decisions to be made, the objective and the constraints in words using = or = in the constraints. (Submit copy of Handwritten answer, 5 pts) b. Set each of your decisions in (a) equal to 10 and then compute the corresponding numerical values for your objective and constraints. Is this solution feasible and what is the corresponding value of the objective? (Submit copy of Handwritten answer, 5 pts) c. Define your decisions in part (a) algebraically as decision variables. Then, using your objective and constraints in part (a), formulate the problem as an algebraic linear optimization model. (Submit copy of Handwritten answer, 5 pts) d. Write your algebraic model from (c) as an EXCEL model. (Submit answer in an Excel file, 5 pts) e. Using your Excel model with a value of 10 for each decision cell, compute the values for the objectives and the constraints. Do you get the same values as in part (b)? (Submit answer in an Excel file, 5 pts) f. Using your EXCEL model and Solver, optimize the staffing. What is the minimum number of part-time workers required? What hours would you recommend that each part-time person works? (Submit copy of Handwritten answer, 5 pts) g. In your optimized model, what hours of the day have surplus workers? What hour of the day has the largest surplus? (Submit copy of Handwritten answer, 5 pts) 2. Staffing at a Distribution Center (35 points) A large distribution center is open for business from 8AM to 5PM on Mondays through Fridays. The center has a number of full-time workers. In addition, the manager of the center wants to increase the quality of customer service by adding some part-time workers. Based on her estimates, the minimum number of part-time workers needed varies hour-by-hour as summarized below. Time 8-9 9-10 10 - 11 11 - 12 12-1 1-2 2-3 3-4 4-5 Minimum #required 5 12 15 12 11 18 17 19 14 Part-time workers will work 4-hour shifts. a. State the decisions to be made, the objective and the constraints in words using = or = in the constraints. (Submit copy of Handwritten answer, 5 pts) b. Set each of your decisions in (a) equal to 10 and then compute the corresponding numerical values for your objective and constraints. Is this solution feasible and what is the corresponding value of the objective? (Submit copy of Handwritten answer, 5 pts) c. Define your decisions in part (a) algebraically as decision variables. Then, using your objective and constraints in part (a), formulate the problem as an algebraic linear optimization model. (Submit copy of Handwritten answer, 5 pts) d. Write your algebraic model from (c) as an EXCEL model. (Submit answer in an Excel file, 5 pts) e. Using your Excel model with a value of 10 for each decision cell, compute the values for the objectives and the constraints. Do you get the same values as in part (b)? (Submit answer in an Excel file, 5 pts) f. Using your EXCEL model and Solver, optimize the staffing. What is the minimum number of part-time workers required? What hours would you recommend that each part-time person works? (Submit copy of Handwritten answer, 5 pts) g. In your optimized model, what hours of the day have surplus workers? What hour of the day has the largest surplus? (Submit copy of Handwritten answer, 5 pts)