Question 3. (40 points) A local firm manufactures children's toys. The sales are somewhat seasonal, and the firm is planning its workforce level and production level on June 30st for

the next six months. Table below shows the demand forecasts. During a 26 workday period where there were 100 workers, the company produced 12,000 toys.The hire cost and layoff cost are $125 and $300, respectively. Also, the holding cost per toy per month is 75 cents. As of Jun 30, the company has 86 workers and expects to have 4,500 toys in stock. The company also desires to have a minimum buffer inventory of 1,000 toys each month. The company plans tostart January with 3,000 toys on hand. a) Base on the given information, find the minimum number of constant workforce for the company over the next six months and determine the holding, hiring, and firing costs associated with that plan. b) Formulate the problem constraints)as a linear program. (clearly define the decision variables and c) Develop a spreadsheet to find the optimal solution for this problem. (You need to submit your excel file for this part of the question. You also need to present your obtained optimal solution and explain your findings in your answer sheet (the PDF file that you submit)). d) Suppose that training a new worker takes one month. This means that a worker cannot start the work until the training period is completed. What constraint(s) do you need to addt he LP you developed in part b? e) How will the assumption in part d affect your solution obtained in part c? (create a separateworksheet to show your work for this part)

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