Problem 1. (20 pts.) Jerry is a production manager of company XYZ that produces packaged fruit...

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Problem 1. (20 pts.) Jerry is a production manager of company XYZ that produces packaged fruit baskets. The company employs agency personnel from a professional staffing firm. The contract for a number of employees is signed at the beginning of the year and the number of employees cannot change during the year. The marketing department provided a quarterly demand estimate (in units of packaged fruit baskets) for the next year along with the number of working days each quarter. Please help Jerry determine the minimum number of employees XYZ will need to avoid any shortages in the forecasted demand. The current number of agency employees is 40; the last quarter production was 22,080 units; the working number of days in the last quarter was 92. The inventory at the end of last year is 200. (a) (10 pts.) Use the constant workforce plan to determine number of agencies required for the next year. (The table below is provided for your convenience. You can use as many columns as you need). Quarter #Working Days Demand 1st 89 17,000 2nd 90 23,000 3rd 91 26,000 4th 88 20,000 (b) (10 pts.) Suppose the constant workforce plan determined in part (a) is going to be deployed, and each agency can work up to 8 hours as regular production time each day (assuming the 22,080 units in the problem statement are produced by the 40 workers working exactly 8 hours each day during the quarter). Assume that regular hourly rate XYZ pays to the staffing company is $12 per agency. Assume each agency can work overtime at 1.5 rate. The overtime cannot exceed 25% of the regular production time. Also, XYZ needs to pay tax for the existing inventory at the end of each quarter. The quarterly tax for each item in inventory is $2. Formulate an integer program to find minimum cost plan for the upcoming year. Problem 1. (20 pts.) Jerry is a production manager of company XYZ that produces packaged fruit baskets. The company employs agency personnel from a professional staffing firm. The contract for a number of employees is signed at the beginning of the year and the number of employees cannot change during the year. The marketing department provided a quarterly demand estimate (in units of packaged fruit baskets) for the next year along with the number of working days each quarter. Please help Jerry determine the minimum number of employees XYZ will need to avoid any shortages in the forecasted demand. The current number of agency employees is 40; the last quarter production was 22,080 units; the working number of days in the last quarter was 92. The inventory at the end of last year is 200. (a) (10 pts.) Use the constant workforce plan to determine number of agencies required for the next year. (The table below is provided for your convenience. You can use as many columns as you need). Quarter #Working Days Demand 1st 89 17,000 2nd 90 23,000 3rd 91 26,000 4th 88 20,000 (b) (10 pts.) Suppose the constant workforce plan determined in part (a) is going to be deployed, and each agency can work up to 8 hours as regular production time each day (assuming the 22,080 units in the problem statement are produced by the 40 workers working exactly 8 hours each day during the quarter). Assume that regular hourly rate XYZ pays to the staffing company is $12 per agency. Assume each agency can work overtime at 1.5 rate. The overtime cannot exceed 25% of the regular production time. Also, XYZ needs to pay tax for the existing inventory at the end of each quarter. The quarterly tax for each item in inventory is $2. Formulate an integer program to find minimum cost plan for the upcoming year.