Unimart is a copy center and office supplies seller at IU's Al building. Currently, they are preparing a large oder of Lecture Notes for 2 departments: Department of English, Department of Physics, Department of Mathematics. The center operates 2 four-hour shift per day, 6 days per week, 52 weeks per year. The manager believes that a capacity cushion of 20% is the best. The center currently has 3 copy machines and makes multiple copies (the lot size) of each report. The processing time to run, collate, and bind each copy depends on, among other factors, the number of pages, as shown in the below table: Item English Dept. Physics Dept. Mathematics Dept. Annual demand, D (copies) 3,200 4,700 4,300 Standard processing time, p (hours/copy) 0.70 0.60 0.50 Average lot size, Q (copies/lot) 100 110 Standard setup time, s (hours) 0.25 0.40 0.30 120 a. What is the minimum number of machines needed at the copy center to meet the forecast annual of these 3 departments? (20 points) b. If the center currently has 3 copy machines, how many additional machines should be bought so that Unimart can guarantee the supply to these 3 departments? (15 points) c. If the center currently has 2 copy machines, what is the capacity gap? (15 points) Unimart is a copy center and office supplies seller at IU's Al building. Currently, they are preparing a large oder of Lecture Notes for 2 departments: Department of English, Department of Physics, Department of Mathematics. The center operates 2 four-hour shift per day, 6 days per week, 52 weeks per year. The manager believes that a capacity cushion of 20% is the best. The center currently has 3 copy machines and makes multiple copies (the lot size) of each report. The processing time to run, collate, and bind each copy depends on, among other factors, the number of pages, as shown in the below table: Item English Dept. Physics Dept. Mathematics Dept. Annual demand, D (copies) 3,200 4,700 4,300 Standard processing time, p (hours/copy) 0.70 0.60 0.50 Average lot size, Q (copies/lot) 100 110 Standard setup time, s (hours) 0.25 0.40 0.30 120 a. What is the minimum number of machines needed at the copy center to meet the forecast annual of these 3 departments? (20 points) b. If the center currently has 3 copy machines, how many additional machines should be bought so that Unimart can guarantee the supply to these 3 departments? (15 points) c. If the center currently has 2 copy machines, what is the capacity gap? (15 points)