Knott\'s Industries manufactures standard and super premium backyard swing sets.
ID: 331851 • Letter: K
Question
Knott's Industries manufactures standard and super premium backyard swing sets. Currently it has four identical swing-set-making machines, which are operated 300 days per year and 8 hours each day. A capacity cushion of 25 percent is desired. The following information is also known: Annual Demand Standard Processing Time Average Lot Size Standard Setup Time per Lot Standard Model 20,000 7 min Super Premium Model 10,000 25 min 30 45 min 30 min a. Does Knott's have sufficient capacity to meet annual demand? Knott's does have sufficient capacity to meet annual demand because 4. machines are needed. (Enter your response rounded up to the next whole number.) b. If Knott's was able to reduce the setup time for the Super Premium Model from 45 minutes to 30 minutes, would there be enough current capacity to produce 20,000 units of each type of swing set? If Knott's was able to reduce the setup time for the Super Premium Model from 45 minutes to 30 minutes, there would not be enough capacity to produce 20,000 units of each type of swing set because 7 machines are needed. (Enter your response rounded up to the next whole number.)Explanation / Answer
a) Capacity required for Standard model = Annual demand * (Standard processing time + Standard setup time per lot / Average lot size) = 20000*(7+30/55) = 150,909 minutes
Capacity required for Super Premium model = Annual demand * (Standard processing time + Standard setup time per lot / Average lot size) = 10000*(25+45/30) = 265,000 minutes
Total time required for both models = 150909+265000 = 415909 minutes
Considering 25 % capacity cushion, total capacity required = 415909/(1-25%) = 554,545.5 minutes per year
Machines needed = Total capacity required / (300 days per year * 8 hours day * 60 minutes per hour) = 554545.5/(300*8*60) = 3.85 ~ 4 machines
Total capacity available = 4 machines * 300 days * 8 hours per day * 60 minutes per hour = 576,000 minutes
Knott's does have sufficient capacity to meet annual demand, because 4 machines are needed.
b)
Capacity required for Super Premium model = Annual demand * (Standard processing time + Standard setup time per lot / Average lot size) = 20000*(25+30/30) = 520,000 minutes
Total time required for both models = 150909+520000 = 670,909 minutes
Considering 25 % capacity cushion, total capacity required = 670909/(1-25%) = 894,545.3 minutes per year
Machines needed = Total capacity required / (300 days per year * 8 hours day * 60 minutes per hour) = 894545.3/(300*8*60) = 6.21 ~ 7 machines
If Knott's was able to reduce the setup time for the Super Premium Model from 45 minutes to 30 minutes, there would not be enough capacity to produce 20,000 units of each type of swing set, because 7 machines are needed.
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