Knott\'s Industries manufactures standard and super premium backyard swing sets.

Question

Knott's Industries manufactures standard and super premium backyard swing sets. Currently it has four identical swing-set-making machines, which are operated 250 days per year and 8 hours each day. A capacity cushion of 20 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 5 min 60 30 min Super Premium Model 0,000 25 min 30 45 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. I Knott's was able to reduce the setup time for the Super Prem um Model from 4 minutes to 30 minutes would then be enough. cumen ca acit 0) roduce 0 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. Under Standard model: (i) Total processing time required = Annual demand X standard processing time = 20,000 X 5 min =         1,00,000 min (ii) Total set up time required = (Annual demand / Average lot size) X Standard set up time per lot = (20,000 / 60) X 30 =             40,000 min Under Super Premium model: (iii) Total processing time required = Annual demand X standard processing time = 10,000 X 25 min =         2,50,000 min (iv) Total set up time required = (Annual demand / Average lot size) X Standard set up time per lot = (10,000 / 30) X 45 =             15,000 min Total Processing and Set up time required [(i) + (ii) + (iii) + (iv)] = 1,00,000 + 40,000 + 2,50,000 + 15,000 =         4,05,000 min Capacity cushion required = 20% = Total Processing and Set up time required X Capacity cushion required = 4,05,000 min X 20%             81,000 min Design capacity required = Total Processing and Set up time required - Capacity cushion required = 4,05,000 min- 81,000 min =         3,24,000 min Time available per year = 250 days X 8 hours X 60 min =         1,20,000 min Number of identical machines required = Design capacity required / Time available per year = 3,24,000 / 1,20,000 = 2.70 machines = 3 (rounded off to next whole number) = 3 machines b. Under Super Premium model: New set up time for Super Model = 30 Capacity to produce = 20000 swing sets Total processing time required = Annual demand X standard processing time = 20,000 X 25 min =         5,00,000 Total set up time required = (Annual demand / Average lot size) X Standard set up time per lot = (20,000 / 30) X 30 =             20,000 Total Processing and Set up time required = 1,00,000 + 40,000 + 5,00,000 + 20,000 =         6,60,000 Capacity cushion required = 20% = Total Processing and Set up time required X Capacity cushion required = 6,60,000 min X 20%         1,32,000 min Design capacity required = Total Processing and Set up time required - Capacity cushion required = 6,60,000 min- 1,32,000 min =         5,28,000 min Time available per year = 250 days X 8 hours X 60 min =         1,20,000 min Number of identical machines required = Design capacity required / Time available per year = 5,28,000 / 1,20,000 =                  4.40 =                        4 (rounded off )

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