Answer :
approximately 71,752 machines are needed to meet the projected demand with a 12% cushion.To determine the number of machines needed, we need to calculate the maximum production rate per machine. For product A, the processing time per unit is 8 minutes, and for product B, it is 10 minutes. Assuming an 8-hour workday, the total available production time per machine is 8 hours x 60 minutes = 480 minutes.
For product A, the lot size is 100 units, so the setup time per lot is 1 hour = 60 minutes. Therefore, the maximum production time per lot is 480 - 60 = 420 minutes.
For product B, the lot size is 120 units, so the setup time per lot is 1.5 hours = 90 minutes. Therefore, the maximum production time per lot is 480 - 90 = 390 minutes.
Considering the projected demand and a 12% cushion, we can calculate the number of lots needed for each product:
For product A: (8000 units + 12%) / 100 units = 89.6 lots.
For product B: (10000 units + 12%) / 120 units = 85.6 lots.
Since we cannot have a fractional number of lots, we need to round up to the nearest whole number:
For product A: 90 lots.
For product B: 86 lots.
To calculate the number of machines needed, we divide the number of lots by the maximum number of lots that can be produced by one machine:
For product A: 90 lots / 420 minutes = 0.214 lots/minute.
For product B: 86 lots / 390 minutes = 0.221 lots/minute.
Considering the slower production rate for product B, we need to choose the higher value, which is 0.221 lots/minute.
Finally, to determine the number of machines needed, we divide the total demand by the production rate per minute:
Number of machines = (8000 + 10000) units / (0.221 lots/minute) = 71751.6 machines.
Therefore, approximately 71,752 machines are needed to meet the projected demand with a 12% cushion.
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