How many machines are needed?

Consider two product varieties, A and B, made in the plant. Each is projected to have demands of 8,000 and 10,000 units, respectively, and is made in lot sizes of 100 and 120 units, respectively.

The production process takes 8 minutes of processing time per unit for product A and 10 minutes for product B on the same machine. There is a 1-hour setup time for product A and a 1.5-hour setup time for product B. The machine operates 8 hours per day throughout the year, only on weekdays.

The plant manager has planned a 12% cushion.

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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