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To find the constant rate of change, we can calculate the difference in the number of parts produced divided by the difference in time.
The difference in the number of parts is 3375 - 1350 = 2025.
The difference in time is 5 - 2 = 3.
Therefore, the constant rate of change of parts produced per hour is 2025 / 3 = 675 parts per hour.
So, the correct answer is 675 parts per hour.