A bottling machine has a theoretical capacity of 100 bottles per minute. During every ten hour shift it operates continuously except for when it is shut down twice each shift for 30 minutes each time for cleaning, inspection, and lubrication.
What is its rated capacity?
While bottling machine is running it averages 8% downtime for over the course of the remaining time of the shift, then the rated capacity is 506,000 bottles per shift.
The bottling machine operates for 10 hours during each shift, but is shut down once for 45 minutes for cleaning, inspection, and lubrication. Therefore, the machine operates for a total of 9 hours and 15 minutes per shift.
During the operating time of 9 hours and 15 minutes, the machine has an average downtime of 8%, or 0.08. This means that the machine operates effectively for 92% of the time, or 0.92.
The theoretical capacity of the machine is 100 bottles per minute. Therefore, the rated capacity of the machine per shift is:
100 bottles/minute * 60 minutes/hour * 9.25 hours * 0.92 = 506,100 bottles
Rounding this value to the nearest 1000, we get a rated capacity of 506,000 bottles per shift.
In summary, to calculate the rated capacity of the bottling machine per shift, we first determined the total operating time, which is 9 hours and 15 minutes. We then calculated the effective operating time by subtracting the average downtime of 8%.
Finally, we multiplied the effective operating time by the theoretical capacity of the machine to obtain the rated capacity per shift, which was rounded to the nearest 1000.
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