A typical 24-hour activity of a mobile crusher plant is shown. The utilization, in %, of the plant, is ______. (round off up to 2 decimals)
Understand the Problem
The question asks to calculate the utilization percentage of a mobile crusher plant during a 24-hour period based on the breakdown of hours into different categories. The key task is to identify the total working hours in relation to the overall hours.
Answer
The utilization of the plant is $12.50\%$.
Answer for screen readers
The utilization of the plant is 12.50%.
Steps to Solve
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Identify Total Hours The total hours in a day are 24.
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Analyze the Activity Chart From the chart, identify each category and count their durations:
- Working Hours (black): 3 hours (from 16 to 19)
- Scheduled Maintenance Hours (yellow): 1 hour (from 20 to 21)
- Break Down Hours (blue): 1 hour (from 6 to 7)
- Idle Hours (white): The remaining hours (0 to 6, 7 to 8, 9 to 16, and 21 to 24)
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Calculate Total Working Hours The total working hours is simply the hours categorized as working:
- Working Hours = 3 hours
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Calculate the Utilization Percentage The utilization percentage can be calculated using the formula: $$ \text{Utilization} = \left( \frac{\text{Working Hours}}{\text{Total Hours}} \right) \times 100 $$ Substituting in the values: $$ \text{Utilization} = \left( \frac{3}{24} \right) \times 100 = 12.5% $$
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Round the Result Finally, round off the result to two decimal places, which is: $$ 12.50% $$
The utilization of the plant is 12.50%.
More Information
The utilization percentage indicates how effectively the mobile crusher plant operates within a 24-hour period. A higher percentage signifies better efficiency.
Tips
- Misidentifying the categories from the chart or missing certain hours may lead to inaccurate calculations. Carefully reviewing each hour can help avoid this.
- Not rounding off to two decimal places as required by the question can lead to incorrect answers.
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