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 is asking to calculate the utilization percentage of a mobile crusher plant based on its activity over a 24-hour period as depicted in the given chart. To solve this, we will determine the total working hours compared to the total hours and then calculate the percentage.
Answer
The utilization of the plant is $12.50\%$.
Answer for screen readers
The utilization of the plant is $12.50%$.
Steps to Solve
- Identify Working Hours From the chart, the working hours (black color) are observed from hours 0-1, 16-17, and 19-20. The total working hours can be calculated as:
- From 0 to 1: 1 hour
- From 16 to 17: 1 hour
- From 19 to 20: 1 hour
Total working hours = $1 + 1 + 1 = 3$ hours.
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Identify Total Hours The total observation period is 24 hours.
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Calculate Utilization Percentage Utilization percentage can be calculated using the formula:
$$ \text{Utilization} (%) = \left( \frac{\text{Total Working Hours}}{\text{Total Hours}} \right) \times 100 $$
Substituting the values we have:
$$ \text{Utilization} (%) = \left( \frac{3}{24} \right) \times 100 $$
- Perform Calculation Calculating the above expression:
$$ \text{Utilization} (%) = \left( \frac{3}{24} \right) \times 100 = 12.5 % $$
The utilization of the plant is $12.50%$.
More Information
Utilization percentage indicates the efficiency of the plant over a given period. A higher percentage reflects better utilization, while a lower percentage may suggest inefficiencies or downtime.
Tips
- Confusing the active hours with scheduled maintenance or breakdown hours. It's important to only count the working hours.
- Not converting the fraction to a percentage correctly. Remember to multiply by 100 after dividing.
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