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 for the utilization percentage of a mobile crusher plant over a 24-hour period based on the given activity chart. To solve this, we need to calculate the total working hours compared to the total available hours (24 hours) and express it as a percentage, rounding off to two decimals.

Answer

The utilization of the plant is $12.50\%$.

Steps to Solve

Identify Working Hours From the activity chart, we note the working hours are marked in black. The working hours are from hour 0 to 1, from hour 7 to 8, and from hour 19 to 20. So, total working hours are:

1 hour (0-1)
1 hour (7-8)
1 hour (19-20)

Total working hours = (1 + 1 + 1 = 3) hours.

Calculate Total Available Hours The total available hours in a day are given as 24 hours.
Calculate Utilization Percentage Utilization is calculated as the ratio of working hours to total available hours, expressed as a percentage: $$ \text{Utilization} = \left( \frac{\text{Working Hours}}{\text{Total Available Hours}} \right) \times 100 $$

Substituting in the values: $$ \text{Utilization} = \left( \frac{3}{24} \right) \times 100 $$

Compute the Final Value Carrying out the calculation: $$ \text{Utilization} = \left( \frac{3}{24} \right) \times 100 = 12.5% $$

The utilization of the plant is $12.50%$.

More Information

Utilization percentage is a critical measure in operations management, indicating how much of the available resources are being effectively used. In this case, it shows that the mobile crusher plant is utilized for 12.5% of the day.

Tips

Mistakenly counting non-working hours as working hours.
Forgetting to convert the fraction into a percentage, or miscalculating the multiplication by 100.
Rounding errors when formatting the answer to two decimal places.

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