Suppose that a scheduling problem has 11 tasks and is to be completed by 5 processors. When you add up the times to complete the tasks, you get a total of 24 hours. Given this information, we know that the optimal processing time is...
Options:
No more than 11/5 hours
At least 24/11 hours
No more than 24/11 hours
No more than 24/5 hours
At least 11/5 hours
At least 24/5 hours

In this scheduling problem, there are 11 tasks to be completed by 5 processors, with a total of 24 hours of task time. To determine the **optimal processing time**, we're concerned with the **minimum possible time** in which all processors could ideally complete the tasks. This is found by dividing the total task time by the number of processors, assuming the load can be perfectly distributed among the processors.

The optimal processing time per processor, given that the total task time is 24 hours and there are 5 processors, is:

\[
\text{Optimal Processing Time} = \frac{\text{Total Task Time}}{\text{Number of Processors}} = \frac{24}{5} = 4.8 \text{ hours}
\]

Thus, the total processing time for the entire set of tasks will be no more than 4.8 hours, which corresponds to the option:

**No more than 24/5 hours.**

### Would you like any further details or clarifications?

Here are some follow-up questions to deepen your understanding:

1. How does load balancing affect the total processing time in this context?
2. What happens if the tasks are not evenly divisible among the processors?
3. Can the total processing time be lower than the optimal processing time?
4. How do different scheduling algorithms affect the processing time distribution?
5. What would the optimal processing time be if there were 10 processors?

**Tip**: When solving problems like this, always divide the total task time by the number of processors to estimate the lower bound for the processing time.

Suppose that a scheduling problem has 11 tasks and is to be completed by 5 processors. When you add up the times to complete the tasks, you get a total of 24 hours. Given this information, we know that the optimal processing time is...

Discover how to calculate the optimal processing time for a scheduling problem involving 11 tasks distributed among 5 processors with a total task time of 24 hours. Learn key scheduling and load balancing concepts and the formula to determine the processing time per processor. Suitable for students in Grades 10-12.

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