Questions: (e) Use the next-fit decreasing (NFD) heuristic to find how many typists are needed if the typing needs to be finished in one hour. Do the same for the worst-fit decreasing (WFD) heuristic. typists needed (NFD): typists needed (WFD): (f) Is there an optimal solution for finishing the typing in one hour? An optimal schedule with 12 typists exists.

To solve the problem using the next-fit decreasing (NFD) and worst-fit decreasing (WFD) heuristics, we need to understand the context of the problem, which involves scheduling tasks (in this case, typing) to be completed within a given time frame (one hour) using a certain number of typists.

1. Sort the Tasks: First, sort the typing tasks in decreasing order of their duration.
2. Assign Tasks: Start with the first typist and assign tasks to them until adding another task would exceed one hour. Then, move to the next typist and continue assigning tasks in the same manner.

The number of typists needed using the NFD heuristic is determined by how many times you need to move to a new typist when the current one cannot accommodate another task without exceeding the one-hour limit.

1. Sort the Tasks: Again, sort the typing tasks in decreasing order of their duration.
2. Assign Tasks: Assign each task to the typist who currently has the least amount of work (i.e., the most available time left before reaching one hour).

The number of typists needed using the WFD heuristic is determined by how many typists are required to accommodate all tasks without any typist exceeding the one-hour limit.

The problem states that an optimal schedule with 12 typists exists. This means that, theoretically, it is possible to complete all tasks within one hour using exactly 12 typists. The optimal solution would be the one that uses the fewest number of typists while still completing all tasks within the given time frame.

• Typists needed (NFD): The number of typists required using the next-fit decreasing heuristic.
• Typists needed (WFD): The number of typists required using the worst-fit decreasing heuristic.
• Optimal Solution: An optimal schedule exists with 12 typists.

To provide specific numbers for NFD and WFD, the actual task durations and their sorted order would be needed. However, the process described outlines how to determine the number of typists for each heuristic.