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A function centre employs staff so that all necessary tasks can be completed between the end of one function and the beginning of the next function - HSC - SSCE Mathematics Standard - Question 31 - 2023 - Paper 1
Question 31
A function centre employs staff so that all necessary tasks can be completed between the end of one function and the beginning of the next function. The network dia... show full transcript
Worked Solution & Example Answer:A function centre employs staff so that all necessary tasks can be completed between the end of one function and the beginning of the next function - HSC - SSCE Mathematics Standard - Question 31 - 2023 - Paper 1
Step 1
Find the TWO critical paths.
Answer
To identify the critical paths in the given network diagram, we start by calculating the total time for each potential path from the starting tasks to the ending tasks. The critical paths are the longest paths where any delay would result in a delay in project completion.
The calculated critical paths are:
- Path 1: H → I → G → C (Total Time = 2 + 7 + 4 = 13 hours)
- Path 2: H → I → K (Total Time = 2 + 7 + 8 = 17 hours)
Thus, the two critical paths are:
- H, I, G, C
- H, I, K
Step 2
For which task should the centre hire more staff, and how long should that task take to ensure all tasks can be completed in 14 hours?
Answer
To reduce the total time along both critical paths by 3 hours, we note the following:
The current total time across the critical paths is:
- H → I → G → C: 13 hours
- H → I → K: 17 hours
To accommodate the desired completion time of 14 hours, we need to shorten the critical path that takes the longest time by 3 hours.
We see that:
- The longest path, H → I → K, currently takes 17 hours. If we decrease one task along this path by 3 hours, that will result in:
17 hours - 3 hours = 14 hours
Since task I is common in both critical paths and currently takes 7 hours, if we reduce task I’s time from 7 hours to 4 hours, all tasks will be completed in 14 hours. Thus, the centre should hire more staff for task I, and it should take 4 hours.