Part C – 30 Points
The Ministry of Public Works, in collaboration with local organizations, is planning a project to implement a potable water network in various rural communities across the country. Given the complexity of the initiative—which includes technical, administrative, and social tasks—it has been decided to use the PERT approach to better plan and control the uncertainty in execution times.
In Sheet C of your dataset (image), all project activities are listed along with their respective precedencies and duration distribution (in days): optimistic time (OT), most likely time (MLT), and pessimistic time (PT).
Questions
Develop the project diagram according to the PERT methodology.
Determine ES (Early Start), EF (Early Finish), LS (Late Start), and LF (Late Finish). Indicate the critical path, its estimated duration, and variance.
Calculate the probability that the project will be completed in 90 days or less. Now, if it is required that the project be completed by day 75 with 95% confidence, what should be the maximum allowed variance (of the critical path) to meet that requirement?
There is an opportunity for an international financing contract that offers a $100 bonus if the potable water network implementation project is completed on or before a specific date, and a $240 penalty if it is completed after that date. On which day should the project be completed to be indifferent to the contract terms? Now, if the contract sets the completion date as day 81 and applies the same bonus, what penalty should be set to remain indifferent?
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