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In a PERT network the expected time to finish one activity is 22 days and variance of the activity is 16 days. The ratio of pessimistic time to optimistic time if most likely time for finishing the activity is 23 days is
- a)4
- b)8
- c)10
- d)12
Correct answer is option 'A'. Can you explain this answer?
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In a PERT network the expected time to finish one activity is 22 days ...
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In a PERT network the expected time to finish one activity is 22 days ...
PERT Network
- PERT (Program Evaluation and Review Technique) is a project management technique used to analyze and represent the tasks involved in completing a project.
- It is a network-based scheduling method that considers both the time and resources required to complete each activity in a project.
Expected Time and Variance
- In a PERT network, each activity is assigned an expected time (te) and a variance (σ^2).
- The expected time represents the most likely time required to complete the activity.
- The variance provides a measure of the uncertainty or variability associated with the expected time.
Ratio of Pessimistic Time to Optimistic Time
- In PERT, the expected time (te) is calculated as a weighted average of the optimistic time (to), most likely time (tm), and pessimistic time (tp) for each activity.
- The formula to calculate expected time is: te = (to + 4tm + tp) / 6
- Given that the expected time for the activity is 22 days, we can substitute this value into the formula and solve for the ratio of pessimistic time (tp) to optimistic time (to).
Calculation
- te = (to + 4tm + tp) / 6
- 22 = (to + 4(23) + tp) / 6
- 132 = to + 92 + tp
- to + tp = 132 - 92
- to + tp = 40
- We are given that the variance (σ^2) of the activity is 16 days.
- The variance is calculated using the formula: σ^2 = ((tp - to) / 6)^2
- Substituting the given values into the formula, we can solve for tp/to.
Calculation
- 16 = ((tp - to) / 6)^2
- 4 = (tp - to) / 6
- 24 = tp - to
- tp = 24 + to
- Now we can substitute the value of tp into the equation to + tp = 40.
Calculation
- to + (24 + to) = 40
- 2to = 40 - 24
- 2to = 16
- to = 8
- Finally, the ratio of pessimistic time to optimistic time is tp/to = (24 + to) / to = (24 + 8) / 8 = 32 / 8 = 4.
Answer
- Therefore, the correct answer is option A) 4.
- PERT (Program Evaluation and Review Technique) is a project management technique used to analyze and represent the tasks involved in completing a project.
- It is a network-based scheduling method that considers both the time and resources required to complete each activity in a project.
Expected Time and Variance
- In a PERT network, each activity is assigned an expected time (te) and a variance (σ^2).
- The expected time represents the most likely time required to complete the activity.
- The variance provides a measure of the uncertainty or variability associated with the expected time.
Ratio of Pessimistic Time to Optimistic Time
- In PERT, the expected time (te) is calculated as a weighted average of the optimistic time (to), most likely time (tm), and pessimistic time (tp) for each activity.
- The formula to calculate expected time is: te = (to + 4tm + tp) / 6
- Given that the expected time for the activity is 22 days, we can substitute this value into the formula and solve for the ratio of pessimistic time (tp) to optimistic time (to).
Calculation
- te = (to + 4tm + tp) / 6
- 22 = (to + 4(23) + tp) / 6
- 132 = to + 92 + tp
- to + tp = 132 - 92
- to + tp = 40
- We are given that the variance (σ^2) of the activity is 16 days.
- The variance is calculated using the formula: σ^2 = ((tp - to) / 6)^2
- Substituting the given values into the formula, we can solve for tp/to.
Calculation
- 16 = ((tp - to) / 6)^2
- 4 = (tp - to) / 6
- 24 = tp - to
- tp = 24 + to
- Now we can substitute the value of tp into the equation to + tp = 40.
Calculation
- to + (24 + to) = 40
- 2to = 40 - 24
- 2to = 16
- to = 8
- Finally, the ratio of pessimistic time to optimistic time is tp/to = (24 + to) / to = (24 + 8) / 8 = 32 / 8 = 4.
Answer
- Therefore, the correct answer is option A) 4.
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In a PERT network the expected time to finish one activity is 22 days and variance of the activity is 16 days. The ratio of pessimistic time to optimistic time if most likely time for finishing the activity is 23 days isa)4b)8c)10d)12Correct answer is option 'A'. Can you explain this answer?
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In a PERT network the expected time to finish one activity is 22 days and variance of the activity is 16 days. The ratio of pessimistic time to optimistic time if most likely time for finishing the activity is 23 days isa)4b)8c)10d)12Correct answer is option 'A'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about In a PERT network the expected time to finish one activity is 22 days and variance of the activity is 16 days. The ratio of pessimistic time to optimistic time if most likely time for finishing the activity is 23 days isa)4b)8c)10d)12Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a PERT network the expected time to finish one activity is 22 days and variance of the activity is 16 days. The ratio of pessimistic time to optimistic time if most likely time for finishing the activity is 23 days isa)4b)8c)10d)12Correct answer is option 'A'. Can you explain this answer?.
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