Madhur L

verified

This problem has been solved

by verified expert Madhur L

100% free to try

Question

Q1. A small project is composed of 9 activities whose time estimates are listed in the table below. Activities are identified by their beginning (i) and ending (j) node numbers. (show your work for each part). Activity | Estimated Duration in Days i-j | Optimistic | Most Likely | Pessimistic 1-4 | 17 | 20 | 23 1-5 | 7 | 10 | 13 2-3 | 8 | 9 | 16 2-4 | 16 | 19 | 22 3-7 | 11 | 14 | 17 3-8 | 2 | 3 | 16 4-7 | 2 | 5 | 8 4-8 | 1 | 4 | 7 5-6 | 12 | 15 | 18 (a) (15 pts.) Draw the project network and find critical activities and slack times and project duration. (b) (10 pts.) What is the maximum number of activities that can be delayed for the project to be on-time? Explain why. (c) (10 pts.) Calculate the total usable slack time without delaying the project duration. (d) (10 pts.) What is the probability that the project will be completed at least 3 days earlier than expected? (e) (10 pts.) What is the probability that the project will be completed no more than 3 days later than expected? (f) (10 pts.) What is the probability that the project will be completed between 3 days earlier and 3 days later than expected?

          Q1. A small project is composed of 9 activities whose time estimates are listed in the table below. Activities are identified by their beginning (i) and ending (j) node numbers. (show your work for each part).

Activity | Estimated Duration in Days
i-j | Optimistic | Most Likely | Pessimistic
1-4 | 17 | 20 | 23
1-5 | 7 | 10 | 13
2-3 | 8 | 9 | 16
2-4 | 16 | 19 | 22
3-7 | 11 | 14 | 17
3-8 | 2 | 3 | 16
4-7 | 2 | 5 | 8
4-8 | 1 | 4 | 7
5-6 | 12 | 15 | 18

(a) (15 pts.) Draw the project network and find critical activities and slack times and project duration.
(b) (10 pts.) What is the maximum number of activities that can be delayed for the project to be on-time? Explain why.
(c) (10 pts.) Calculate the total usable slack time without delaying the project duration.
(d) (10 pts.) What is the probability that the project will be completed at least 3 days earlier than expected?
(e) (10 pts.) What is the probability that the project will be completed no more than 3 days later than expected?
(f) (10 pts.) What is the probability that the project will be completed between 3 days earlier and 3 days later than expected?

Show more…

Q1. A small project is composed of 9 activities whose time estimates are listed in the table below. Activities are identified by their beginning (i) and ending (j) node numbers. (show your work for each part).

Activity | Estimated Duration in Days
i-j | Optimistic | Most Likely | Pessimistic
1-4 | 17 | 20 | 23
1-5 | 7 | 10 | 13
2-3 | 8 | 9 | 16
2-4 | 16 | 19 | 22
3-7 | 11 | 14 | 17
3-8 | 2 | 3 | 16
4-7 | 2 | 5 | 8
4-8 | 1 | 4 | 7
5-6 | 12 | 15 | 18

(a) (15 pts.) Draw the project network and find critical activities and slack times and project duration.
(b) (10 pts.) What is the maximum number of activities that can be delayed for the project to be on-time? Explain why.
(c) (10 pts.) Calculate the total usable slack time without delaying the project duration.
(d) (10 pts.) What is the probability that the project will be completed at least 3 days earlier than expected?
(e) (10 pts.) What is the probability that the project will be completed no more than 3 days later than expected?
(f) (10 pts.) What is the probability that the project will be completed between 3 days earlier and 3 days later than expected?

Added by Leslie P.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Madhur L

08/14/2023

Step 1

The expected duration (TE) and standard deviation (SD) can be calculated using the following formulas: TE = (Optimistic + 4 * Most Likely + Pessimistic) / 6 SD = (Pessimistic - Optimistic) / 6 Show more…

Show all steps

lock

Thanks for your feedback!

A small project is composed of 9 activities whose time estimates are listed in the table below. Activities are identified by their beginning (i) and ending (j) node numbers. (show your work for each part). Activity | Estimated Duration in Days i-j | Optimistic | Most Likely | Pessimistic 1-4 | 17 | 20 | 23 1-5 | 7 | 10 | 13 2-3 | 8 | 9 | 16 2-4 | 16 | 19 | 22 3-7 | 11 | 14 | 17 3-8 | 2 | 3 | 16 4-7 | 2 | 5 | 8 4-8 | 1 | 4 | 7 5-6 | 12 | 15 | 18 (a) (15 pts.) Draw the project network and find critical activities and slack times and project duration. (b) (10 pts.) What is the maximum number of activities that can be delayed for the project to be on-time? Explain why. (c) (10 pts.) Calculate the total usable slack time without delaying the project duration. (d) (10 pts.) What is the probability that the project will be completed at least 3 days earlier than expected? (e) (10 pts.) What is the probability that the project will be completed no more than 3 days later than expected? (f) (10 pts.) What is the probability that the project will be completed between 3 days earlier and 3 days later than expected?

Play audio

Feedback

Powered by NumerAI

Madhur L and 80 other subject Intro Stats / AP Statistics educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Recommended Videos

Recommended Textbooks

Transcript

00:01 Hello students for the given problem we are provided with the project network and critical path.

00:06 So first we need to calculate the expected duration which is denoted by te which is equal to a plus 4m plus b divided by 6 and variance for each activity using the provided optimistic alpha that is most likely m and pessimistic b time estimate.

00:25 So variance equal to b minus a the whole square upon 32.

00:28 Now we will use the provided data to calculate it.

00:32 So te is equal to 114 upon 6 which is equal to 9.

00:42 Next we need to construct the project network diagram with the code representing the activity and directed edges representing the sequence.

00:51 Next we need to perform the forward pass to calculate the earliest start that is easiest and earliest finish.

00:58 So for activity 1 to 4 earliest start is equal to 0 and earliest finish is equal to te which is equal to 9.

01:09 For subsequent activity es that is early start of the current activity is the ef of the deciding activity and ef is es plus te.

01:22 So performing the backward pass to calculate the latest start and latest finish time for each activity.

01:27 So for last activity 5 to 6 lf is equal to ef and ls is equal to lf minus te.

01:39 Now we will calculate the slack time.

01:45 Slow slack is equal to ls minus es and slack is also equal to lf minus ef...

Ace is your personal tutor. It breaks down any question with clear steps so you can learn.

Start Using Ace