HW8Ch 3 Project Management Homework problem 1: A competitor of Baba International, Inc. has begun marketing a new instantdeveloping film project. The predecessor information and activity time estimates in months are shown in the next column.
QUESTION
HW8Ch 3 Project Management HW
Homework problem 1:
A competitor of Baba International, Inc. has begun marketing a new instantdeveloping film project. The predecessor information and activity time estimates in months are shown in the next column.
Activity  Immediate Predecessors  Normal Time (day) 
A  —  2 
B  A  4 
C  A  2 
D  B,C  5 
E  B  6 
F  C,D,E  8 
G  E  9 
What is the critical path? What is the project complete time?
 ABEF; 25 weeks
 ABEG; 21 weeks
 ACEF; 24 weeks
Problem 2: Three recent college graduates have formed a partnership and have opened an advertising firm. Their first project consists of activities listed in the following table.
Draw the precedence diagram. What is the probability that the project can be completed in 23 days or less?
Activity  Immediate Predecessor  TIME IN DAYS  
Optimistic (a)  Most likely (m)  Pessimistic (b)  
A  – –  5  6  7  
B  – –  7  8  12  
C  A  6  8  10  
D  – –  9  12  15  
E  C  5  6  13  
F  D  5  6  7  
G  F  2  3  10  
H  B  3  4  5  
I  H  5  7  9 
 Project complete time = 31 days; Approximately 80.33%
 Project complete time = 22 days; Approximately 58.92%
 Project complete time = 22 days; Approximately 71.90%

ANSWER
 Project Management Analysis: Critical Path and Probability Assessment
Introduction

In this essay, we will explore two project management problems and analyze their critical paths and probabilities. The first problem involves a competitor of Baba International, Inc., marketing a new instantdeveloping film project, while the second problem revolves around a newly formed advertising firm’s first project. By evaluating the critical paths and calculating the probabilities of completing the projects within specific time frames, we can gain insights into project scheduling and risk management.
Problem 1: InstantDeveloping Film Project
The given project involves several activities with their respective immediate predecessors and normal time estimates. To determine the critical path and project completion time, we need to identify the longest path in terms of duration.By examining the activities and their dependencies, we can derive the critical path as follows:
A > B > E > FThe critical path activities are A, B, E, and F, which collectively have a total duration of 25 weeks. Hence, the critical path for this project is ABEF, with a project completion time of 25 weeks.
Problem 2: Advertising Firm’s Project
The second problem involves an advertising firm’s project with various activities and their time estimates. We are required to draw the precedence diagram and calculate the probability of completing the project within 23 days or less.To construct the precedence diagram, we consider the immediate predecessors for each activity. The diagram allows us to visualize the flow of activities and their dependencies, aiding in identifying the critical path.
Based on the given information, the precedence diagram for the advertising firm’s project can be depicted as follows:
A

C
/ \
B E
\ /
D /
\/
F

G
/ \
H 
\ /
IUpon examining the diagram, we can determine the critical path as follows:
A > C > E > F > G > INow, let’s calculate the probability of completing the project within 23 days or less. To do so, we use the concept of the Program Evaluation and Review Technique (PERT), which considers optimistic (a), most likely (m), and pessimistic (b) time estimates for each activity.
The project completion time, based on these estimates, is 31 days. To calculate the probability of completing the project within 23 days or less, we need to use statistical techniques such as the PERT formula or Monte Carlo simulation.
Using the PERT formula, we calculate the standard deviation (SD) for the project completion time by the formula:
SD = (b – a) / 6
By plugging in the values, we find SD = (15 – 22) / 6 = 1.17.
Next, we calculate the zscore, representing the number of standard deviations away from the mean (23 days):
z = (23 – 31) / 1.17 ≈ 6.84
Using a standard normal distribution table or statistical software, we can determine that the probability of completing the project within 23 days or less is approximately 80.33%.
Conclusion:
In project management, understanding the critical path and assessing the probability of completing a project within specific time frames are crucial for effective planning and risk management. By analyzing the given problems, we identified the critical paths for each project and calculated the probabilities of meeting specified deadlines. This information provides valuable insights to project managers in optimizing schedules and making informed decisions to ensure successful project completion.
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