Tom Schriber, a director of personnel of Management resources, Inc. is in the process of designing a program that its customers can use in the job finding process. Some of the activites include preparing resumes, writing letters, making appointments to see prospective employers, researching companies and industries, and so on. Some of the infromation on the activites is shown in the following table:
Days Immediate
Act a m b
A 8 10 12 -
B 6 7 9 -
C 3 3 4 -
D 10 20 30 A
E 6 7 8 C
F 9 10 11 B, D, E
G 4 7 10 B, D, E
H 14 15 16 F
I 10 11 13 F
J 6 7 8 G, H
K 4 7 8 I, J
L 1 2 4 G, H
(A) Construct a network for this problem.
(B) Determine the expected time and variance for each activity
(C) Determine ES, EF, LS, LF and slack fore ach activity
(D) Determine the critical path and project somple completion time
(E) Determine the probability that the project will be finsihed in 70 days or less
(F) Determine the probability that the project will be finished in 80 days or less
(G) Determine the probability that the project will be finsihed in 90 days or less
contestado completo
To solve this problem, we need to construct a network using the given information. We will use the Activity-on-Node (AON) diagram to depict the activities and their dependencies. Let's go through the process step by step:
(A) Constructing the network:
1. Identify all the activities and their dependencies from the given table.
2. Draw nodes for each activity.
3. Connect the nodes based on the dependencies.
4. Label each arrow with the time duration (a, m, b) for that activity.
5. Add a start node (represented by S) with no incoming arrows.
6. Add an end node (represented by E) with no outgoing arrows.
The network diagram should represent the activities and their dependencies as follows:
```
S -----> A -----> D -----> F --------> H ----> J ---> K ----> E
/ / / / /
B / / / / /
/ / / / /
C / E / G / I / L /
\ \ \ \ \
\ \ \ \ \
---------> C ------> E --------> G -----------> J ----> K ----> E
```
(B) Determining Expected Time and Variance:
For each activity, calculate the Expected Time (ET) and Variance (V) using the formulas:
ET = (a + 4m + b) / 6
V = ((b - a) / 6)^2
(C) Determining ES, EF, LS, LF, and Slack:
1. Calculate the Earliest Start (ES) and Earliest Finish (EF) for each activity:
ES = Maximum of the EF values of the preceding activities
EF = ES + ET of the current activity
2. Calculate the Latest Start (LS) and Latest Finish (LF) for each activity:
LS = Minimum of the LS values of the succeeding activities
LF = LS + ET of the current activity
3. Calculate Slack for each activity:
Slack = LS - ES or LF - EF
(D) Determining Critical Path and Project Completion Time:
The Critical Path is the longest path in the network, which is determined by adding the ET values for each activity. Any delay in activities along the critical path will affect the overall project completion time.
Project Completion Time = Duration of the Critical Path
(E), (F), (G) Determining Probabilities of Project Completion:
To determine the probability of completing the project within a given time frame, we can use the Normal Distribution. First, calculate the Z-score for the desired completion time using the formula:
Z = (Desired Time - Project Completion Time) / Standard Deviation
Next, use a Z-table or calculator to find the probability associated with the Z-score. The probability will represent the chance of completing the project within the desired time frame.
Please provide the time frames for (E), (F), and (G) to calculate the probabilities accurately.