Practice pert gantt
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The document provides information on activities, their predecessors, and estimated times to create a Gantt chart, PERT network, and identify critical activities for two assignments. The first assignment lists activities A through J without predecessors and their estimated times. The second assignment lists activities A through K with their optimistic, most likely, and pessimistic times to calculate the estimated time using the formula provided. Both assignments ask to draw the Gantt chart, PERT network, and identify critical activities based on the activity information given.
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1LocationFixed CostsVariable Costs per unitA=BB=CC=DA$85,000260006.docx
1LocationFixed CostsVariable Costs per unitA=BB=CC=DA$85,000260006666.66666666677500B$55,0007C$35,00010D$65,0006average weekly demand50unitsstandard deviation 8units95%1.645Safety Stock 13unitsTherefore Target inventory level= lead time demand + safety stockLead time2WeeksLead time demand100Target inventory level=113
2Activity a=Optimistic Time Estimate(weeks)m=Most likely Time Estimates (weeks)b=Pessimistic Time Estimates(weeks)Immediate predecessor(s)T€=(a+4m+b)/6Var=((b-a)/6)^2Std.devA369none611B357A50.44444444440.6666666667C4712A7.33333333331.77777777781.3333333333D4810B7.666666666711E51016C10.16666666673.36111111111.8333333333F345D,E40.11111111110.3333333333G369D.E611H5610F6.50.69444444440.8333333333I5811G811J333H,I300ABDFHJ32.17ABDGIJ35.67ACEFHJ37.00ACEGIJ40.50CriticalStd.dev6.17probability of completing the project in 44 weeks44Z0.57probability0.71
3Forecast Ft (given a)Abs. ErrorSquare Error2-period moving averageAbs. ErrorSquare ErrorActuals (At)0.2exponential smoothing a= 0.2a= 0.2115172416.51.52.2521816.601.41.96162431416.882.888.2944151141616.300.3040.09241614.51.52.2551316.243.243210.5183462414.51.52.2561615.590.405440.1643815936160010.2325.037.5011.75exponential smoothing a= 0.22-period moving averageMSE4.17161.9583MAD1.70541.2500
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Project Management
(Chapter 16)
Production & Operations Management
INFO 335-71
Week 4
Learning Objectives
Describe project management objectives
Describe the project life cycle
Diagram networks of project activities
Estimate the completion time of a project
Compute the probability of completing a project
by a specific time
Determine how to reduce the length of a project
effectively
Describe the critical chain approach to proje.
Scheduling Problems Complete the following problems covering pro.docx
Scheduling Problems
Complete the following problems covering project scheduling methods.
1. Put the following project management activities in order, by defining immediate predecessors by placing one or more letters in the column labeled “Immediate predecessor”. One of them has been done for you.
Activity
Immediate predecessor
a) Calculate durations along all project paths
b) Calculate Te
c) Define immediate predecessors
h
d) Develop WBS
e) Draw a network diagram
f) Estimate task durations
g) Find the critical paths
h) Generate a complete, detailed task list
i) Identify project objectives
j) Write project scope statement
2. Draw network diagram for the following list of activities and their immediate predecessors. Draw start and end nodes.
Activity
Immediate predecessor
A
--
B
--
C
A, B
D
C
E
C
F
D
G
E
H
F, G
I
C
3. Given the following detailed task list, draw a network diagram, including starting and ending nodes.
Task
Immediate predecessor
A
--
B
A
C
A
D
B
E
C
F
D, E
4. Identify all paths and their summed durations from the following detailed task list.
Task
Estimated duration
Immediate Predecessors
A-define info req
2 wks
-
B- analyze existing infrastruc
1.5 wks
-
C-define network req
1 wk.
B
D-design database
3 wks.
A
E-design network
2.5 wks.
C
F-implement
7 wks.
D, E
G-test
4 wks.
F
H-document database
1 wk.
D
I-user documentation
2 wks.
C
5. What is/are the critical path(s) amongst the following paths through a project?
Path 1: A-B-D = 8.5 mos.
Path 2: B-C-I-J = 10 mos.
Path 3: A-B-E = 5.5 mos.
Path 4: B-F-G-J = 12 mos.
6. What is the shortest possible completion time for a project, given the following paths through a project from start to finish?
A-B-D-F = 14 weeks
A-G = 22 weeks
A-C-H-I-J = 19 weeks
7. Identify all non-critical activities in the project with the following paths:
A-B-C = 22 weeks
B-J-K = 18 weeks
A-B-D-E = 22 weeks
A-B-I = 14 weeks
B-L = 20 weeks
8. Identify all non-critical activities for a project with the following paths
A-B-C = 10 days
A-B-D = 8 days
A-B-E-F = 8 days
A-B-G = 9 days
9. Develop an early start early finish (ES/EF) schedule for the following project.
Activity
Duration
Predecessor
ES
EF
A
Develop specifications
2 wks
B
Design
4
A
C
Documentation
5
A
D
Implementation
8
B, C
E
Testing
4
D
10. Develop an early start, early finish (ES/EF) schedule for the following project.
Activity
Duration
Predecessor
ES
EF
A
Develop specifications
6 wks
B
Design
5 wks
A
C
User Documentation
7 wks
A
D
Implementation
11 wks
B, C
E
Acceptance Testing
8 wks
D
F
Develop marketing literature
8 wks
A
G
Technical documentation
7 wks
B, C, F
PAGE
3
Example Scheduling Problem 1 v3
Before we can schedule a project, we will need to have done the following, in order:
- Identify project objectives
- Write project scope statement
- Develop a WBS
- Generate a co.
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Project Management
PERT Network Diagram 1 illustrates the ten interrelated activities that comprise a certain project.
PERT Network Diagram 1
The information presented in Table 1 represents the optimistic activity time (a), most probable activity time (m), and pessimistic activity time (b) in weeks for each activity associated with the project.
Table 1
Activity
Optimistic (a)
Most Probable (m)
Pessimistic (b)
A
2
3
4
B
1
3
5
C
2
5
8
D
1
2
3
E
2
4
6
F
1
3
5
G
2
4
6
H
1
3
5
I
2
4
6
J
1
4
7
PERT Network Diagram 2
1. Using the information provided in Table 1, calculate the expected activity time (t) in weeks for each activity and then enter this information in the appropriate data field provided for each activity in PERT Network Diagram 2 in order to complete this diagram. Which of the following sequences accurately reflects the expected activity time in weeks for the ten activities arranged in alphabetical order by activity beginning with activity A and ending with activity J?
· 3, 3, 4, 2, 4, 3, 4, 3, 4, 4
· 3, 3, 5, 2, 4, 3, 4, 3, 4, 4
· 3, 3, 5, 2, 4, 3, 5, 3, 4, 4
· 3, 3, 4, 2, 4, 3, 4, 3, 5, 4
2. Using the information provided in Table 1, calculate the variance for the estimated activity time for each activity in order to identify which of the following sequences accurately reflects the variance for the ten activities arranged in alphabetical order by activity beginning with activity A and ending with activity J.
· 0.11, 1.00, 1.00, 0.11, 0.44, 0.44, 0.44, 0.44, 0.44, 1.00
· 0.11, 0.44, 1.00, 0.11, 0.44, 0.11, 0.44, 1.00, 0.44, 1.00
· 0.11, 0.44, 1.00, 0.11, 0.44, 0.44, 0.44, 0.44, 0.44, 1.00
· 0.11, 0.44, 1.00, 1.00, 0.44, 0.44, 0.11, 0.44, 0.44, 1.00
3. Using the information in completed PERT Network Diagram 2, calculate the overall estimated activity time in weeks for each of the following paths through the network in order to determine which of the following paths constitutes the critical path.
· ABCDG = 3+3+5+2+4 = 17 weeks
· ABEFJG = 3+3+4+3+4+4 = 21 weeks
· ABCFJG = 3+3+5+3+4+4= 22 weeks
· HIJG = 3+4+4+4 = 15 weeks
4. Using the information provided in Table 1, calculate the standard deviation for the project.
· 1.86 weeks
· 2.05 weeks
· 1.69 weeks
· 1.94 weeks
5. Using the information provided in Table 1 and completed Project Network Diagram 2, calculate the probability of the project critical path activities being completed in less than or equal to 24 weeks.
· 0.63
· 0.78
· 0.86
· 0.90
The information presented in Table 2 represents the calculated Earliest Start, Earliest Finish, Latest Start and Latest Finish times for each activity.
Table 2
Activity
Earliest Start
Earliest Finish
Latest Start
Latest Finish
A
0
3
0
3
B
3
6
3
6
C
6
11
6
11
D
11
13
16
18
E
6
10
7
11
F
11
14
11
14
G
18
22
18
22
H
0
3
7
10
I
3
7
10
14
J
14
18
14
18
6. Using the information provided in Table 2, calculate the slack time in weeks for each activity in order to i ...
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This document discusses project management and the critical path method technique. It defines project management as planning, directing, and controlling resources to meet time, cost, and technical constraints. The critical path method allows project managers to identify the critical activities and completion time of a project by determining the earliest and latest times of each activity. The document provides examples of constructing critical path networks and calculating key timing metrics to schedule and control a project.
1LocationFixed CostsVariable Costs per unitA=BB=CC=DA$85,000260006.docx
1LocationFixed CostsVariable Costs per unitA=BB=CC=DA$85,000260006666.66666666677500B$55,0007C$35,00010D$65,0006average weekly demand50unitsstandard deviation 8units95%1.645Safety Stock 13unitsTherefore Target inventory level= lead time demand + safety stockLead time2WeeksLead time demand100Target inventory level=113
2Activity a=Optimistic Time Estimate(weeks)m=Most likely Time Estimates (weeks)b=Pessimistic Time Estimates(weeks)Immediate predecessor(s)T€=(a+4m+b)/6Var=((b-a)/6)^2Std.devA369none611B357A50.44444444440.6666666667C4712A7.33333333331.77777777781.3333333333D4810B7.666666666711E51016C10.16666666673.36111111111.8333333333F345D,E40.11111111110.3333333333G369D.E611H5610F6.50.69444444440.8333333333I5811G811J333H,I300ABDFHJ32.17ABDGIJ35.67ACEFHJ37.00ACEGIJ40.50CriticalStd.dev6.17probability of completing the project in 44 weeks44Z0.57probability0.71
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1LocationFixed CostsVariable Costs per unitA=BB=CC=DA$85,000260006666.66666666677500B$55,0007C$35,00010D$65,0006average weekly demand50unitsstandard deviation 8units95%1.645Safety Stock 13unitsTherefore Target inventory level= lead time demand + safety stockLead time2WeeksLead time demand100Target inventory level=113
2Activity a=Optimistic Time Estimate(weeks)m=Most likely Time Estimates (weeks)b=Pessimistic Time Estimates(weeks)Immediate predecessor(s)T€=(a+4m+b)/6Var=((b-a)/6)^2Std.devA369none611B357A50.44444444440.6666666667C4712A7.33333333331.77777777781.3333333333D4810B7.666666666711E51016C10.16666666673.36111111111.8333333333F345D,E40.11111111110.3333333333G369D.E611H5610F6.50.69444444440.8333333333I5811G811J333H,I300ABDFHJ32.17ABDGIJ35.67ACEFHJ37.00ACEGIJ40.50CriticalStd.dev6.17probability of completing the project in 44 weeks44Z0.57probability0.71
3Forecast Ft (given a)Abs. ErrorSquare Error2-period moving averageAbs. ErrorSquare ErrorActuals (At)0.2exponential smoothing a= 0.2a= 0.2115172416.51.52.2521816.601.41.96162431416.882.888.2944151141616.300.3040.09241614.51.52.2551316.243.243210.5183462414.51.52.2561615.590.405440.1643815936160010.2325.037.5011.75exponential smoothing a= 0.22-period moving averageMSE4.17161.9583MAD1.70541.2500
Project Management
(Chapter 16)
Production & Operations Management
INFO 335-71
Week 4
Learning Objectives
Describe project management objectives
Describe the project life cycle
Diagram networks of project activities
Estimate the completion time of a project
Compute the probability of completing a project
by a specific time
Determine how to reduce the length of a project
effectively
Describe the critical chain approach to proje.
Scheduling Problems Complete the following problems covering pro.docx
Scheduling Problems
Complete the following problems covering project scheduling methods.
1. Put the following project management activities in order, by defining immediate predecessors by placing one or more letters in the column labeled “Immediate predecessor”. One of them has been done for you.
Activity
Immediate predecessor
a) Calculate durations along all project paths
b) Calculate Te
c) Define immediate predecessors
h
d) Develop WBS
e) Draw a network diagram
f) Estimate task durations
g) Find the critical paths
h) Generate a complete, detailed task list
i) Identify project objectives
j) Write project scope statement
2. Draw network diagram for the following list of activities and their immediate predecessors. Draw start and end nodes.
Activity
Immediate predecessor
A
--
B
--
C
A, B
D
C
E
C
F
D
G
E
H
F, G
I
C
3. Given the following detailed task list, draw a network diagram, including starting and ending nodes.
Task
Immediate predecessor
A
--
B
A
C
A
D
B
E
C
F
D, E
4. Identify all paths and their summed durations from the following detailed task list.
Task
Estimated duration
Immediate Predecessors
A-define info req
2 wks
-
B- analyze existing infrastruc
1.5 wks
-
C-define network req
1 wk.
B
D-design database
3 wks.
A
E-design network
2.5 wks.
C
F-implement
7 wks.
D, E
G-test
4 wks.
F
H-document database
1 wk.
D
I-user documentation
2 wks.
C
5. What is/are the critical path(s) amongst the following paths through a project?
Path 1: A-B-D = 8.5 mos.
Path 2: B-C-I-J = 10 mos.
Path 3: A-B-E = 5.5 mos.
Path 4: B-F-G-J = 12 mos.
6. What is the shortest possible completion time for a project, given the following paths through a project from start to finish?
A-B-D-F = 14 weeks
A-G = 22 weeks
A-C-H-I-J = 19 weeks
7. Identify all non-critical activities in the project with the following paths:
A-B-C = 22 weeks
B-J-K = 18 weeks
A-B-D-E = 22 weeks
A-B-I = 14 weeks
B-L = 20 weeks
8. Identify all non-critical activities for a project with the following paths
A-B-C = 10 days
A-B-D = 8 days
A-B-E-F = 8 days
A-B-G = 9 days
9. Develop an early start early finish (ES/EF) schedule for the following project.
Activity
Duration
Predecessor
ES
EF
A
Develop specifications
2 wks
B
Design
4
A
C
Documentation
5
A
D
Implementation
8
B, C
E
Testing
4
D
10. Develop an early start, early finish (ES/EF) schedule for the following project.
Activity
Duration
Predecessor
ES
EF
A
Develop specifications
6 wks
B
Design
5 wks
A
C
User Documentation
7 wks
A
D
Implementation
11 wks
B, C
E
Acceptance Testing
8 wks
D
F
Develop marketing literature
8 wks
A
G
Technical documentation
7 wks
B, C, F
PAGE
3
Example Scheduling Problem 1 v3
Before we can schedule a project, we will need to have done the following, in order:
- Identify project objectives
- Write project scope statement
- Develop a WBS
- Generate a co.
Project management
This document discusses key aspects of project management including defining a project, project management activities, structuring project organizations, work breakdown structures, critical path scheduling, and time-cost tradeoff models. It provides examples to illustrate work breakdown structures, critical path diagrams, expected time calculations, and probability calculations for project duration. The document outlines assumptions and limitations of critical path methodology for project scheduling.
Engineering design process 3rd edition haik solutions manual
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Pert Diagram & Gantt chart
This is a documentation about Pert Diagram & Gantt chart.
You can know how it can work & whats its rules.
Project management
The document contains information about project activities including their predecessors, normal time, normal cost, crash time and crash cost. It then provides the calculations to determine the critical path and total project duration for the uncrashed schedule. The total project cost is calculated as Rs. 168,000 which includes a direct cost of Rs. 108,000 and indirect cost of Rs. 60,000. No activities have been crashed in the initial schedule.
Critical path method (cpm)
The document outlines the activities and critical path required to build a new athletic complex on a university campus. It identifies 8 key activities - A through H - with their durations. Activity B through F and H make up the critical path of 14 weeks to complete the project. The summary also provides the activity schedule showing the earliest and latest start and finish times to ensure the project is completed on time.
Kinetic Dependence Graphs
Task graphs or dependence graphs are used in runtime systems to schedule tasks for parallel execution. In problem domains such as dense linear algebra and signal process- ing, dependence graphs can be generated from a program by static analysis. However, in emerging problem domains such as graph analytics, the set of tasks and dependences between tasks in a program are complex functions of runtime values and cannot be determined statically. In this paper, we introduce a novel approach for exploiting parallelism in such programs. This approach is based on a data structure called the kinetic dependence graph (KDG), which consists of a dependence graph together with update rules that incrementally update the graph to reflect changes in the dependence structure whenever a task is completed.
We have implemented a simple programming model that allows programmers to write these applications at a high level of abstraction, and a runtime within the Galois system that builds the KDG automatically and executes the program in parallel. On a suite of programs that are difficult to parallelize otherwise, we have obtained speedups of up to 33 on 40 cores, out-performing third-party implementations in many cases.
Project Management and Statistical Process Control Homework Assign.docx
Project Management and Statistical Process Control Homework Assignment
Project Management
PERT Network Diagram 1 illustrates the ten interrelated activities that comprise a certain project.
PERT Network Diagram 1
The information presented in Table 1 represents the optimistic activity time (a), most probable activity time (m), and pessimistic activity time (b) in weeks for each activity associated with the project.
Table 1
Activity
Optimistic (a)
Most Probable (m)
Pessimistic (b)
A
2
3
4
B
1
3
5
C
2
5
8
D
1
2
3
E
2
4
6
F
1
3
5
G
2
4
6
H
1
3
5
I
2
4
6
J
1
4
7
PERT Network Diagram 2
1. Using the information provided in Table 1, calculate the expected activity time (t) in weeks for each activity and then enter this information in the appropriate data field provided for each activity in PERT Network Diagram 2 in order to complete this diagram. Which of the following sequences accurately reflects the expected activity time in weeks for the ten activities arranged in alphabetical order by activity beginning with activity A and ending with activity J?
· 3, 3, 4, 2, 4, 3, 4, 3, 4, 4
· 3, 3, 5, 2, 4, 3, 4, 3, 4, 4
· 3, 3, 5, 2, 4, 3, 5, 3, 4, 4
· 3, 3, 4, 2, 4, 3, 4, 3, 5, 4
2. Using the information provided in Table 1, calculate the variance for the estimated activity time for each activity in order to identify which of the following sequences accurately reflects the variance for the ten activities arranged in alphabetical order by activity beginning with activity A and ending with activity J.
· 0.11, 1.00, 1.00, 0.11, 0.44, 0.44, 0.44, 0.44, 0.44, 1.00
· 0.11, 0.44, 1.00, 0.11, 0.44, 0.11, 0.44, 1.00, 0.44, 1.00
· 0.11, 0.44, 1.00, 0.11, 0.44, 0.44, 0.44, 0.44, 0.44, 1.00
· 0.11, 0.44, 1.00, 1.00, 0.44, 0.44, 0.11, 0.44, 0.44, 1.00
3. Using the information in completed PERT Network Diagram 2, calculate the overall estimated activity time in weeks for each of the following paths through the network in order to determine which of the following paths constitutes the critical path.
· ABCDG = 3+3+5+2+4 = 17 weeks
· ABEFJG = 3+3+4+3+4+4 = 21 weeks
· ABCFJG = 3+3+5+3+4+4= 22 weeks
· HIJG = 3+4+4+4 = 15 weeks
4. Using the information provided in Table 1, calculate the standard deviation for the project.
· 1.86 weeks
· 2.05 weeks
· 1.69 weeks
· 1.94 weeks
5. Using the information provided in Table 1 and completed Project Network Diagram 2, calculate the probability of the project critical path activities being completed in less than or equal to 24 weeks.
· 0.63
· 0.78
· 0.86
· 0.90
The information presented in Table 2 represents the calculated Earliest Start, Earliest Finish, Latest Start and Latest Finish times for each activity.
Table 2
Activity
Earliest Start
Earliest Finish
Latest Start
Latest Finish
A
0
3
0
3
B
3
6
3
6
C
6
11
6
11
D
11
13
16
18
E
6
10
7
11
F
11
14
11
14
G
18
22
18
22
H
0
3
7
10
I
3
7
10
14
J
14
18
14
18
6. Using the information provided in Table 2, calculate the slack time in weeks for each activity in order to i ...
Pert cpm
The document discusses network analysis techniques used for project planning and management. It covers key concepts like work breakdown structure, network diagrams, critical path method (CPM), program evaluation and review technique (PERT), activity times, event relationships, slack, floats, crashing, and normal vs crash schedules. The document contains examples of network diagrams and questions related to calculating activity times, identifying critical paths, and crashing project schedules.
LectureProjectPlanning.ppt
Here are the steps to solve this problem:
1. Draw the network diagram and calculate early/late start and finish times
2. Determine the critical path
3. Calculate how many weeks each critical path activity can be shortened
4. Determine the cost per week to shorten each activity
5. Shorten activities in order of least cost to try to meet the 25 week deadline
6. Calculate the total cost of crashing activities vs the $100k bonus
Lecture - Project, Planning and Control.pdf
Geometric method impossible in higher dimensions
• Algebraical methods:
• Simplex method (George B. Dantzig 1949):
skim through the feasible solution polytope.
Similar to a "Gaussian elimination".
Very good in practice, but can take an
exponential time
LalitBDA2015V3
An efficient map-reduce algorithm is presented for computing formal concepts from binary datasets in a single iteration. The algorithm first uses map-reduce to generate a sufficient set of concepts that can be used to enumerate the entire lattice of formal concepts. It then processes the reduced output on a single machine to generate the sufficient set. Finally, it selectively enumerates all formal concepts in the lattice by using the sufficient set, which avoids computing the entire lattice. This approach improves efficiency over previous algorithms that required multiple map-reduce iterations or sequential processing of the entire lattice.
Counting Sort and Radix Sort Algorithms
Counting sort is an integer sorting algorithm that works by counting the number of objects that have each distinct key value and using arithmetic to determine the position of each object in the sorted output. It runs in O(n+k) time where n is the number of elements and k is the largest element. It requires an extra array to store counts of each key value. Radix sort is an extension of counting sort that sorts elements based on individual digits by performing counting sort repeatedly on each digit, from least to most significant.
Chapter 6 Solutions.doc
The document provides solutions to various problems related to operations management concepts like assembly line balancing, facility layout, and queuing theory. For problem 1, the key outputs and cycle times are calculated for a production line with a given operating time. Problem 2 involves determining the cycle time needed to meet a desired output rate. Subsequent problems involve balancing tasks across work stations for different assembly line scenarios. The last few problems deal with determining optimal facility layouts based on interdepartmental workflow.
CPM-PERT-Examples .pptx
The critical path method is used to analyze a project schedule network diagram to determine the longest path of activities. Key steps are:
1) Draw the network diagram of activities and dependencies
2) Perform forward and backward passes to calculate early and late start/finish times
3) Identify the critical path(s) with the longest total duration as the schedule cannot be shortened without changing these activities
4) Determine the float of non-critical activities which can be delayed without affecting the project completion date.
Pert cpm
The document discusses project scheduling techniques like PERT and CPM. It provides an example of using these methods to schedule the building of an elaborate parade float. Key activities, durations, and dependencies are laid out. Calculations are shown to determine the critical path, earliest and latest start/finish times, and project completion time. For activities with uncertain durations, a three-time estimate approach is described to model duration as a distribution and calculate the probability of on-time completion.
Pert cpm
The document discusses project scheduling techniques PERT and CPM. It provides an example of using these methods to schedule the building of an elaborate parade float. Key activities, durations, and dependencies are laid out. Earliest and latest start/finish times are calculated. The critical path is identified as several critical activities that must be completed on schedule. The project completion time is estimated at 18 days based on the critical path. Uncertain activity times and calculating the probability of on-time project completion are also discussed.
Chapter 5 - PERT-CPM
This document provides an overview of the Project Evaluation and Review Technique (PERT) and Critical Path Method (CPM) for project management. It defines key terms like activities, events, and network diagrams. It explains how to construct a network diagram and calculate the critical path, expected activity times, total float, and free float. An example project is used to demonstrate how to perform the calculations to determine the critical activities, expected completion time, and probability of finishing within given timeframes when activity times are estimated as PERT distributions rather than fixed durations.
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- 1. Assignment part 1 Q- 2 Use the following information to 1.Draw Gantt Chart 2.Draw PERT Network 3.Identify Critical Activities Activity Immediate Predecessor Estimated Time A - 9 B - 8 C - 10 D B 3 E B 4 F A 4 G A 3 H G 5 I G 4 J C, E, F, H 8
- 2. Assignment part 2 1.Draw Gantt Chart 2.Draw PERT Network 3.Identify Critical Activities Q-1: Calculate the Estimated Time from the given table and then perform the above mentioned activities Estimated Time = (optimistic + 4X most likely + pessimistic) / 6 Activity Immediate Predecessor Optimistic Time (Hrs) Most Likely Time (Hrs) Pessimistic Time (Hrs) A - 4 6 8 B - 1 4.5 5 C A 3 3 3 D A 4 5 6 E A 0.5 1 1.5 F B, C 3 4 5 G B, C 1 1.5 5 H E, F 5 6 7 I E, F 2 5 8 J D, H 2.5 2.75 4.5 K G, I 3 5 7