***4 Questions. Will pay $20, 5 star rating once finished*** See attachment for questions. Please put answers on microsoft excel in separate tabs. Please show how you came up with the answer.

1 A series of activities must be completed in a coordinated fashion to complete a

landscaping overhaul. The following table shows the activities their optimistic, most

likely and pessimistic durations and their immediate predecessors

Activity

A

m

b

Immediate Predecessors

A

4

8

12

B

4

10

13

A

C

7

14

18

B

D

9

16

20

B

E

6

9

12

B

F

2

4

6

D,E

G

4

7

13

C,F

H

3

5

7

G

I

2

3

4

G,H

A Determine the expected times and variances for each activity

B Construct a project network for this problem

C Determine the EST, EFT, LST, LFT and slack for each activity. Also determine the

critical path and project completion time.

D What is the probability that the project will be finished in less than 57 days?

E What is the probability that the project will need at least 50 days?

2 The expected project completion time for the construction of a pleasure yacht is 21

months and the project variance is 6. What is the probabliltity that the project will

(a)

(b)

(c)

(d)

Require at least 17 months?

Be completed within 20 months?

Require a least 23 months?

Be completed within 25 months?

3 Bowman Builders manufactures steel storage sheds for commercial use. Joe Bowman,

president of Bowman Builders, is contemplating producing sheds for home use. The

activities necessary to build an experimental model and related data given in the table on

the next page. The project completion time using standard times in 14 weeks.

Set up and solve an LP model using Excel to crash the project to 10 weeks. How

much does it cost to reduce the duration of this project from 14 to 10 weeks?

4 Getting a degree from a college or university can be a long and difficult task certain

courses must be completed before other courses can be taken develop a network diagram

in which every activity is a particular course that you must take for you degree program.

The immediate predecessors will be course prerequisites don?t forget to include all

University College and departmental course requirements. Then try to group these

courses into semesters or quarters for our particular school. How long do you think it will

take you to graduate? Which course, if not taken in the proper sequence could delay your

graduation?

1- A series of activities must be completed in a coordinated fashion to complete a landscaping overhaul. The following table shows the activities their optimistic, most likely and pessimistic durations and their immediate predecessors Activity A B C D E F G H I A 4 4 7 9 6 2 4 3 2 m 8 10 14 16 9 4 7 5 3 b 12 13 18 20 12 6 13 7 4 Immediate Predecessors --A B B B D,E C,F G G,H A- Determine the expected times and variances for each activity B- Construct a project network for this problem C- Determine the EST, EFT, LST, LFT and slack for each activity. Also determine the critical path and project completion time. D- What is the probability that the project will be finished in less than 57 days? E- What is the probability that the project will need at least 50 days? 2 The expected project completion time for the construction of a pleasure yacht is 21 months and the project variance is 6. What is the probabliltity that the project will (a) Require at least 17 months? (b) Be completed within 20 months? (c) Require a least 23 months? (d) Be completed within 25 months? 3 Bowman Builders manufactures steel storage sheds for commercial use. Joe Bowman, president of Bowman Builders, is contemplating producing sheds for home use. The activities necessary to build an experimental model and related data given in the table on the next page. The project completion time using standard times in 14 weeks. Set up and solve an LP model using Excel to crash the project to 10 weeks. How much does it cost to reduce the duration of this project from 14 to 10 weeks? 4 Getting a degree from a college or university can be a long and difficult task certain courses must be completed before other courses can be taken develop a network diagram in which every activity is a particular course that you must take for you degree program. The immediate predecessors will be course prerequisites don't forget to include all University College and departmental course requirements. Then try to group these courses into semesters or quarters for our particular school. How long do you think it will take you to graduate? Which course, if not taken in the proper sequence could delay your graduation? Question 1A Activity A B C D E F G H I Optimistic Most Likely Pessimistic 4 8 12 4 10 13 7 14 18 9 16 20 6 9 12 2 4 6 4 7 13 3 5 7 2 3 4 Question 1B 1 A Expected time 8 9.5 13.5 15.5 9 4 7.5 5 3 Variance 1.78 2.25 3.36 3.36 1.00 0.44 2.25 0.44 0.11 C 2 B 3 D F 5 6 G H 7 8 I 9 D2 E D1 4 Question 1C Activity A B C D E F G H I Duration 8 9.5 13.5 15.5 9 4 7.5 5 3 EST 0 8 17.5 17.5 17.5 33 37 44.5 49.5 EFT 8 17.5 31 33 26.5 37 44.5 49.5 52.5 LST 0 8 23.5 17.5 24 33 37 44.5 49.5 LFT 8 17.5 37 33 33 37 44.5 49.5 52.5 HES 0 0 0 0 6.5 0 0 0 0 Therefore, critical path is path A-B-D-F-G-H-I and project completion time is 52.5 days Question 1D Probablity that the project will be finished in less than 57 days, can be given by p(Z) Now, Z (57-52.5)/10.64 => Z = 1.38 Therefore, p(Z) = 91.62% Question 1E probability that the project will need at least 50 days, can be given by [1- p(Z)] Now, Z = (50-52.5)/10.64 => Z = -0.77 Therefore, [1-p(Z)] = 1 - .2207 = 77.93% TES 0 0 0 0 0 0 0 0 0 Total float Free Float 0 0 0 0 6 6 0 0 0 6.5 0 0 0 0 0 0 0 0 Independent float 0 0 6 0 0 0 0 0 0 Given, = 21 months variance = 6 Question 2A Probablity that the project will need atleast 17 months, can be given by [1- p(Z)] Now, Z = (17-21)/6 => Z = -1.63 Therefore, [1-p(Z)] = 1 - .0515 = 94.85% Question 2B Probablity that the project will be finished within 20 months, can be given by p(Z) Now, Z = (20-21)/6 => Z = -0.41 Therefore, p(Z) = 34.09% Question 2C Probablity that the project will need atleast 23 months, can be given by [1- p(Z)] Now, Z = (23-21)/6 => Z = .82 Therefore, [1-p(Z)] = 1 - .7939 = 20.61% Question 2D Probablity that the project will be finished within 25 months, can be given by p(Z) Now, Z = (25-21)/6 => Z = 1.63 Therefore, p(Z) = 94.85%