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EMGT 501 HW #3 10.3-5 10.4-5 Due Day: Sep 27

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EMGT 501

HW #3

10.3-5

10.4-5

Due Day: Sep 27

10.3-5.

You are given the following information about a project consisting of six activities:

(a) Construct the project network for this project.

(b) Find the earliest times, latest times, and slack for each activity. Which of the paths is a critical path?

(c) If all other activities take the estimated amount of time, what is the maximum duration of activity D without delaying the completion of the project?

Start

0

10.3-5

a)

A

5

B

1

4

2

E

6

D

C

3

F

Finish

0

b)

Critical Path: StartAEFFinish

Length = 14 months

c) 6 (=2+4) months

10.4-5

Sharon Lowe, vice president for marketing for the Electronic Toys Company, is about to begin a project to design an advertising campaign for a new line of toys. She wants the project completed within 57 days in time to launch the advertising campaign at the beginning of the Christmas season.

Sharon has identified the six activities (labeled A, B, …, F) needed to execute this project. Considering the order in which these activities need to occur, she also has constructed the following project network.

A

C

E

F

START

FINISH

B

D

Using the PERT three-estimate approach, Sharon has obtained the following estimates of the duration of each activity.

Optimistic Most Likely Pessimistic

Activity Estimate Estimate Estimate

A 12 days 12 days 12 days

B 15 days 21 days 39 days

C 12 days 15 days 18 days

D 18 days 27 days 36 days

E 12 days 18 days 24 days

F 2 days 5 days 14 days

(a) Find the estimate of the mean and variance of the duration of

each activity.

(b) Find the mean critical path.

(c) Use the mean critical path to find the approximate probability

that the advertising campaign will be ready to launch within

57 days.

(d) Now consider the other path through the project network.

Find the approximate probability that this path will be

completed within 57 days.

(e) Since these paths do not overlap, a better estimate of the

probability that the project will finish within 57 days can be

obtained as follows. The project will finish within 57 days if

both paths are completed within 57 days. Therefore, the

approximate probability that the project will finish within 57

days is the product of the probabilities found in parts (c) and

(d). Perform this calculation. What does this answer say

about the accuracy of the standard procedure used in part (c)?

10.4-5

a)

Activity

A

12

0

B

23

16

C

15

1

D

27

9

E

18

4

F

6

4

b)

(from the Normal table)

(from the Normal table)