The product development group at Landon Corporation has been working on a new computer software product that has the potential to capture a large market share. Through outside sources, Landon's management learned that a competitor is working to introduce a similar product. As a result, Landon's top management increased its pressure on the product development group. The group's leader turned to PERT/CPM as an aid to scheduling the activities remaining before the new product can be brought to the market. The project network is depicted in the following diagram. A project network with 12 activities and 15 directed arcs is shown. Activity Start is connected to activity A and to activity B. Activity A is connected to activity D. Activity B is connected to activity C, to activity E, and to activity F. Activity C is connected to activity D. Activity D is connected to activity I. Activity E is connected to activity G and to activity H. Activity F is connected to activity J. Activity G is connected to activity I. Activity H is connected to activity J. Activity I is connected to activity Finish. Activity J is connected to activity Finish. Activity Finish has no arcs directed to other activities. The activity time estimates (in weeks) are listed in the following table. Activity Optimistic Most Probable Pessimistic A 3 4 5 B 3 3.5 7 C 4 5 6 D 2 3 4 E 7 10 13 F 6.5 7.5 11.5 G 4.5 6 7.5 H 4 5 12 I 2 2.5 6 J 4 5 6 (a) Develop an activity schedule for this project and identify the critical path activities. (Enter your answers as a comma-separated list.) (b) Based solely on the critical path, what is the probability that the project will be completed so that Landon Corporation may introduce the new product within 24 weeks? (Round your answer to four decimal places.) (c) Based solely on the critical path, what is the probability that the project will be completed so that Landon Corporation may introduce the new product within 30 weeks? (Round your answer to four decimal places.)

The product development group at Landon Corporation has been working on a new computer software product that has the potential to capture a large market share. Through outside sources, Landon's management learned that a competitor is working to introduce a similar product. As a result, Landon's top management increased its pressure on the product development group. The group's leader turned to PERT/CPM as an aid to scheduling the activities remaining before the new product can be brought to the market. The project network is depicted in the following diagram. A project network with 12 activities and 15 directed arcs is shown. Activity Start is connected to activity A and to activity B. Activity A is connected to activity D. Activity B is connected to activity C, to activity E, and to activity F. Activity C is connected to activity D. Activity D is connected to activity I. Activity E is connected to activity G and to activity H. Activity F is connected to activity J. Activity G is connected to activity I. Activity H is connected to activity J. Activity I is connected to activity Finish. Activity J is connected to activity Finish. Activity Finish has no arcs directed to other activities. The activity time estimates (in weeks) are listed in the following table. Activity Optimistic Most Probable Pessimistic A 3 4 5 B 3 3.5 7 C 4 5 6 D 2 3 4 E 7 10 13 F 6.5 7.5 11.5 G 4.5 6 7.5 H 4 5 12 I 2 2.5 6 J 4 5 6 (a) Develop an activity schedule for this project and identify the critical path activities. (Enter your answers as a comma-separated list.) (b) Based solely on the critical path, what is the probability that the project will be completed so that Landon Corporation may introduce the new product within 24 weeks? (Round your answer to four decimal places.) (c) Based solely on the critical path, what is the probability that the project will be completed so that Landon Corporation may introduce the new product within 30 weeks? (Round your answer to four decimal places.)

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

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Question

The project network is depicted in the following diagram.

A project network with 12 activities and 15 directed arcs is shown.

Activity Start is connected to activity A and to activity B.
Activity A is connected to activity D.
Activity B is connected to activity C, to activity E, and to activity F.
Activity C is connected to activity D.
Activity D is connected to activity I.
Activity E is connected to activity G and to activity H.
Activity F is connected to activity J.
Activity G is connected to activity I.
Activity H is connected to activity J.
Activity I is connected to activity Finish.
Activity J is connected to activity Finish.
Activity Finish has no arcs directed to other activities.

The activity time estimates (in weeks) are listed in the following table.

Activity	Optimistic	Most Probable	Pessimistic
A	3	4	5
B	3	3.5	7
C	4	5	6
D	2	3	4
E	7	10	13
F	6.5	7.5	11.5
G	4.5	6	7.5
H	4	5	12
I	2	2.5	6
J	4	5	6

(a)

Develop an activity schedule for this project and identify the critical path activities. (Enter your answers as a comma-separated list.)

(b)

Based solely on the critical path, what is the probability that the project will be completed so that Landon Corporation may introduce the new product within 24 weeks? (Round your answer to four decimal places.)

(c)

Based solely on the critical path, what is the probability that the project will be completed so that Landon Corporation may introduce the new product within 30 weeks? (Round your answer to four decimal places.)

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