The project detailed in the table below is contracted for delivery in 11 weeks, with a penalty clause requiring the contractor to pay a penalty of $2000 for each week late. The project must therefore be expedited. The possible reductions and associated costs are shown in the table. Times in the table are given in weeks. Only activity 4 can be expedited two weeks. The other activities can be expedited one week. (a) Determine the critical path(s), the expected duration of the project, and the slack time for each activity (indicate value on network)? What is the total project cost with penalty included? (b) How could the project time be reduced to 11 weeks and what is the total project cost? ActivityImmediate predecessorNormal timeExpedited timeNormal cost ($)Expedited cost ($) 1-435,0006,900 2-223,0003,000 31547,0009,200 42649,00011,000 52546,0007,800 63, 4324,0006,500 74, 5548,00011,000 ANSWERS: (a) Critical path(s): ________________, Expected duration of the project_______, Total project cost ________ b) How could the project time be reduced to 11 weeks and what is the total project cost?___________________________________________________________________________________________________________________________________________________________________________________

Answered: The project detailed in the table below…

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 detailed in the table below is contracted for delivery in 11 weeks, with a penalty clause requiring the contractor to pay a penalty of $2000 for each week late. The project must therefore be expedited. The possible reductions and associated costs are shown in the table. Times in the table are given in weeks. Only activity 4 can be expedited two weeks. The other activities can be expedited one week. (a) Determine the critical path(s), the expected duration of the project, and the slack time for each activity (indicate value on network)? What is the total project cost with penalty included? (b) How could the project time be reduced to 11 weeks and what is the total project cost?

Activity	Immediate predecessor	Normal time	Expedited time	Normal cost ($)	Expedited cost ($)
1	-	4	3	5,000	6,900
2	-	2	2	3,000	3,000
3	1	5	4	7,000	9,200
4	2	6	4	9,000	11,000
5	2	5	4	6,000	7,800
6	3, 4	3	2	4,000	6,500
7	4, 5	5	4	8,000	11,000

ANSWERS:

(a) Critical path(s): ________________, Expected duration of the project_______, Total project cost ________

b) How could the project time be reduced to 11 weeks and what is the total project cost?

___________________________________________________________________________________________________________________________________________________________________________________

Expert Solution

Step 1

A project network diagram is a graphic depiction of a project's process. A network diagram is a chart containing boxes indicating tasks and responsibilities, as well as arrows indicating the timetable and order in which the work must be accomplished.

The term critical path can be understood as the longest path that can be taken in order to accomplish the entire project. This helps in decision-making by identifying the critical path that requires the most resources.