2. Consider the following project network, where the number over each node is the time required for the corresponding activity. Consider the problem of finding the longest path (the largest total time) through this network from start to finish, since the longest path is the critical path. 0 START 5 3 B 3 1 + (C) 4 7 0 FINISH (a) For the dynamic programming formulation of this problem, how many stages are there, and what are the states for each stage? (b) Use dynamic programming to solve this problem. However, instead of using the usual tables, show your work graphically. In particular, fill in the values of the various f (Sn) under the corresponding nodes, and show the resulting optimal arc to traverse out of each node by drawing an arrowhead near the beginning of the arc. Then identify the optimal path (the longest path) by following these arrowheads from the Start node to the Finish node. If there is more than one optimal path, identify them all. (c) Use dynamic programming to solve this problem by constructing the usual tables for each stage.

2. Consider the following project network, where the number over each node is the time required for the corresponding activity. Consider the problem of finding the longest path (the largest total time) through this network from start to finish, since the longest path is the critical path. 0 START 5 3 B 3 1 + (C) 4 7 0 FINISH (a) For the dynamic programming formulation of this problem, how many stages are there, and what are the states for each stage? (b) Use dynamic programming to solve this problem. However, instead of using the usual tables, show your work graphically. In particular, fill in the values of the various f (Sn) under the corresponding nodes, and show the resulting optimal arc to traverse out of each node by drawing an arrowhead near the beginning of the arc. Then identify the optimal path (the longest path) by following these arrowheads from the Start node to the Finish node. If there is more than one optimal path, identify them all. (c) Use dynamic programming to solve this problem by constructing the usual tables for each stage.

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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I need help in formulating the constraints for this problem. So, help with part (a) is all I need.
From this selected reference: Bixby, A., B. Downs, and M. Self: “A Scheduling andCapable-to-Promise Application for Swift & Company,” Interfaces, 36(1): 69–86, January–February 2006.https://www.academia.edu/34766673/A_Scheduling_and_Capable-toPromise_Application_for_Swift_and_Company) Summarize the background that led to undertaking this study.
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