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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Solve the given problem by linear programming.
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The university administration would like to add some additional parking locations. To make everyone happy, they would like each building to be within a 5 minute walk of one set of new parking spaces (the spaces will be added in blocks of 10 parking spaces). The university is considering six locations for the new parking spaces, but would like to minimize the overall cost of the project. In addition to the walking time requirement, the university would like to add at least 40 new parking spaces (at least 4 blocks of 10). To help with the decision, the management science department formulated the following linear programming model: Min 430x1 + 455x2 + 460x3+ 445x4 + 355x5 + 360×6 S.t. x1 + x2 + x5 + x6 > 1 (Residence Hall A constraint) x1 + x2 + x3 > 1 (Residence Hall B constraint) x4 + x5 + x6 2 1 (Science building constraint} x1 + x4 + x5 2 1 (Music building constraint} x2 + x3 + x4 > 1 (Math building constraint} x3 + x4 + x5 2 1 (Business building constraint) x2 + x5 + x6 2 1…
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