Answered: Sample Problem: Find the least…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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In a high school class, there are students of different talents (ex. music, art, debate, sports, etc.). A committee needs to be formed consisting of the maximum number of students such that the committee is diverse – no two students with the same talent are in the committee. Transform this problem to a graph theoretic problem. What are the vertices of the graph? What are the edges of the graph? What do you have to find in the graph?
Among each pair of the CEOs of N companies there is (a) mutual like; (b) mutual dislike; (c) neutral feeling. A trade delegation of the maximum size needs to be formed such that it does not have any pair of members with mutual dislike. Transform this problem to a graph theoretic problem. What are the vertices of the graph? What are the edges of the graph? What do you have to find in the graph?
What is the purpose of graph theory in urban services
(a) Represent the above diagram as a graph with vertices representing land masses and edges representing the bridges. Scan or photograph your graph and upload the file. (b) Is it possible to walk around the city starting and ending at the same point and crossing each bridge exactly once? Explain using graph theory why or why not you can do this.
Note: kindly make it look something like the provided image Graph Theory:1) Create 1 problem. Problem must REALISTIC and LOCALIZED, within the place (province or municipality) where you live as of the moment. Note: I live on the Negros Islands in the Philippines so any problem about shipping or farming will do. Thank you 2) Design your own problem and graph that have a practical value. 3) Identify the vertices and conditions for the adjacency of the vertices. Come up with your analysis of the graph. The graph must be a weighted graph.
A major hotel chain is constructing a new resort hotel complex in Greenbranch Springs, WestVirginia. The resort is in a heavily wooded area, and the developers want to preserve as much ofthe natural beauty as possible. To do so, the developers want to connect all the various facilitiesin the complex with a combination walking–riding path that will minimize the amount of pathwaythat will have to be cut through the woods. The following network shows possible connectingpaths and corresponding distances (in yards) between the facilities: Determine the path that will connect all the facilities with the minimum amount of constructionand indicate the total length of the pathway.
You and your friends want to tour the southwest by car. You will visit the nine statesbelow, with the following rather odd rule: you must cross each border betweenneighboring states exactly once (so, for example, you must cross the Colorado-Utahborder exactly once). Can you do it? If so, does it matter where you start your road trip?What fact about graph theory solves this problem? Hint: Draw a graph with a vertex in each state, and connect vertices if their states sharea border. States names can be found on standard map as shown below..
Question to ask Math teacher : In the DIRECTED WEIGHTED GRAPH (Minimum Cut = maximu Flow network): If widthof pipe 20mm allows for 3Litres/min flow is the length of pipe relevant at all? ie. Pipe A is 20mm wide and 2m long. Pipe B is 20mm wide and 20m long. In network diagram will Pipe A and Pipe B both show 3L /min ? - or will they have different values because of the length of pipe?
Graph Familiarity Create own graphs (should not come from the net) using the following conditions.
Alex and Leo are a couple, and they organize a party together with 4 other couples.There are a number of greetings but, naturally, nobody says hello to their own partner. At theend of the party Alex asks everyone how many people did they greet, receiving nine differentanswers. How many people did Alex greet and how many people did Leo greet?Hint: Describe a graph that models the situation. Find out how many people did each memberof a couple greet.
A company has a graph that shows the money it generates by selling x units of its product. It also has a graph that shows its cost of producing x units of its product. The point of intersection of these graphs is called the company’s -------------------------
A process manufactures plastic tapes in batches of 50 units (tapes). The inspection records of the last 30 batches produced during one week individually by 30 workers of this process revealed the following results: (IMAGE) ) (IT IS IN SPANISH, BUT IT IS UNDERSTANDABLE) worker --- defective tapes --- worker ---- defective tapes The production supervisor, will award a prize to the most outstanding worker of the week and in addition a party will be given in his honor. a) Draw a graph of worker vs. % of non-conforming product. b) What is the average quality level of the week obtained by the workers in this process? c) To whom should the award be assigned?Who was the best worker? Who was the worst worker? d) What would you do to improve the results of this process?

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Sample Problem: Find the least expensive set of telephone lines needed to connect every telephones in the states involved. DISTANCE Boston 860 San Francisco 1855 Chicago 191 908 722 957 New York 349 Denver 1736 1372 Los Angeles 1235 Dallas 798 645