1. Use the MINIMAL SPANNING TREE algorithm to solve this problem.Figure 6.34 gives the mileage of the feasible links connecting nine offshore natural gaswellheads with an inshore delivery point. Because wellhead 1 is the closest to shore, itis equipped with sufficient pumping and storage capacity to pump the output of the re-maining eight wells to the delivery point. Determine the minimum pipeline network thatlinks the wellheads to the delivery point.321510520203S412Delivery point5715141358

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Answered: 1. Use the MINIMAL SPANNING TREE…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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5)- tburlie633@myn x Step Forward-NorQuest Colle x Unit 1-Assignment #1 A.pdf ent/1/Unit%201%20-%20Assignment%20%231%20%20A.pdf Joseph Boyden | Th. Brightburn (2019) F. New Tab New Tab >> /13 100% High School Math Prep Foundations Unit 1 Assignment Carmen cut a 12 meter piece of cloth into three pieces. The first two pieces were each 3- meters long. What was the length of the other piece? 4.
A national truck rental services has a surplus of one truck in each of the cities, 1, 2, 3, 4, 5, and 6 and a deficit of one truck in each of the cities 7,8,9,10,11 and 12.The distance (in kilometers) between the cities with a surplus and cities with deficit are displayed below:a) How should the trucks be displayed so as to minimize the total distance travelled? 1 2 3 4 5 6 7 41 72 39 52 25 51 8 22 29 49 65 81 50 9 27 39 60 51 32 32 10 45 50 48 52 37 43 11 82 40 40 60 51 30
2) Consider the following weighted graph: F a 15 8 12 A E 2 G 13 7 10 11 4 17 3 B 5 2 1 Use Kruskal's Algorithm to determine the minimum cost spanning tree for this graph. Then, please draw the tree and give its cost.
Draw and analyse the arrow network for the following activities by using PERT method assuming three estimated duration for each activity which are shown I the table below. Then, find: 1. The probability of completing the work of the whole project in 20 weeks 2. The completion time of the project at probability of 95% 3. The completion time of the project at probability of 100% Estimated duration (weeks) Activities Followed by to tm tp 8. A 4 6. B,G В 2 4 J C 2 8 D,E D 1 3 G E 7 9. F F 1/2 1 3/2 Н.К G 3 8. 7 I 1/2 1 3/2 I I 1 7 7 J J 3 4 11 K 1 3
4. Graph Theory 10 48 4 25 30 G A 43 10 8. 29 17 в 15 39 J [The total weight of the network is 293] Figure 2 models a network of roads. The number on each edge gives the time, in minutes, taken to travel along the corresponding road. (a) Use Dijkstra's algorithm to find the shortest time needed to travel from A to J. State the quickest route.
Only handwritten please. dony use excel.
6. A pipeline is to be built that will link six cities. The cost (in hundreds of millions of Yuan) of constructing each potential link is shown in the weighted graph. Find a system of pipelines to connect all the cities and yet minimize the total cost. (1) Show the system of pipelines. Give the minimum total cost. (2) A. 19 C' 25 29 12 15 16 F 17 22 D 11 18 E
A B UD C D E F A B c|1775| 12 39 39 17 25 с 25 E F 23 31 40 4 20 1 7 35 D 12 15 18 32 23 4 31 20 7 15 40 1 35 18 32 -- The weights of edges in a graph are shown in the table above. Find the minimum cost spanning tree on the graph above using Kruskal's algorithm. What is the total cost of the tree?
Consider the following transshipment network for finding the shortest route from node 1 to node 7. 18 3. 3 6. (a) Formulate a linear programming model of the problem. (Express your answers using x, where each x, is either 0 or 1 for the arc from node i to node j.) Min s.t. Node 1 Flows Node 2 Flows Node 3 Flows Node 4 Flows Node 5 Flows Node 6 Flows Node 7 Flows For all x; = 0, 1. (b) Find the shortest route from node 1 to node 7 in the network shown. (Enter your answers as a comma-separated list.) path = 1,
An unmanned rover must be routed to visit four sites labeled A, B, C, and D on the surface of the moon. Assuming the rover landed at C, find an optimal tour.
4. (a) Use Dijkstra's algorithm to find the shortest path from node A to node F in the following network and give its length. A с 2 5 B 24 13 6 3 F D 14 Weight [kg] 40 50 60 40 250 200 70 190 1 E (b) A museum wants to ship 8 Roman statues for a special exhibition. They are to be transported in crates each holding a maximum weight of 300 kilograms. The numbers in the table represent the weight in kilograms of the statues: Statue Mercury Venus Tellus Mars Jupiter Saturn Caelus Neptune (i) Find the lower bound for the number of crates required to fit all statues. (ii) Use the first fit decreasing algorithm to estimate the minimum number of crates required to ship all statues. Does the first fit decreasing algorithm give an optimal solution? (iii) Find by trial and error a solution needing only & crates.
(4) Assume that a website www.funwithmath1600.ag has three pages: Page A: KingAlgebra Page B: Learn1600andWin • Page C: Linear AlgbraIsEverywhere Each page has some links to the other pages of this website and no pages links to any page outside this website. Page A has three links to page B and only one link to page C. • Page B has three links to page A and two links to page C. • Page C has one link to page A and two links to page B. A student decides to explore this website starting from page A. Since reading content is always a boring task (is it?!) they decide to choose one of the links in page A with equal probability and click on the link to see the next page. As a result, on the next step, they will end up on page B with probability 3/4 and on the page C with probability 1/4. This process is then continued by the student with the same rule: Go the next page by clicking, with equal probability, on one of the existing links that are on the present page. (Use only fractions in your…

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