2. Consider the following network (G, w).V121V2V3V4214422V51(i) an increase of w(v3v4) from 1 to 2;(ii) a decrease of w(v6v7) from 2 to 1;(iii) a decrease of w(v3v5) from 4 to 1.V622V7(a) Use Dijkstra's algorithm to find a shortest v₁-07-path. Give V(T) and E(T)after each iteration of the algorithm.(b) Explain the effect each of the following changes of the length of a single edgewould have on the length of a shortest v₁-V7-path:

Ans-a) (a) Using Dijkstra's algorithm, we can find a shortest v₁-v7-path as follows: Iteration 0:…

Answered: 2. Consider the following network (G,…

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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4. Consider the following LP: max z = 6x1 + x2 X1 + x2 5 5 2x, + x2 < 6 st. X1,x2 2 0 (a) Solve this problem using the Simplex Algorithm and obtain the optimal tableau for this problem. (b) If we add a new variable x3 such that: max z = 6x1 + x2 + x3 X1 + x2 + ax3 S 5 2x, + x2 + bx356 X1, X2, X3 20 where a and b are scalar values, define the conditions under which the current basis stay st. optimal.
Bezier curve, B(t) is constructed by four control points, Po(0.3,0.1), P₁ (0.9,0.6), P₂(1.3, 0.1) dan P3 (0.7,-0.4). Find the points at B (3) by using the de Casteljau algorithm. Use Computational Geometry based solution. A
please answer the question in the attached picture with work shown, thanks! #9
We consider the Traveling Salesman Problem with the cost matrix 0 87 1 5 1086 3 7 10 15 9 2 70 5 8 2620 and apply Little's branch and bound algorithm. What is the initial lower bound on possible solutions at the very first step of the algorithm? Which edge (which entry of the cost matrix) is used for the first inclusion/exclusion branching? Enter the indices of vertices at both end points of this edge without any separators between them. (For example,if the edge (12) (or,in other words,the matrix entry c12) is chosen for inclusion/exclusion, enter 12 in the text box.) What is the lower bound on the solutions in the exclusion branch (after the fırst inclusion/exclusion branching)?
b-give the simplifications made on a Newton-Raphson load flow which yield the fast-decoupled load flow algorithm
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.
Suppose the following Branch-and-Bound tree is obtained for a pure integer maximization LP:
A student is tracing the following algorithm. The function INT gives the integer part of any number, eg INT(2.3) = 2 and INT (6.7) = 6. Line 10 Input A, B Line 20 Let C = INT(A ÷ B) Line 30 Let D = B × C Line 40 Let E = A – D Line 50 If E = 0 then go to line 90 Line 60 Let A = B Line 70 Let B = E Line 80 Go to line 20 Line 90 Print B Line 100 Stop Trace the algorithm in the case where the input values are: (a) (i) A = 36 and B = 16; (ii) A = 11 and B = 7. (b) State the purpose of the algorithm.
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.
The table gives the weights of a weighted graph G on vertices U, V, W, X, Y, Z. All the edges appear in the table (so for instance VZ is not an edge in the graph). Edge Weight Edge Weight Edge Weight UX 1 UV 3 UW 5 VX 1 YZ 3 XY 6 WY 1 WX 4 XZ 8 VW 2 WZ 5 UZ 9 i. Use Dijkstra's algorithm to find a minimal path from U to Z. ii. We now consider an graph G' whose vertices and edges are the same as G, but which is not a weighted graph. Sketch a planar diagram of G'. iii. Is it possible to add a new edge to G' and maintain planarity? Justify your answer either with a planar diagram or a proof of non-planarity.
Identify which BFS are degenerate (if any) and which BFS are non-degenerate. Among all BFS, identify one with largest objective function value.
Consider the following network, where each number along a link represents the actual distance between the pair of nodes connected by that link. The objective is to find the shortest path from the origin to the destination. (a) For the forward recursion formulation of this problem, how many stages are there, and what arethe states for each stage? Stage 1: n = 1 Stage 2: n = 2 origin) ( Stage 3: n = 3 S A B C (b) Use forward recursion to solve this problem. However, instead of using the usual tables, show your work graphically. In particular, start with the given network, where the answers already are given for f (Sn) for four of the nodes; then solve for and fill in f2 (B) and fi* (0). Draw an arrowhead that shows the optimal link to traverse out of each of the latter two nodes. Finally, identify the optimal path by following the arrows from node O onward to node T. (c) Use forward recursion to solve this problem by manually constructing the usual tables for n = 3, n = 2, and n = 1.…

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