All Matches

Solution Library

Expert Answer

Textbooks

Search Textbook questions, tutors and Books

Oops, something went wrong!

Change your search query and then try again

Result Not Found

Books FREE
Tutors
Study Help
Ask a Question

Search
Sign In
Register

study help
mathematics
advanced engineering mathematics

Questions and Answers of Advanced Engineering Mathematics

Can you obtain a bipartite subgraph in Prob. 4 by omitting two edges? Any two edges? Any two edges without a common vertex? Data from Prob. 4 If you answer is yes, find S and T:
Write a computer program for the algorithm in Table 23.1. Test the program with the graph in Example 1. Apply it to Probs. 1–3 and to some graphs of your own choice. Table 23.1
Find the adjacency matrix of the given graph or digraph.
What is combinatorial optimization? Which sections of this chapter involved it? Explain details.
Find the maximum flow by Ford-Fulkerson:In Prob. 15Data from Prob. 15 (1) S - (2) 10,3 5,3 6,0 4, 2 3, 1 (3) 8,5 (4) 1, 1 (5) t
Find a shortest spanning tree by Prim’s algorithm.
When will the adjacency matrix of a digraph be symmetric?
Find a minimum cut set and its capacity for the network:In Fig. 499 s (1) 8,4 7,5 4 2 6, 1 6,5 8,5 4, 2 5 (3 2, 1 4,2 10, 8 (6) 6, 1 7
Write a corresponding program.
What are the basic ideas and concepts in handling flows?
For each graph find the shortest paths. (1) 17 (3) 10 2 6 (2) 3 4
If you answer is yes, find S and T: (1) (6) (2) (G) 5 (3) (4)
Show that the adjacency matrix of a graph is symmetric.
Find a shortest spanning tree by Kruskal’s algorithm. Sketch it.
Give typical applications involving spanning trees.
How does Prim’s algorithm prevent the generation of cycles as you grow T?
How does Ford–Fulkerson prevent the formation of cycles?
Find further situations that can be modeled by a graph or diagraph.
Find T and cap (S, T ) for:Fig 499, S = {1, 2, 4, 5} 8,4 7,5 4 6, 1 6,5 8,5 4, 2 5 3 2, 1 4, 2 10, 8 6 6, 1 7) t
Find a shortest spanning tree by Kruskal’s algorithm. Sketch it.
What situations can be handled in terms of the traveling salesman problem?
For each graph find the shortest paths. (5) 2 4 3 1 (4) 3 LO 5 1 (2) 2 (1)
If you answer is yes, find S and T: (1 7 (3) 5 4 6 2 (8
Show that if vertex v has label λ(v) = k, then there is a path s→v of length k.
Worker can do jobs J1, J3, J4, worker W2 job J3, and worker W3 jobs J2, J3, J4. Represent this by a graph.
Find a shortest spanning tree by Kruskal’s algorithm. Sketch it.
What is a shortest path problem? Give applications.
What is the result of applying Prim’s algorithm to a graph that is not connected?
How would you represent a net of two-way and one way streets by a digraph?
Which are the “bottleneck” edges by which the flow in Example 1 is actually limited? Hence which capacities could be decreased without decreasing the maximum flow?
Find T and cap (S, T ) for:Fig 498, S = {1, 2, 3} (1) 20, 8 10, 6 2 4 Cut 11, 11 4,3 7,6 3 5,0 (5) 13, 11 3,3 (6) t
Find a shortest spanning tree by Kruskal’s algorithm. Sketch it.
State from memory how graphs can be handled on computers.
Show that in Dijkstra’s algorithm, at each instant the demand on storage is light (data for fewer than n edges).
Find a shortest path P: s→t and its length by Moore’s algorithm. Sketch the graph with the labels and indicate P by heavier lines as in Fig. 482. S
Sketch the graph consisting of the vertices and edges of a triangle. Of a pentagon. Of a tetrahedron.
State some typical problems that can be modeled and solved by graphs or digraphs.
When will S = E at the end in Prim’s algorithm?
Find T and cap (S, T ) for:Fig 498, S = {1, 2, 4, 5} 8 20,8 10, 6 2 4 Cut 11, 11 4,3 7,6 3 5,0 5 13, 11 3,3 6) t
Find a shortest spanning tree by Kruskal’s algorithm. Sketch it.
What is a graph, a digraph, a cycle, a tree?
The net of roads in Fig. 488 connecting four villages is to be reduced to minimum length, but so that one can still reach every village from every other village. Which of the roads should be
If you answer is yes, find S and T: (1) 3 (2)
Find a shortest path P: s→t and its length by Moore’s algorithm. Sketch the graph with the labels and indicate P by heavier lines as in Fig. 482. S
Universal Electric, Inc., manufactures and sells two models of lamps, L1 and L2 , the profit being $150 and $100, respectively. The process involves two workers W1 and W2 who are available
Maximize or minimize as indicated.Minimize f = 2x1 - 10x2 subject to x1 - x2 ≤ 4, 2x1 + x2 ≤ 14, x1 + x2 ≤ 9, -x1 + 3x2 ≤ 15.
Giant Ladders, Inc., wants to maximize its daily total output of large step ladders by producing x1 of them by a process P1 and x2 by a process P2, where P1 requires 2 hours of labor and 4
Maximize or minimize as indicated.Maximize f = 10x1 + 20x2 subject to x1 ≤ 5, x1 + x2 ≤ 6, x2 ≤ 4.
United Metal, Inc., produces alloys B1 (special brass) and B2 (yellow tombac). B1 contains 50% copper and 50% zinc. (Ordinary brass contains about 65% copper and 35% zinc.) B2 contains
Graph or sketch the region in the first quadrant of the x1x2-plane determined by the following inequalities.
Graph or sketch the region in the first quadrant of the x1x2-plane determined by the following inequalities.
Maximize or minimize the given objective function f subject to the given constraints.Maximize f = 20x1 + 30x2 subject to 4x1 + 3x2 ≥ 12, x1 - x2 ≥ -3, x2 ≤ 6, 2x1 - 3x2 ≤ 0.
(a) Write a program for graphing a region R in the first quadrant of the x1x2-plane determined by linear constraints.(b) Write a program for maximizing z = α1x1 + α2x2 in R.(c) Write a program
Graph or sketch the region in the first quadrant of the x1x2-plane determined by the following inequalities.
Graph or sketch the region in the first quadrant of the x1x2-plane determined by the following inequalities.
Maximize or minimize the given objective function f subject to the given constraints.Maximize f = 5x1 + 25x2 in the region in Prob. 5.Data from Prob. 5Describe and graph the regions in the first
Write in normal form and solve by the simplex method, assuming all xj to be nonnegative.Maximize f = 34x1 + 29x2 + 23x3 subject to 8x1 + 2x2 + x3 ≤ 54, 3x1 + 8x2 + 2x3 ≤ 59, x1 + x2 + 5x3 ≤ 39.
In Prob. 10, could you start from [0 0]T and do 5 steps?Data form Prob. 10Apply the method of steepest descent to f(x) = 9x21 + x22 + 18x1 - 4x2, 5 steps. Start from x0 = [2
Write in normal form and solve by the simplex method, assuming all xj to be nonnegative.Prob. 22 in Problem Set 22.2.Data from Prob. 22 in Sec 22.2Foods A and B have 600 and 500 calories, contain 15
(a) Write a program for the method.(b) Apply your program to f(x) = x21 + 4x22, experimenting with respect to speed of convergence depending on the choice of x0.(c) Apply your program to f(x) = x21 +
What happens in Example 1 of Sec. 22.1 if you replace f(x) = x21 + 3x22 with f(x) = x21 + 5x22? Start from x0 = [6 3]T. Do 5 steps. Is the convergence faster or slower?
What is the meaning of the slack variables x3, x4 in Example 2 in terms of the problem in Example 1?
Maximize f = 2x1 + 3x2 + 2x3, x1 ≥ 0, x2 ≥ 0, x3 ≥ 0, x1 + 2x2 - 4x3 ≤ 2, x1 + 2x2 + 2x3 ≤ 5.
Write in normal form and solve by the simplex method, assuming all xj to be nonnegative.Maximize f = 2x1 + x2 + 3x3 subject to 4x1 + 3x2 + 6x3 = 12
What are slack variables? Why did we introduce them?
What is an objective function? A feasible solution?
Could we find a profit f(x1, x2) = α1x1 + α2x2 whose maximum is at an interior point of the quadrangle in Fig. 474? Give reason for your answer.
Maximize f = 5x1 + 8x2 + 4x3 subject to xj ≥ 0(j = 1, · · ·, 5) and x1 + x3 + x5 = 1, x2 + x3 + x4 = 1.
Do steepest descent steps when:f(x) = x21 + cx22, x0 = (c, 1). Show that 2 steps give (c, 1) times a factor, -4c2/(c2 - 1)2. What can you conclude from this about the speed of convergence?
What is the basic idea of linear programming?
What is the method of steepest descent for a function of a single variable?
Describe and graph the regions in the first quadrant of the x1x2-plane determined by the given inequalities. -x1 + x2 ≥ 0 x1 + x2 ≤ 5-2x1 +
Do Prob. 4 with the last two constraints interchanged. Comment on the resulting simplification. Data from Prob. 4 Maximize the daily output in producing x1 steel sheets by process PA and x2 steel
Do steepest descent steps when:f(x) = αx1 + bx2, α ≠ 0, b ≠ 0. First guess, then compute.
Write in normal form and solve by the simplex method, assuming all xj to be nonnegative.Minimize f = 5x1 - 20x2 subject to -2x1 + 10x2 ≤ 5, 2x1 + 5x2 ≤ 10.
Describe and graph the regions in the first quadrant of the x1x2-plane determined by the given inequalities. -x1 + x2 ≤ 5 2x1 + x2 ≥ 10
Write down an algorithm for the method of steepest descent.
Describe and graph the regions in the first quadrant of the x1x2-plane determined by the given inequalities.-0.5x1 + x2 ≤ 2 x1 + x2 ≥ 2
Maximize the daily output in producing x1 steel sheets by process PA and x2 steel sheets by process PB subject to the constraints of labor hours, machine hours, and raw material supply:
Do steepest descent steps when:f(x) = 2x21 + x22 - 4x1 + 4x2, x0 = 0, 3 steps
Write in normal form and solve by the simplex method, assuming all xj to be nonnegative.Maximize f = 3x1 + 2x2 subject to 3x1 + 4x2 ≤ 60, 4x1 + 3x2 ≤ 60, 10x1 + 2x2 ≤ 120.
State the idea and the formulas of the method of steepest descent.
What is unconstrained optimization? Constraint optimization? To which one do methods of calculus apply?
Describe and graph the regions in the first quadrant of the x1x2-plane determined by the given inequalities.x1 - 3x2 ≥ -6x1 + x2 ≤ 6
Solve ut = uxx (0 ≤ x ≤ 1, t ≥ 0),u(x, 0) = x2(1 - x), u(0, t) = u(1, t) = 0 by Crank–Nicolson with h = 0.2, k = 0.04, 5 time steps.
Find the potential in Fig. 472, using the given grid and the boundary values: u(P10) = u(P30) = 960, u(P20) = -480, u = 0 elsewhere on the boundary
Find the solution of the vibrating string problemutt = uxx, u(x, 0) = x(1 - x), ut = 0, u(0, t) = u(1, t) = 0 by the method with h = 0.1 and k = 0.1 for t = 0.3.
Find rough approximate values of the electrostatic potential at P11, P12, P13 in Fig. 471 that lie in a field between conducting plates (in Fig. 471 appearing as sides of a rectangle) kept at
Solve Prob. 19 by RK with h = 0.1, 5 steps. Compute the error. Compare with Prob. 19.Data from Prob. 19Solve y' = 1 + y2, y(0) = 0 by the improved Euler method, h = 0.1, 10 steps.
Consider the initial value problem (solution: y = 1/[2.5 - S(x)] + 0.01x2 where S(x) is the Fresnel integral (38).(a) Solve (17) by Euler, improved Euler, and RK methods for 0 ? x ? 5 with step h =
Do 10 steps. Compare as indicated. Show details.y' = 4x3y2, y(0) = 0.5, h = 0.1
What p0 in (18) should we choose for Prob. 16? Apply the ADI formulas (17) with that value of p0 to Prob. 16, performing 1 step. Illustrate the improved convergence by comparing with the
In what method for PDEs did we have convergence problems?
Extend Example 3 as follows.(a) Verify the values in Table 21.13 and show them graphically as in Fig. 452.Data from Table 21.13Fig 452(b) Compute and graph Euler values for h near the ?critical? h =
Solve (1)–(3) by Crank–Nicolson with r = 1 (5 steps), where:f(x) = x(1 - x), h = 0.2
Do 10 steps. Compare as indicated. Show details.y' + y tan x = sin 2x, y(0) = 1, h = 0.1
(a) Accurate starting is important in (7a), (7b). Illustrate this in Example 1 of the text by using starting values from the improved Euler?Cauchy method and compare the results with those in Table
What potential do we have in Prob. 13 if V on the axes and u = 0 on the other portion of the boundary?Data from Prob. 13Solve the Laplace equation in the region and for the boundary values shown in
Can we expect a difference equation to give the exact solution of the corresponding PDE?
Find the isotherms for the square and grid in Prob. 13 if u = sin1/4 πx on the horizontal and -sin1/4πy on the vertical edges. Try to sketch some isotherms.Data from Prob. 13For the square 0 ≤ x

Showing 1600 - 1700 of 3884

First
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
Last

Get In Touch

About Us
Contact Us
Career
Jobs
FAQ
Campus Ambassador

Company Info

Security
Copyrights
Privacy Policy
Terms & Condition
SolutionInn Fee
Scholarship

Services

Sitemap
Fun
Definitions
Become Tutor
Study Help Categories
Recent Questions
Expert Questions

Copyright © 2024 SolutionInn All Rights Reserved.

Get the SolutionInn - Study Help App