1. Develop a system of linear equations for the network by writing an equation for each router (A, B, C, D, and E). Make sure to write your final answer as Ax=b where A is the 5x5 coefficient matrix, x is the 5x1 vector of unknowns, and b is a 5x1 vector of constants.2. construct the augmented matrix [A b] and then perform row reduction using the rref() function. Write out your reduced matrix and identify the free and basic variables of the system.3. Use MATLAB to compute the LU decomposition of A, i.e., find A = LU. For this decomposition, find the transformed set of equations Ly = b, where y = Ux. Solve the system of equations Ly = b for the unknown vector y.4. Compute the inverse of U using the inv() function.5. Compute the solution to the original system of equations by transforming y into x, i.e., compute x = inv(U)y6. Check your answer for x1 using Cramer’s Rule. Use MATLAB to compute the required determinants using the det() function. You are employed as a network engineer and have been asked to analyze a communication network to determine the current data rates andensure that the links aren't at risk of "reaching capacity." In the following figure of the network, the sender is transmitting data at a total rate of100+50= 150 megabits per second (Mbps). The data is transmitted from the sender to the receiver over a network of five different routers.These routers are labeled A, B, C, D, and E. The connections and data rates between the routers are labeled as x1, x2, x3, x4, and x5.A ())B (())Sender10050X₂c ())X3X₂X₁X5X5X4:D ()),X3120Receiver NetworkLinkX1X2X3X4X5RecommendedCapacity (Mbps)605010010050Solution[Insert text][Insert text][Insert text][Insert text][Insert text]Recommendation[Insert text][Insert text][Insert text][Insert text][Insert text][Insert text][Insert text][Insert text][Insert text][Insert text]Explanation

MATLAB stands for MATrix Laboratory. Matlab was developed by MathWorks. As per rules, I answered…

Answered: Develop a system of linear equations…

Operations Research : Applications and Algorithms

4th Edition

ISBN:9780534380588

Author:Wayne L. Winston

Publisher:Wayne L. Winston

Chapter20: Queuing Theory

Section20.10: Exponential Queues In Series And Open Queuing Networks

Problem 8P

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1. Develop a system of linear equations for the network by writing an equation for each router (A, B, C, D, and E). Make sure to write your final answer as Ax=b where A is the 5x5 coefficient matrix, x is the 5x1 vector of unknowns, and b is a 5x1 vector of constants.

2. construct the augmented matrix [A b] and then perform row reduction using the rref() function. Write out your reduced matrix and identify the free and basic variables of the system.

3. Use MATLAB to compute the LU decomposition of A, i.e., find A = LU. For this decomposition, find the transformed set of equations Ly = b, where y = Ux. Solve the system of equations Ly = b for the unknown vector y.

4. Compute the inverse of U using the inv() function.

5. Compute the solution to the original system of equations by transforming y into x, i.e., compute x = inv(U)y

6. Check your answer for x1 using Cramer’s Rule. Use MATLAB to compute the required determinants using the det() function.

You are employed as a network engineer and have been asked to analyze a communication network to determine the current data rates and
ensure that the links aren't at risk of "reaching capacity." In the following figure of the network, the sender is transmitting data at a total rate of
100+50= 150 megabits per second (Mbps). The data is transmitted from the sender to the receiver over a network of five different routers.
These routers are labeled A, B, C, D, and E. The connections and data rates between the routers are labeled as x1, x2, x3, x4, and x5.
A ())
B (())
Sender
100
50
X₂
c ())
X3
X₂
X₁
X5
X5
X4
:D ()),
X3
120
Receiver

Network
Link
X1
X2
X3
X4
X5
Recommended
Capacity (Mbps)
60
50
100
100
50
Solution
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Recommendation
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Explanation

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