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.

Problem 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 the final answer as Ax=bwhere A is the 5x5 coefficient matrix, xis the 5x1 vector of unknowns, and bis a 5x1 vector of constants.

You are given a diagram of the network attached.

B Sender 100 A (p)) X1 X3 X2 X1 E (p)). X5 XA D 50 c (p) X5 (p)) X2 X3 (p)) 120 Receiver