The network in the figure shows the traffic flow in vehicles

The network in the figure shows the traffic flow (in vehicles per hour) over several one-way streets in the downtown area of a certain city during a typical lunch time. Determine the general flow pattern for the network. In other words, find the general solution of the system of equations that describes the flow. In your general solution let x_4 be free. x_1 - 600 - X_4 x2 = 400 - x_4 x_3 = 300 + x_4 x_4 is free x_6 = 300 x_1 = 500 + x_4 x_2 = 400 - x_4 x_3 = 300 - x_4 x_4 is free x_5-200 x_1 = 600 + x_5 x_2 - 400 - x_5 x_3 = 300 - x_5 x_4 = 300 x_5 is free x_1 = 600 - x_4 x_2 = 400 + x_4 x_3 = 300 - x_4 x_4 is free x_5 = 300

Solution

The correct answer is Option D

since the x4 is free

In the Left hand side corner, the equation is

(400+200-x4) = x1

x1 = 600 - x4

The left hand side below corner

x4 + x3 = 300

x3 = 300 - x4

Hence the correct answer is Option D