The volume of traffic for a collection of intersections is s

The volume of traffic for a collection of intersections is shown in the figure below. (A graphing calculator is recommended.) Find all possible values for x_1, x_2, x_3 and x_4. (Use s_1 as your parameter.) (x_1, x_2, x_3, x_4) = () What is the minimum volume of traffic from C to D? vehicles

Solution

A

x2 + 70 = 75 - 40 -x1

x2 + x1 = -35

C

100 + x1 = x4+70

x1-x4 = -30

B

40 +10 + 15 +x3 = x2+20

x3 - x2 = -45

D

x4 + 20 = x3+50

x4 - x3 = 30

solving the system of equations for x1,x2,x3,x4

x1 = -40

x2 = 5

x3 = -40

x4 = -10

minimum traffic from C TO D is -10