Chapter 9.2, Problem 45PE

For Exercises 45-48, assume that traffic flows freely through the intersections $A,B,C$ , and $D$ . The values $x_1,x_2,x_3$ , and $x_4$ and the other numbers in the figures represent flow rates in vehicles per hour.(See Example 6)

a. Write an equation representing equal flow into and out of intersection $A$ .

b. Write an equation representing equal flow into and out of intersection $B$ .

c. Write an equation representing equal flow into and out of intersection $C$

d. Write the system of equations from parts (a)-(c) in standard form.

e. Write the reduced row-echelon form of the augmented matrix representing the system of equations from part (d).

f. If the flow rate between intersections $A$ and $C$ is $120$ vehicles per hour, determine the flow rates $x_1$ and $x_2$ .

g. If the flow rate between intersections $A$ and $C$ is between $100$ and $150$ vehicles per hour, inclusive, determine the flow rates $x_1$ , and $x_2$ .