At rush hours, substantial traffic congestion is encountered at the traffic intersections shown in the figure. (All streets are one-way.) The city wishes to improve the signals at these corners to speed the flow of traffic. The traffic engineers first gather data. As the figure shows, 700 cars per hour come down M Street to intersection and 300 cars per hour come to intersection on 10 th Street. A total of of these cars leave on Street, while cars leave on 10 th Street. The number of cars entering must equal the number leaving, which suggests the following equation.
For intersection cars enter on Street, and cars enter on 11 th Street. As the figure shows, 900 cars leave on 11 th, while 200 leave on which leads to the following equation.
At intersection cars enter on Street and 300 on 11 th Street, while leave on 11 th Street and leave on Street.
Finally, intersection has cars entering on and entering on There are 400 cars leaving on 10 th and 200 leaving on . (a) Set up an equation for intersection (b) Use the four equations to write an augmented matrix, and then transform it so that 1 s are on the diagonal and 0 s are below. This is triangular form. (c) since you got a row of all 0 s, the system of equations does not have a unique solution. Write three equations, corresponding to the three nonzero rows of the matrix. Solve each of the equations for (d) One of your equations should have been What is the greatest possible value of so that is not negative? (e) Another equation should have been Find the least possible value of so that is not negative. (f) Find the greatest possible values of and so that neither variable is negative. (g) Use the results of parts (a)-(f) to give a solution for the problem in which all the equations are satisfied and all variables are nonnegative. Is the solution unique?
At rush hours, substantial traffic congestion is encountered at the traffic intersections shown in the figure. (All streets are one-way.) The city wishes to improve the signals at these corners to speed the flow of traffic. The traffic engineers first gather data. As the figure shows, 700 cars per hour come down M Street to intersection and 300 cars per hour come to intersection on 10 th Street. A total of of these cars leave on Street, while cars leave on 10 th Street. The number of cars entering must equal the number leaving, which suggests the following equation.

For intersection cars enter on Street, and cars enter on 11 th Street. As the figure shows, 900 cars leave on 11 th, while 200 leave on which leads to the