Chapter 4, Problem 53RE

Traffic flow. The rush-hour traffic flow (in vehicles per hour) for a network of four one-way streets is shown in the figure.

(A) Write the system of equations determined by the flow of traffic through the four intersections.

(B) Find the solution of the system in part (A).

(C) What is the maximum number of vehicles per hour that can travel from Oak Street to Elm Street on $1\text{st}$ Street? What is the minimum number?

(D) If traffic lights are adjusted so that $500$ vehicles per hour travel from Oak Street to Elm Street on $1\text{st}$ Street, determine the flow around the rest of the network.