Project #8092 - Traffic Modeling

Figure 1 is an intersection of five one-way streets.

 

The letters a,b,c,d,e,f and g represent the number of cars moving between two intersections. To keep the traffic moving smoothly, the number of cars entering the intersection per hour must equal the number of cars leaving per hour.

1. Describe the situation.

2. Create a system of linear equations using a,b,c,d,e,f and g that models continually flowing traffic.

3. Solve the system of equations. Variables f and g should turn out to be independent.

4. Answer the following questions:

a. List acceptable traffic flows for two different values of the independent variables.

b. The traffic flow on Maple Street between I5 and I6 must be greater than what vaule to keep traffic moving?

c. If g=100, what is the maximum value for f?

d. If g=100, the flows represented by b,c and d must be greater than what values? In this situation, what are the minimum values for a and e?

e. This model has five one-way streets. What would happen if the model had five two-way streets?

Subject Mathematics
Due By (Pacific Time) 6/23/13
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