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4. A portion of a street network of one-way streets is shown below. There are four intersections A, B, C, D, and the numbers represent the average number of vehicles per minute entering or exiting each intersection: 10 x2 15 10 20 A x1 B Ꭰ ᏆᎪ C 15 10 5 13 15 • Assume that a car entering an intersection also exits the intersection. • There are four unknown traffic flow rates (x₁, x2, X3, X^). Solve each of the following problems. (a) Using the conservation of flow at each intersection, set up the appropriate linear system that models this network flow problem. You should get a linear system of 4 equations in 4 variables. (b) If this linear system is expressed as Ax = b, then determine rref(A) to identify the leading variables and free variables. (c) Based on the assumption that the traffic flow rates are nonnegative, determine the maximum and min- imum traffic flow rates possible for this particular scenario.

4. A portion of a street network of one-way streets is shown below. There are four intersections A, B, C, D, and the numbers represent the average number of vehicles per minute entering or exiting each intersection: 10 x2 15 10 20 A x1 B Ꭰ ᏆᎪ C 15 10 5 13 15 • Assume that a car entering an intersection also exits the intersection. • There are four unknown traffic flow rates (x₁, x2, X3, X^). Solve each of the following problems. (a) Using the conservation of flow at each intersection, set up the appropriate linear system that models this network flow problem. You should get a linear system of 4 equations in 4 variables. (b) If this linear system is expressed as Ax = b, then determine rref(A) to identify the leading variables and free variables. (c) Based on the assumption that the traffic flow rates are nonnegative, determine the maximum and min- imum traffic flow rates possible for this particular scenario.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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4. A portion of a street network of one-way streets is shown below. There are four intersections A, B, C, D, and the numbers represent the average number of vehicles per minute entering or exiting each intersection: 10 X2 15 10 20 A I1 B 5 X3 D A C 10 15 15 • Assume that a car entering an intersection also exits the intersection. • There are four unknown traffic flow rates (x1, x2, x3, x₁). Solve each of the following problems. (a) Using the conservation of flow at each intersection, set up the appropriate linear system that models this network flow problem. You should get a linear system of 4 equations in 4 variables. (b) If this linear system is expressed as Ax = b, then determine rref(A) to identify the leading variables and free variables. (c) Based on the assumption that the traffic flow rates are nonnegative, determine the maximum and min- imum traffic flow rates possible for this particular scenario.
Transcribed Image Text:4. A portion of a street network of one-way streets is shown below. There are four intersections A, B, C, D, and the numbers represent the average number of vehicles per minute entering or exiting each intersection: 10 X2 15 10 20 A I1 B 5 X3 D A C 10 15 15 • Assume that a car entering an intersection also exits the intersection. • There are four unknown traffic flow rates (x1, x2, x3, x₁). Solve each of the following problems. (a) Using the conservation of flow at each intersection, set up the appropriate linear system that models this network flow problem. You should get a linear system of 4 equations in 4 variables. (b) If this linear system is expressed as Ax = b, then determine rref(A) to identify the leading variables and free variables. (c) Based on the assumption that the traffic flow rates are nonnegative, determine the maximum and min- imum traffic flow rates possible for this particular scenario.
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