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Question A network of one-way streets is shown in the accompanying diagram. The rate of flow of cars into intersection A is 500 cars per hour, and 400 and 100 cars per hour emerge from B and C, respectively. B 400 fi f2 500 fa fo fs CŢ100 a) Deduce the set of linear equations from this flow problem. b) Apply the Gaussian Elimination technique to transform the system into a Row- Echelon form and determine all the possible flows along each street.

Question A network of one-way streets is shown in the accompanying diagram. The rate of flow of cars into intersection A is 500 cars per hour, and 400 and 100 cars per hour emerge from B and C, respectively. B 400 fi f2 500 fa fo fs CŢ100 a) Deduce the set of linear equations from this flow problem. b) Apply the Gaussian Elimination technique to transform the system into a Row- Echelon form and determine all the possible flows along each street.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 16EQ
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Question A network of one-way streets is shown in the accompanying diagram. The rate of flow of cars into intersection A is 500 cars per hour, and 400 and 100 cars per hour emerge from B and C, respectively. 500 A fi B 400 f2 fa f3 fo fs 100 a) Deduce the set of linear equations from this flow problem. b) Apply the Gaussian Elimination technique to transform the system into a Row- Echelon form and determine all the possible flows along each street. c) Are all the solutions acceptable in real situations? If not, state the constraint(s) that might be imposed to ensure that all the solutions are realistic.
Transcribed Image Text:Question A network of one-way streets is shown in the accompanying diagram. The rate of flow of cars into intersection A is 500 cars per hour, and 400 and 100 cars per hour emerge from B and C, respectively. 500 A fi B 400 f2 fa f3 fo fs 100 a) Deduce the set of linear equations from this flow problem. b) Apply the Gaussian Elimination technique to transform the system into a Row- Echelon form and determine all the possible flows along each street. c) Are all the solutions acceptable in real situations? If not, state the constraint(s) that might be imposed to ensure that all the solutions are realistic.
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