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Problem 13.4 Consider the network of streets with intersections A, B, C, D and E below. The arrows indicate the direction of traffic flow along the one-way streets, and the numbers refer to the exact number of cars observed to enter or leave A, B, C, D and E during one minute. Each x; denotes the unknown number of cars which passed along the indicated streets during the same period. 50 B x4 x5 X6 A 60 70 x3 x1 x2 E D 100 60 a) Write down a system of linear equations which describes the the traffic flow, together with all the constraints on the variables xi, i = 1,..., 6. b) *The reduced row-echelon form of the augmented matrix of the system in part (a) is [1 0 0 0 -1 1 │ 60 0100-1 0 1 -40 -1 20 0 0 0 0 0 0 | 0 0 0 0 1 -1 0-50 Give the general solution. (Ignore the constraints from (a) at this point.) c) If ED were closed due to roadwork, find the minimum flow along AC, using your results from (b).

Problem 13.4 Consider the network of streets with intersections A, B, C, D and E below. The arrows indicate the direction of traffic flow along the one-way streets, and the numbers refer to the exact number of cars observed to enter or leave A, B, C, D and E during one minute. Each x; denotes the unknown number of cars which passed along the indicated streets during the same period. 50 B x4 x5 X6 A 60 70 x3 x1 x2 E D 100 60 a) Write down a system of linear equations which describes the the traffic flow, together with all the constraints on the variables xi, i = 1,..., 6. b) *The reduced row-echelon form of the augmented matrix of the system in part (a) is [1 0 0 0 -1 1 │ 60 0100-1 0 1 -40 -1 20 0 0 0 0 0 0 | 0 0 0 0 1 -1 0-50 Give the general solution. (Ignore the constraints from (a) at this point.) c) If ED were closed due to roadwork, find the minimum flow along AC, using your results from (b).

Algebra: Structure And Method, Book 1
Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter8: Introduction To Functions
Section8.2: Points, Lines, And Their Graphs
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Problem 13.4 Consider the network of streets with intersections A, B, C, D and E below. The arrows indicate the direction of traffic flow along the one-way streets, and the numbers refer to the exact number of cars observed to enter or leave A, B, C, D and E during one minute. Each x; denotes the unknown number of cars which passed along the indicated streets during the same period. 50 B x4 x5 X6 A 60 70 x3 x1 x2 E D 100 60 a) Write down a system of linear equations which describes the the traffic flow, together with all the constraints on the variables xi, i = 1,..., 6. b) *The reduced row-echelon form of the augmented matrix of the system in part (a) is [1 0 0 0 -1 1 │ 60 0100-1 0 1 -40 -1 20 0 0 0 0 0 0 | 0 0 0 0 1 -1 0-50 Give the general solution. (Ignore the constraints from (a) at this point.) c) If ED were closed due to roadwork, find the minimum flow along AC, using your results from (b).
Transcribed Image Text:Problem 13.4 Consider the network of streets with intersections A, B, C, D and E below. The arrows indicate the direction of traffic flow along the one-way streets, and the numbers refer to the exact number of cars observed to enter or leave A, B, C, D and E during one minute. Each x; denotes the unknown number of cars which passed along the indicated streets during the same period. 50 B x4 x5 X6 A 60 70 x3 x1 x2 E D 100 60 a) Write down a system of linear equations which describes the the traffic flow, together with all the constraints on the variables xi, i = 1,..., 6. b) *The reduced row-echelon form of the augmented matrix of the system in part (a) is [1 0 0 0 -1 1 │ 60 0100-1 0 1 -40 -1 20 0 0 0 0 0 0 | 0 0 0 0 1 -1 0-50 Give the general solution. (Ignore the constraints from (a) at this point.) c) If ED were closed due to roadwork, find the minimum flow along AC, using your results from (b).
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