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The downtown core of Gotham City consists of one-way streets, and the traffic flow has been measured at each intersection. For the city block shown in the figure, the numbers represent the average numbers of vehicles per minute entering and leaving intersections A, B, C, and D during business hours. 10| 25 10 A B st 15 20 D C 10 1s calcPad +- Operations Functions (a) Set up and solve a system of linear equations to find the possible flows f,.., fa. (Use the parametert as necessary.) Symbols Relations Sets o! Vectors (b) If traffic is regulated on CD so that f,- 10 vehicles per minute, what will the average flows on the other streets be? Trig Greek (c) What are the minimum and maximum possible flows on each street?

The downtown core of Gotham City consists of one-way streets, and the traffic flow has been measured at each intersection. For the city block shown in the figure, the numbers represent the average numbers of vehicles per minute entering and leaving intersections A, B, C, and D during business hours. 10| 25 10 A B st 15 20 D C 10 1s calcPad +- Operations Functions (a) Set up and solve a system of linear equations to find the possible flows f,.., fa. (Use the parametert as necessary.) Symbols Relations Sets o! Vectors (b) If traffic is regulated on CD so that f,- 10 vehicles per minute, what will the average flows on the other streets be? Trig Greek (c) What are the minimum and maximum possible flows on 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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The downtown core of Gotham City consists of one-way streets, and the traffic flow has been measured at each intersection. For the city block shown in the figure, the numbers represent the average numbers of vehicles per minute entering and leaving intersections A, B, C, and D during business hours.

The downtown core of Gotham City consists of one-way streets, and the traffic flow has been measured at each intersection. For the city block shown in the figure, the numbers represent the average numbers of vehicles per minute entering and leaving intersections A, B, C, and D during business hours. 10 25 10 fi A B 20 15 D 10 1s1 calcPad Operations Functions (a) Set up and solve a system of linear equations to find the possible flows f,, ... , f4: (Use the parameter t as necessary.) Symbols Relations (f,, f2, f3, fa) = Sets Vectors (b) If traffic is regulated on CD so that f, = 10 vehicles per minute, what will the average flows on the other streets be? Trig Greek f1 = f = f = O Help (c) What are the minimum and maximum possible flows on each street? s fi s s fz s s f3 s s f, s (d) How would the solution change if all of the directions were reversed? O Reversing all of the directions would change the sign of f, only. O Reversing all of the directions would have no effect. O Reversing all of the directions would change all of the signs. O Reversing all of the directions would change the signs of f, and f,. O Reversing all of the directions would change the signs of f, and f.
Transcribed Image Text:The downtown core of Gotham City consists of one-way streets, and the traffic flow has been measured at each intersection. For the city block shown in the figure, the numbers represent the average numbers of vehicles per minute entering and leaving intersections A, B, C, and D during business hours. 10 25 10 fi A B 20 15 D 10 1s1 calcPad Operations Functions (a) Set up and solve a system of linear equations to find the possible flows f,, ... , f4: (Use the parameter t as necessary.) Symbols Relations (f,, f2, f3, fa) = Sets Vectors (b) If traffic is regulated on CD so that f, = 10 vehicles per minute, what will the average flows on the other streets be? Trig Greek f1 = f = f = O Help (c) What are the minimum and maximum possible flows on each street? s fi s s fz s s f3 s s f, s (d) How would the solution change if all of the directions were reversed? O Reversing all of the directions would change the sign of f, only. O Reversing all of the directions would have no effect. O Reversing all of the directions would change all of the signs. O Reversing all of the directions would change the signs of f, and f,. O Reversing all of the directions would change the signs of f, and f.
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