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4.43 Traffic congestion is encountered at the intersections
shown in the figure. All the streets are one-way and in the
directions shown. In order for effective movement of traffic, it
is necessary that for every car that arrives at a given corner,
another car must leave so that the number of cars arriving per
unit time must equal the number of cars leaving per unit time.
Traffic engineers gather the following information:
•
600 cars per hour come down Amsterdam Ave. to intersec-
tion #1 and 300 cars per hour enter intersection #1 on 108th
St.
•
650 cars per hour leave intersection #2 along Amsterdam Ave. and 50 cars per hour leave intersection
#2 along 107th St.
•
350 cars per hour come up Columbus Ave. to intersection #3 and 50 cars per hour enter intersection #3
along 107th St.
•
400 cars per hour leave intersection #4 along Columbus Ave. and 300 cars per hour enter intersection #4
from 108th St.
Find , , , and , where denotes the number of cars traveling per hour along Amsterdam Ave.
from intersection #1 to intersection #2, denotes the number of cars traveling per hour along 107th St.
from intersection #3 to intersection #2, denotes the number of cars traveling per hour along Columbus
Ave. from intersection #3 to intersection #4, and denotes the number of cars traveling per hour along
108th St. from intersection #1 to intersection #4.
Amsterdam Ave.
Columbus Ave.
1
2
34
108th St.
107th St.
n1
n2
n3
n4
n1
n2
n3
n4
2
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Solution with MATLAB:
>> A=[1 0 0 1; 1 1 0 0; 0 1 1 0; 0 0 1 -1];
>> B=[900; 700; 400; 100];
>> x=A\B
x =
650
50
350
250
Thus: x1=650 cars per hour, x2 = 50 cars per hour, x3=350 cars per hour, and x4=250 cars per
hour.
900
x
1001
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