During rush hours, substantial traffic congestion is encountered at the intersec

Question

During rush hours, substantial traffic congestion is encountered at the intersections shown in the figure. (The arrows indicate one-way streets) The city wishes to improve the signals at these corners to speed the flow of traffic. The traffic engineers first gather data As the figure shows, 700 cars per hour come down M Street to intersection A, and 300 cars per hour come down 10th Street to intersection A xt of these cars leave A on M Street, and x, cars leave A on 10th Street The number of cars entering A must equal the number leaving, so that x x 1000 Similarly, for intersection B, x21300 Complete parts (a) through (e) below. 300 in out M St x1 B 400 da N St. 400 out 300 in 0th St 11th St

Explanation / Answer

(a)
At C, x2+x3 = 800
At D, x3+x4 = 500

(b)
At A, x1+x4 = 1000 ==> x1=1000-x4
At B, x1+x2 = 1300 ==> x2=1300-x1 = 300+x4
At C, x2+x3 = 800 ==> x3=800-x2 = 500-x4
At D, x3+x4 = 500
Therefore, Option C will be the answer.

(c)
For Largest value of x1, I can take x1 as 1000 and x4=0, x2=300, x3 = 500
For smallest value of x1, I can take x4=500, Then, x1=500, x2=700, x3 = 000
For Largest value of x2, I can take x4=500, Then, x1=500, x2=700, x3 = 000
For smallest value of x2, I can take x4 as 000 and x1=1000, x2=300, x3 = 500
For Largest value of x3, I can take x4 as 000 and x1=1000, x2=300, x3 = 500
For smallest value of x3, I can take x4=500, Then, x1=500, x2=700, x3 = 000

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