Question

The figure shows the flow of traffic (in vehicles per hour) through a network of streets. (Assume a = 100 and b = 400.) X1 a X4 (a) Solve this system for Xi, i = 1, 2, 3, 4. (If the system has an infinite number of solutions, express x1, x2, x3, and x4 in terms of the parameter t.) (x1, x2, x3, x4) = (b) Find the traffic flow when X4 = 0. (X1, X2, X3, X4) (c) Find the traffic flow when X4 = 100. (X1, X2, X3, X4) = (d) Find the traffic flow when *1 = 5x2. (x1, x2, x3, x4) =

Answer 1

Soin b Given. L x2 ar loo a b=400 X3 xu a> from figure 2,5 400 2, + loo -> 73 (::X,=400) X3 = 500 Xy 7 Xz - 400 (: * x3 =500) 24: 100 22 = 24-100 x2=0 b> When xy =o Xų -100 = 22 21 = 12 + 400 (**Ay=-100) 223-100 24, > 300 X, +100 - X3 ; 17327400 cy when xy=100 xy-100 = x2 7 +100=43 Xa=0 2-400 23-7500

D> when x = 5xa Чоо ха + чоо -15х2 5. 100 Х2 Joo х, - оо xy 2 .: x, - 5х, ; |x75оо 5х2 + 100 гz, C: x2=100) y You X3 - Boo х3 – чоо -34 ху - #00