10 ! 15 (a) Set up and solve a system onnee equations to find the possible flows

Question

10 ! 15 (a) Set up and solve a system onnee equations to find the possible flows fr .. (Use the pararmeter t as necessary.) (b) If traffic is regulated on CD so thait fa 10 vehicles per flows on the other streets be? (d) Haw would the solution change if all of the directions were reversed? O Reversing all of the directions would change the signs of Fi and f. Reversing all of the directions would change the signs off, and f. O Reversing all of the directions would change the sign of fi anly. O Reversing all of the directions would change all of the signs. ell of the d 732 AM

Explanation / Answer

Question

Here w = 5, x = 5, y = 15 and z = 10

For Node A :

x + 10 = f1 + f2

f1 + f2 = 15

For Node B :

f1 + f3 = y + 5

f1 + f3 = 20

for Node C :

z + 15 = f4 + f3

f3 + f4 = 25

for node D :

15 + w = f2 + f4

f2 + f4 = 20

so the 4 equation are

f1 + f2 = 15 ...(i)

f1 + f3 = 20 ..(ii)

f3 + f4 = 25 ...(iii)

f2 + f4 = 20 ...(iv)

(b) if f4 = 10

then f2 = 10

f3 = 15

and f1 = 5

so the values are (5,10,15,10)

(3) maximum and minimum value

for f1 -> 0 <= f1 < = 15

for f2 -> 0 < = f2 < = 15

for f3 -> 0 <= f3 < = 20

for f4 -> 0 <= f4 < =20

(d) If all the directions are reverswd then it would make no efffect. Option E is correct as it will not effect any value.

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