Consider the above figure. (a) Set up and solve a system of linear equations to

Question

Consider the above figure.

(a) Set up and solve a system of linear equations to find the possible flows in the network shown in the figure. (Use the parameters s and t as necessary.) (f1, f2, f3, f4, f5, f6, f7).

(c) If f4 = 0,

what will the range of flow be on each of the other branches? (Enter your answers using interval notation.)   

Consider the above figure. (a) Set up and solve a system of linear equations to find the possible flows in the network shown in the figure. (Use the parameters s and t as necessary.) (f1, f2, f3, f4, f5, f6, f7). (c) If f4 = 0, what will the range of flow be on each of the other branches? (Enter your answers using interval notation.)

Explanation / Answer

Since this is a linear algebra problem, I presume that once givenequations you can solve the problem.

Now to form equations we need to keep in mind that outward flowshould be equal to the total inward flow at a junction, this comesfrom what we call as Kirchoff's Current Law.

E.g. At juction A, total outward flow = 100 + F1 while total inwardflow = F3 + 200
so, we have an equation here 100 + F1 = F3 + 200
                               or, F1 - F3 = 100 .............(1)
Similarly, we can find other equations and as we have learnedproperties of a system of linear equations, we can answer all theparts.
All I can do now is to answer (b) direct from figure, (using resultfrom answer(a) leaving for you as an exercise)
If F6=150 then total inward flow at junction D = 150 + 100 = 250and hence outward flow F3= 250 -200 = 50, which means totalinward flow at A = 200 + 50 = 250, hence outward flow F1=250-100=150 , clearly F1 can not be 100 in this case.

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