(Solved): The figure below shows a network of water pipes with flows measured in liters per minute. The figur ...

The figure below shows a network of water pipes with flows measured in liters per minute. (a) Set up and solve a system of linear equations to find the possible flows. (Use the parameter $t$ as necessary.) $\left(f_1,f_2,f_3\right)=($ (b) If the flow through $AB$ is restricted to $35\mathrm{L}/\min$, what will the flows through the other two branches be? $\begin{array}{l}{f}_1=\\ f_3=\end{array}$ (c) What are the minimum and maximum possible flows through each branch? $\begin{array}{l}?f_1?\\ ?f_2?\\ ?f_3?\end{array}$ (d) We have been assuming that flow is always positive. What would negative flow mean, assuming we allowed it? Give an illustration for this example. If a negative flow were allowed, it would mean a flow in the direction, so that a negative flow on $f_2$ would mean a flow from into