Please answer with the actual matlab code. A proposed network of irrigation canals is described in the accompanying diagram. At peak demand, the flows at interchanges A$,$ B$,$ C$,$ and D are as shown.

Problem $1$: Find the possible flows. Assume $\backslash ($ f$\_\{2\}=5\backslash )$ and $\backslash ($ f$\_\{5\}=5\backslash ).$

Hint: Define this system as a linear system. The flows should be positive integers. The coefficient matrix may come out to be singular. A singular matrix may signal that either there is no solution or we have a very large number of solutions. Accordingly, you may create an auxiliary equation by assigning an arbitrary value to one of the flows. For example, you might add $\backslash ($ f $5=5\backslash )$ to the set of equations and then solve using the new matrices. Also, remember the flows should be positive integers.

Problem $2$: Represent the network of irrigation canals as an adjacency matrix called B$1$ and plot in MATLAB. Label the edges with the flows found in the previous problem. Use a line width of $2$ for plotting the graph.

Problem $3$: Suppose the capacity of the canals are $\backslash ($ C $1=10,$ C $2=5,$ C $3=10,$ C $4=20,$ C $5=10\backslash ).$ Find the maximum possible flow from $\backslash ($ A $\backslash )$ to $\backslash ($ C $\backslash )$ and plot graph with flows. Add the edge flows as well as the edge names and use a line width of $2.$ Call the adjacency matrix as B$2.*****$ Make sure to call the variable containing the maximum flow value with the following name: mf $******$