a) Write the flow balance equations. b) Write the matrix form of the flow balance equations. Order variables as x12,x13,x23,x24,x25,x35,x45. c) Write the general solution in a parametric vector form for the system in (b). d) Write the basic solution obtained by setting all of the free variables to zero. e) Draw the spanning tree for the network. f) Write the solution obtained by setting the free variable x35 to 4 (leaving all other free variables at zero) and solving for the basic variables. g) How large you can make x35 (leaving all other free variables at zero) without causing one of the basic variables to go to a negative value? What is the new solution obtained by making x35 that large? h) Draw the resulting spanning tree. Figure 1: Network flow for Problem 1