An application of linear systems of inequalities. The water supply problem example

An example of a water supply network is used to illustrate systems of inequalities. First a linear system of equalities models all possible alternatives for supply when the capacity of the pipes is unlimited. The solution of this problem can be obtained without any algorithm, because the dimension of the linear space in the solution is the number of holes in the network and the basis vectors and the particular solution can be easily obtained. When we limit capacities of the pipes, the solution is a polytope. Playing with the structure of this solution we decide the overdimensioned pipes, the pipes that can fail without affecting the supply, and other interesting practical questions.