Examples of applications

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.

A linear programming example. Table manufacturing

An example of a company manufacturing two sets of tables is presented. The objective is to decide the number of tables to be manufactured each day to maximize benefits for a given set of constraints.

How to obtain all solutions of linear programming problems

In this lesson we explain hpw the knowledge of the set of all solution permits solving linear programming problems very easily. The example of a truncated cube is used to illustrate the methods.