## Linear Inequalities

Linear Programming is an optional area on the Leaving Certificate Ordinary Mathematics course. This topic is introduced with Linear
Inequalities and then followed by Linear Programming. It is a topic that is familiar to students. Students have studied linear equations
and co-ordinate geometry for the Junior Certificate and both of these areas are applied in this section.

Linear Inequalities can be used in a practical way (Hence the name Linear Programming) to solve real life practical problems. Even if it may
seem quite theoretical in a first approach, linear programming has a lot of practical applications in real problems. Especially, it is
often used in industry, governmental organizations, ecological sciences...to minimize objective functions (that can be production costs,
numbers of employees to hire, quantity of pollutants released) given a set of constraints (availability of workers, of machines, ...).
Hence this topic is an integral part of Industrial Engineering courses. We will begin this subject area by dealing with Linear Inequalities. As with all areas of Mathematics we will learn "by doing" so lots of examples are worked through with great emphasis given to past papers. Click on the first link below to revise graphing lines and learn about Linear Inequalities.