The Canonical Form of a Linear Programming Problem

The standard linear programming problem is in the form of a set of linear inequalities - constraints - and an objective function, also linear which is to be maximised. We write this system to a 'canonical form' by introducing 'slack variables', and writing all the inequalities as equations. The slack variables are used because a solution which maximises the objective function may be maximised for at least one of the inequalities being a strict inequality. Introducing slack variables allows a matrix method of solution.
Example: Convert the linear programming problem below to canonical form.
Maximise    subject to



.
Introduce slack variables   and rewrite the system as
Maximise    subject to



.
The slack variables must all be greater than or equal to zero because there must be positive slack.