introducing slack and surplus variables

Example: Product Planning

Let us consider the same problem that was formulated algebraically - Example: Product planning LP model and solved graphically optimum point :

number of units of product A to be produced

number of units of product B to be produced

P total profit

Maximise: 

Subject to 

All constrains are of  type, so two slack variables should be added. The model changes to:

Maximise: 

Subject to 

Interpretation of slack variables:

unused capacity of machine 1 (hours)

unused capacity of machine 2 (hours)