It was pointed out in Section 1.2 that a linear programming model demands that the objective function and constraints involve linear expressions. Nowhere can we have terms such as appearing. For many practical problems, this is a considerable limitation and rules out the use of linear programming. Non-linear expressions can, however, sometimes be converted into a suitable linear form. The reason why linear programming models are given so much attention in comparison with non-linear programming models is that they are much easier to solve. Care should also be taken, however, to make sure that a linear programming model is only fitted to situations where it represents a valid model or justified approximation. It is easy to be influenced by the comparative ease with which linear programming models can be solved compared with non-linear ones.
It is worth giving an indication of why linear programming models can be solved more easily than non-linear ones. In order to do this, we use a two-variable model, as it can be represented geometrically.
The values of the variables x1 and x2 can be regarded as the coordinates of the points in Figure 3.1.
The optimal solution is represented by point A where ...