## 2.4 Graphical Method for Solving Linear Programming Problems

Note: if you cannot remember how to setup a linear programming problem, revise notes for 2.3 Linear Programming.

### Sliding Line Method

- By drawing lines on a graph representing the minimum/maximum conditions as allowed by the systems inequalities, we bound a region. This region is known as the
**feasible region**. - Any point within the feasible region represents a possible solution to this system. However, in general, we do not want just any possible solution, we want the “
**best**” solution, known as the**optimal solution**. Often this is the combination of decision variable values that produces a maximum or minimum allowed value from the objective function. - If we substitute a point from the feasible region into the objective function we get a possible value for the quantity being optimised. If we then equate the objective function to this value, we produce a line of the form where a, b and c are constants and x and y are the decision variables. If we do this for another point, we will produce another equation which is parallel to the one just derived with the only difference being a different c value shifting the line upwards or downwards.