Linear Programming involves creating a function that represents a real life problem. The aim is to optimise this function given certain constraints. Simple examples of linear programming will have few variables and constraints, however, real life situations will have many more variables and constraints that will need to be considered. Problems with two variables or less can be represented graphically. With the constraints plotted, a feasible region is highlighted. The optimal solution will lie in this region. This problem involves the manager of a high street shop recruiting staff given a set of constraints.

Linear programming: presentation - an introduction to the problem outlining the student task and putting the task into context.

Linear programming: problem - a student version of the problem outlined in the introduction.

Linear programming: solution - one possible suggested solution for the problem.

The OR Society have developed these problems for use in Decision mathematics lessons. The problems can be used as an introduction to a topic, part of the learning process or as a plenary exercise.

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