This unit introduces the topic of linear modelling, which is modelling by means of linear inequalities. Such problems arise in every aspect of industry, economics, planning, and management, and the modelling and solution of such problems has become a vital and central part of modern applied mathematics. The emphasis in the unit is on modelling: the creation of a mathematical model to describe a problem. Students are introduced to basic concepts through two and three dimensional graphs, as well as to some standard solution methods, such as the well-known Simplex Algorithm. The unit also investigates particular problems which have their own specific methods of modelling and solution, such as the transport and assignment problems. There is also discussion of integer programming – modelling where all the solutions must be integers (whole numbers) – and some of the heuristic means of solution. (Integer programming is, in general, much more difficult than standard linear programming).