A box with six sides has to have a volume of 1 m3

. What shape should the box be in order to minimise the surface area of the box?

These first three exercises are simple examples of optimisation, a branch of mathematics and statistics that is used in almost every area of science, and many areas of business and engineering. For example, the subdisciplines of product optimisation and process optimisation are important tools in business and industrial decision making. The problems are usually not as simple as this one here, but the basic approach is similar.