Some optimisation problems revisited

We consider some simple optimisation problems and employ a non-traditional method to solve them. We try to model both the problem and solution domains as algebraic structures, attempting to characterise the join operations on these domains. In each of the examples chosen, these structures turn out to be monoids and we make use of the homomorphisms between the problem and solution structures to construct recursive programs. We argue that this method employs a particular conceptual model which is easy to use and may produce nice results.